WO2017090749A1

WO2017090749A1 - Shape acquisition device, target surface shape-equipped object production device, target surface shape-equipped object production method, and program

Info

Publication number: WO2017090749A1
Application number: PCT/JP2016/085042
Authority: WO
Inventors: 卓前川; 正仁竹澤
Original assignee: 国立大学法人横浜国立大学
Priority date: 2015-11-27
Filing date: 2016-11-25
Publication date: 2017-06-01
Also published as: JP6331207B2; JPWO2017090749A1

Abstract

This shape acquisition device is equipped with: a target surface curvature line acquisition unit for obtaining a plurality of maximum principal strips and a plurality of minimum principal strips on a formed target surface; and a planar region acquisition unit for acquiring data indicating the shape of a region on a corresponding plane, for each of a plurality of regions obtained by dividing the formed target surface along the maximum and minimum principal strips.

Description

Shape acquisition apparatus, target surface shape object manufacturing apparatus, target surface shape object manufacturing method, and program

The present invention relates to a shape acquisition device, a target surface shape object manufacturing apparatus, a target surface shape object manufacturing method, and a program.
This application claims priority on November 27, 2015 based on Japanese Patent Application No. 2015-232125 filed in Japan, the contents of which are incorporated herein by reference.

Patent Document 1 discloses a technique for accurately obtaining the curvature of a curvature line.

Japanese Unexamined Patent Publication No. 2014-191487

If you want to form the surface to be formed from a plane, if the shape of the part of the surface to be formed can be formed on the plane using the curvature line, the shape of the part is formed on the plane and the parts are combined to form The shape of the surface can be formed. The operation of forming the component can be performed relatively easily in that the shape of the component may be formed on a plane.
When forming the shape of the part of the surface to be formed on a plane, an error occurs in that the shape on the curved surface is developed on the plane. If this error can be distributed to each part on the plane, it is possible to prevent local concentration of strain on the formed surface.

The present invention provides a shape acquisition device, a target surface shape object manufacturing apparatus, a target surface shape object manufacturing method, and a program capable of dispersing errors that occur when forming the shape of a part of a target surface on a flat surface. To do.

According to the first aspect of the present invention, the shape acquisition apparatus includes a target surface curvature line acquisition unit that obtains a plurality of maximum main curvature lines and a plurality of minimum main curvature lines on the formation target surface, and the formation target surface includes the maximum An on-plane area acquisition unit that obtains data indicating the shape of the area on the corresponding plane for each area divided by the main curvature line and the minimum main curvature line.

The on-plane area acquisition unit is configured to obtain the maximum principal curvature obtained by mapping a plane including a maximum principal curvature line partial line in which the maximum principal curvature line is a line divided by the minimum principal curvature line into a plane. A plane including a maximum main curvature direction corresponding line that is a line on a plane corresponding to the line partial line, and a minimum main curvature line partial line in which the minimum main curvature line is a line divided by the maximum main curvature line A corresponding line acquisition unit that obtains a minimum principal curvature direction corresponding line that is a line on a plane corresponding to the minimum main curvature line partial line, obtained by the mapping developed in the above, and forming the region of the formation target surface The maximum main curvature direction corresponding line and the minimum main curvature direction corresponding to the maximum main curvature line partial line and the minimum main curvature line partial line according to the connection relationship between the maximum main curvature line partial line and the minimum main curvature line partial line. Determining the connection relationship for determining the connection relationship of the corresponding line When, may be provided with.

The on-plane area acquisition unit calculates an angle formed by the maximum principal curvature direction correspondence line and the minimum principal curvature direction correspondence line, which is calculated based on the division area on the formation target surface and the corresponding planar division area. The sum of the squares of the differences between the maximum main curvature line partial line corresponding to the maximum main curvature direction corresponding line and the minimum main curvature line partial line corresponding to the minimum main curvature direction corresponding line is minimized. As described above, an angle determining unit that determines an angle formed by the maximum main curvature direction corresponding line and the minimum main curvature direction corresponding line may be provided.

The surface including the maximum principal curvature line partial line includes a vector of outer products of a normal vector of the formation target surface at a point on the maximum principal curvature line partial line and a tangent vector of the maximum principal curvature line partial line at the point. A plane including the minimum principal curvature line partial line is a cross product of a normal vector of the formation target surface at a point on the minimum principal curvature line partial line and a tangent vector of the minimum principal curvature line partial line at the point A plane including the vector of

The target surface curvature line acquisition unit performs a plurality of processes for obtaining the plurality of maximum main curvature lines and a plurality of minimum main curvature lines from a plurality of calculation start positions specified on the formation target surface while changing the calculation start positions. And the on-plane region acquisition unit is on a plane constituted by the maximum main curvature direction corresponding line and the minimum main curvature direction corresponding line corresponding to the plurality of maximum main curvature lines and the plurality of minimum main curvature lines. Data indicating the shape of the region may be obtained.

The target surface curvature line acquisition unit determines a start point for obtaining a target main curvature line that is either a maximum main curvature line or a minimum main curvature line on the formation target surface, and configures the target main curvature line The processing for obtaining the points following the point in order is to reach the boundary of the formation target surface, reach a region where the Gaussian curvature is equal to or less than the curvature threshold value, or the target of the acquired maximum main curvature line and minimum main curvature line The process may be repeated until the distance between the main curvature line and the same type of curvature line reaches a point that is equal to or less than the distance threshold.

The on-plane area acquisition unit is configured to connect the areas on the plane according to the arrangement in the direction along the maximum principal curvature line of the area on the formation target surface, and the data on the formation target surface. You may make it obtain | require at least any one of the data of the shape which connected the area | region on the said plane according to the arrangement | sequence in the direction along the said minimum main curvature line of each area | region.

According to the second aspect of the present invention, the target surface shape object manufacturing apparatus is arranged on the plane according to the shape acquisition device and the arrangement in the direction along the maximum principal curvature line of the region in the formation target surface. A shape processing unit that processes the material into a shape in which the regions on the plane are connected in accordance with the shape in which the regions are connected, or according to the arrangement in the direction along the minimum principal curvature line of the region on the formation target surface; And a forming target surface forming portion that combines the materials processed by the shape processing portion into a forming target surface shape.

The shape processing portion includes a first member that processes a material into a shape in which the regions on the plane are joined together in accordance with the arrangement in the direction along the maximum principal curvature line of the regions on the formation target surface, and the formation According to the arrangement of the regions on the target surface in the direction along the minimum principal curvature line, a second member obtained by processing the material into a shape obtained by joining the regions on the plane is generated, and the formation target surface forming unit is The first member and the second member may be combined in a staggered manner to form a surface shape for formation.

According to the third aspect of the present invention, the target surface shape object manufacturing method determines a starting point for obtaining a target main curvature line that is either the maximum main curvature line or the minimum main curvature line in the formation target surface, and The process of obtaining the points following the start point constituting the target main curvature line in order is reached by reaching the boundary of the formation target surface, reaching a region where the Gaussian curvature is equal to or less than the curvature threshold, or the acquired maximum main curvature line And the process of determining the start point and the process of determining a point on the target main curvature line until the distance between the target main curvature line and the same type of curvature line among the minimum main curvature lines reaches a point equal to or less than a distance threshold. A plurality of the maximum main curvature lines and a plurality of the minimum main curvature lines are repeatedly obtained, and for each area where the formation target surface is divided by the maximum main curvature lines and the minimum main curvature lines, Shape showing A shape obtained by joining the regions on the plane according to the arrangement in the direction along the maximum principal curvature line of the region on the formation target surface, or the minimum principal curvature of the region on the formation target surface In accordance with the arrangement in the direction along the line, the material is processed into a shape obtained by joining the regions on the plane, and the processed material is combined to obtain a surface shape for formation.

Processing the material generates a first member by processing the material into a shape in which the regions on the plane are joined according to the arrangement in the direction along the maximum principal curvature line of the regions on the formation target surface. And generating a second member obtained by processing the material into a shape in which the regions on the plane are joined according to the arrangement in the direction along the minimum principal curvature line of each region on the formation target surface. In addition, the formation of the surface shape for the purpose of formation may include the formation of the surface shape for the purpose of formation by alternately combining the first member and the second member.

According to the fourth aspect of the present invention, the program causes a computer to obtain a plurality of maximum main curvature lines and a plurality of minimum main curvature lines on the formation target surface, and the formation target surface is the maximum main curvature line and the minimum main curvature line. This is a program for obtaining data indicating the shape of a region on a plane associated with the region for the region divided by the main curvature line.

According to the above-described shape acquisition device, target surface shape object manufacturing device, target surface shape object manufacturing method, and program, it is possible to disperse errors that occur when forming the shape of the part of the target surface on the plane.

It is a schematic block diagram which shows the function structure of the target surface shape thing manufacturing apparatus which concerns on 1st Embodiment. It is explanatory drawing which shows the example of a normal curvature. It is explanatory drawing which shows the example of the maximum main curvature line and the minimum main curvature line. It is explanatory drawing which shows the example of the outer product of the normal vector of a curved surface, and the tangent vector of a curvature line partial line. It is explanatory drawing which shows the example of the developable surface obtained from the outer product of the normal vector of a curved surface, and the tangent vector of a curvature line partial line. It is explanatory drawing which shows the example of the largest main curvature line partial line and the minimum main curvature line partial line which comprise the target surface mesh area | region in 1st Embodiment. It is explanatory drawing which shows the example of the plane mesh area | region in 1st Embodiment. The angle determining unit in the first embodiment temporarily corresponds to the maximum principal curvature direction correspondence line and the minimum principal curvature direction correspondence line so as to completely reproduce the angle between the maximum principal curvature line and the minimum principal curvature line in the target mesh area. It is explanatory drawing which shows the example of the malfunction at the time of trying to determine the angle with. It is explanatory drawing which shows the example of the angle which the maximum main curvature direction corresponding line and minimum main curvature direction corresponding line surrounding a plane mesh area | region form. It is explanatory drawing which shows the example which approximated the planar mesh area | region in 1st Embodiment by N square (N is the number of the vertex of a planar mesh area | region). It is explanatory drawing which shows the example of the expanded view which the shape process part in 1st Embodiment acquires. It is explanatory drawing which shows the example of the external shape of the thing obtained by the combination process which the formation target surface formation part in 1st Embodiment performs. It is a flowchart which shows the example of the procedure of the process which the target surface shape thing manufacturing apparatus in 1st Embodiment performs. It is a schematic block diagram which shows the function structure of the shape acquisition apparatus which concerns on 2nd Embodiment. It is a flowchart which shows the example of the procedure of the process which the shape acquisition apparatus which concerns on 2nd Embodiment performs. It is a figure which shows the example which stops the calculation of the curvature line, when the target surface curvature line acquisition part which concerns on embodiment detects that the distance between curvature lines of the same kind is smaller than a distance threshold value. It is a figure which shows the example which the target surface curvature line acquisition part which concerns on embodiment stops calculation of a curvature line about the area | region where the magnitude | size of a Gaussian curvature is smaller than a curvature threshold value. It is a figure which shows the example in which the edge part of the curvature line which concerns on embodiment does not overlap with the edge of a formation target surface, and other curvature lines. It is a figure which shows the example from which the target surface curvature line acquisition part which concerns on embodiment deleted the part from the edge part of a curvature line to the intersection with another curvature line. It is a flowchart which shows the example of the process sequence in which the target surface curvature line acquisition part which concerns on embodiment calculates | requires a curvature line. It is a figure which shows the example of the some expanded view from which the position of the cut concerning embodiment differs. It is a schematic block diagram which shows the structure of the computer which concerns on at least 1 embodiment.

Embodiments of the present invention will be described below, but the following embodiments do not limit the invention according to the claims. In addition, not all the combinations of features described in the embodiments are essential for the solving means of the invention.

<First Embodiment>
FIG. 1 is a schematic block diagram showing a functional configuration of a target surface shape object manufacturing apparatus according to the first embodiment of the present invention. As shown in FIG. 1, the target surface shape object manufacturing apparatus 100 includes a target surface curvature line acquisition unit 110, an on-plane area acquisition unit 120, a shape processing unit 130, and a formation target surface formation unit 140. The on-plane area acquisition unit 120 includes a corresponding line acquisition unit 121, a connection relationship determination unit 122, and an angle determination unit 123.
The target surface shape object manufacturing apparatus 100 processes a planar material to form a target surface shape. The material referred to here is an original object for generating a target shape object. The target surface shape here is the shape of the formation target surface. A target surface shape object is a thing which has the shape of a formation target surface. The formation target surface is a surface for the formation purpose.
The target surface curvature line acquisition unit 110 obtains a plurality of maximum main curvature lines and a plurality of minimum main curvature lines on the formation target surface.
Here, the maximum main curvature line and the minimum main curvature line will be described with reference to FIGS. 2 and 3.

FIG. 2 is an explanatory diagram showing an example of the normal curvature.
A point P11 in FIG. 2 is a point on the curved surface F11. A normal vector N11 of the curved surface F11 at the point P11 is shown. The point on the surface here is a point included in the surface. Similarly, a line included in a surface is referred to as a line on the surface. Points included in the line are referred to as points on the line. A region included in the surface is referred to as a region on the surface.

The curvature vector k11 in FIG. 2 is a curvature vector at the point P11. This curvature vector k11 can be decomposed into a normal curvature vector k11 _n and a geodesic curvature vector k11 _g . The normal curvature vector k11 _n is a component in the direction of the normal vector N11 of the curvature vector k11 (the normal direction of the curved surface F11). The geodesic curvature vector k11 _g is a component in the direction of the vector U11 obtained by outer product of the normal vector N11 and the tangent vector t11 of the curvature vector k11 (perpendicular to the normal direction of the curved surface F11).
That is, the curvature vector k11 is expressed as in Expression (1).

The normal curvature is a value indicating the direction and size of the normal curvature vector k11 _n . The front and back of the curved surface F11 are defined, and the normal vector N11 is shown on the front side of the curved surface F11. That is, the normal vector N11 is represented by a vector of the direction from the back side to the front side of the curved surface F11. When the direction of the normal curvature vector k11 _{n is} the direction of the normal vector, the normal curvature takes a positive value of the magnitude of the normal curvature vector k11 _n . On the other hand, when the direction of the normal curvature vector k11 _n is opposite to the direction of the normal vector, the normal curvature takes a negative value of the magnitude of the normal curvature vector k11 _n .
In addition, how to determine the front and back of the curved surface F11 is arbitrary. That is, the following description does not depend on which surface of the curved surface F11 is determined as the surface.

Both the direction in which the normal curvature is maximum and the direction in which the normal curvature is minimum are referred to as the main curvature direction.
A curvature line is a line in which each tangent to the curvature line at each point on the curvature line is oriented in the main curvature direction at that point. A line in which the tangent line at each point is directed to the maximum principal curvature direction is referred to as a maximum principal curvature line. A line in which each tangent at each point faces the minimum principal curvature direction is referred to as a minimum principal curvature line.

Therefore, starting from a point on the curved surface (any point other than the umbilic point) and following in the direction of the maximum principal curvature, the maximum principal curvature line can be obtained. Also, starting from a point on the curved surface (any point other than the umbilic point) and tracing in the direction of the minimum principal curvature, a minimum principal curvature line can be obtained. The maximum main curvature line and the minimum main curvature line are collectively referred to as a curvature line. The umbilical point is a point where the normal curvature has the same value in any direction.

FIG. 3 is an explanatory diagram illustrating an example of a maximum main curvature line and a minimum main curvature line.
FIG. 3 shows a curved surface F21, maximum main curvature lines L21-1 to L21-17 of the curved surface F21, and minimum main curvature lines L22-1 to L22-9 of the curved surface F21. For example, starting from the point P21 on the curved surface F21, the maximum main curvature line L21-6 can be obtained by sequentially following the directions of the arrow B211 and the arrow B212 in the maximum main curvature direction. Starting from the point P21, the minimum main curvature line L22-6 is obtained by sequentially following the direction of the arrow B221 and the direction of the arrow B222 in the minimum main curvature direction.

For example, the target surface curvature line acquisition unit 110 acquires data indicating the shape of the formation target surface as CAD (Computer Aided Design) data. Then, the target surface curvature line acquisition unit 110 specifies a plurality of points on the formation target surface, and acquires a plurality of maximum main curvature lines starting from each of the specified plurality of points and sequentially tracing in the maximum main curvature direction. . Further, the target surface curvature line acquisition unit 110 specifies a plurality of points on the formation target surface, and acquires a plurality of minimum main curvature lines starting from each of the specified plurality of points and sequentially tracing in the minimum main curvature direction. . The point specified by the target surface curvature line acquisition unit 110 for obtaining the maximum main curvature line and the point specified for obtaining the minimum main curvature line may be the same point or different points. .
The point specified by the target surface curvature line acquisition unit 110 as the formation target surface corresponds to a calculation start point at which the target surface curvature line acquisition unit 110 starts processing for obtaining the maximum main curvature line and the minimum main curvature line.
The processing performed by the target surface curvature line acquisition unit 110 corresponds to an example of processing in the target surface curvature line acquisition step.

The on-plane area acquisition unit 120 obtains an area on the plane associated with this area for each area where the formation target surface is divided by the maximum main curvature line and the minimum main curvature line. In particular, the on-plane area acquisition unit 120 obtains data indicating the shape of the area on the plane. The process performed by the on-plane area acquisition unit 120 corresponds to an example of the process at the on-plane area acquisition step.
Hereinafter, each region in which the formation target surface is divided by the maximum main curvature line and the minimum main curvature line is referred to as a target surface mesh region. Each of the regions divided by the maximum main curvature line and the minimum main curvature line in FIG. 3 corresponds to an example of the target surface mesh region. A region surrounded by the maximum principal curvature line, the minimum principal curvature line, and the edge (boundary) line of the formation target surface is also an example of the target surface mesh region.
A region on a plane corresponding to the target surface mesh region is referred to as a plane mesh region.

The corresponding line acquisition unit 121 obtains a maximum main curvature direction corresponding line and a minimum main curvature direction corresponding line.
Here, a line in which the maximum main curvature line is divided by the minimum main curvature line is referred to as a maximum main curvature line partial line. Also, the line on the plane corresponding to this maximum main curvature line partial line obtained by mapping the developable surface including the maximum main curvature line partial line to a plane without expansion or contraction is referred to as the maximum main curvature direction corresponding line. Called.
A line in which the minimum main curvature line is divided by the maximum main curvature line is referred to as a minimum main curvature line partial line. Also, the line on the plane corresponding to the minimum main curvature line partial line obtained by mapping the developable surface including the minimum main curvature line partial line to a plane without expansion or contraction is referred to as the minimum main curvature direction corresponding line. Called.
The maximum main curvature line partial line and the minimum main curvature line partial line are collectively referred to as a curvature line partial line.

The developable surface here is a curved surface that can be developed on a plane without being expanded or contracted. It is known that the developable surface and the plane obtained by developing the developable surface on a plane are Isometric Surface. It is also known that the geodesic curvature of the corresponding curves on the Isometric Surface is equal. Therefore, by expanding the developable surface on a plane without expanding or contracting, the curvature line on the expandable surface can be expanded on the plane while maintaining the geodesic curvature of the curvature line. Here, the geodesic curvature is a value indicating the magnitude of the geodesic curvature vector. For Figure 2, the size of the geodesic curvature vector k _g is, corresponds to an example of the geodesic curvature.
Further, by expanding the developable surface on a plane without expanding and contracting, the curvature line on the expandable surface can be expanded on the plane while maintaining the length of the curvature line.

The developable surface used by the corresponding line acquisition unit 121 is the outer product of the normal vector of the formation target surface at this point and the tangent vector of the maximum main curvature line partial line at each point on the maximum main curvature line partial line. And the vector of the outer product of the normal vector of the target surface at this point and the tangent vector of the minimum principal curvature line at this point at each point on the minimum principal curvature line. It may be a surface.

Specifically, the corresponding line acquisition unit 121 calculates the outer product of the normal vector of the formation target surface at this point and the tangent vector of the maximum main curvature line partial line at each point on the maximum main curvature line partial line. The maximum principal curvature direction correspondence line may be acquired by conversion that develops a developable surface including the vector into a plane without expansion and contraction. In addition, the corresponding line acquisition unit 121 calculates the vector of the outer product of the normal vector of the formation target surface at this point and the tangent vector of the minimum main curvature line partial line at this point at each point on the minimum main curvature line partial line. You may make it acquire the minimum main curvature direction corresponding | compatible line by the conversion which expand | deploys the developable surface included in a plane without expansion / contraction.

FIG. 4 is an explanatory diagram showing an example of the outer product of the normal vector of the curved surface and the tangent vector of the curvature line partial line.
In FIG. 4, the curvature line partial line L31 on the curved surface F31 is shown. The point P31 is a point on the curvature line partial line L31. Further, a normal vector N31 of the curved surface F31 at the point P31 and a tangent vector t31 of the curvature line partial line L31 at the point P31 are shown. The vector U31 is a vector of the outer product of the normal vector N31 and the tangent vector t31. That is, the vector U31 is expressed as shown in Equation (2).

FIG. 5 is an explanatory diagram showing an example of a developable surface obtained from the outer product of the normal vector of the curved surface and the tangent vector of the curvature line partial line.
In FIG. 5, the curvature line partial line L41 on the curved surface F41 is shown. The points P41-1, P41-2, and P41-3 are all lines on the curvature line partial line L41. In addition, normal vectors N41-1, N41-2, and N41-3 of the curved surface F41 at points P41-1, P41-2, and P41-3 are shown. In addition, tangent vectors t41-1, t41-2, and t41-3 of the curvature line partial line L41 at the points P41-1, P41-2, and P41-3 are shown.

The vector U41-1 is the outer product of the normal vector N41-1 and the tangent vector t41-1. The vector U41-2 is the outer product of the normal vector N41-2 and the tangent vector t41-2. The vector U41-3 is the outer product of the normal vector N41-3 and the tangent vector t41-3. These vectors U41-1, U41-2, U41-3 are part of the outer product of the normal vector of the curved surface F41 and the tangent vector of the curvature line partial line L41 at each point on the curvature line partial line L41. Applicable.
The curved surface F41 corresponds to an example of a formation target surface. The curved surface F42 corresponds to an example of a surface including the curvature line partial line L41. The curved surface F42 is a surface including a vector of the outer product of the normal vector of the formation target surface at this point and the tangent vector of the curvature line partial line at this point at each point on the curvature line partial line L41. The curved surface F42 is a developable surface.
When the curvature line partial line L42 is the maximum main curvature line partial line, the curved surface F42 corresponds to an example of a surface including the maximum main curvature line partial line. In this case, the surface including the maximum principal curvature line partial line includes an outer product vector of the normal vector of the formation target surface at the point on the maximum principal curvature line partial line and the tangent vector of the maximum principal curvature line partial line at this point.
When the curvature line partial line L42 is the minimum main curvature line partial line, the curved surface F42 corresponds to an example of a surface including the minimum main curvature line partial line. In this case, the surface including the minimum main curvature line partial line includes an outer product vector of the normal vector of the formation target surface at the point on the minimum main curvature line partial line and the tangent vector of the minimum main curvature line partial line at this point.

The corresponding line acquisition unit 121 converts the curvature line partial line included in the expandable surface into a line on the plane by performing conversion to expand the expandable surface into a plane without expansion and contraction. The corresponding line acquisition unit 121 acquires the maximum main curvature direction corresponding line by performing this conversion on the maximum main curvature line partial line. The corresponding line acquisition unit 121 acquires the minimum main curvature direction corresponding line by performing this conversion on the minimum main curvature line partial line.
The processing performed by the corresponding line acquisition unit 121 corresponds to an example of processing in the corresponding line acquisition step.

The connection relationship determining unit 122 acquires a planar mesh region associated with the target surface mesh region according to the connection relationship between the maximum main curvature line partial line and the minimum main curvature line partial line forming the target surface mesh region. Specifically, the connection relationship determination unit 122 determines the maximum main curvature line portion line and the minimum main curvature line portion according to the connection relationship between the maximum main curvature line portion line and the minimum main curvature line portion line that form the target surface mesh region. The connection relationship between the maximum main curvature direction corresponding line and the minimum main curvature direction corresponding line associated with the line is determined.
When the target surface mesh region is configured to include the edge of the formation target surface, the connection relationship determining unit 122 connects the maximum main curvature line partial line, the minimum main curvature line partial line, and the edge of the formation target surface. Accordingly, a plane mesh region associated with the target surface mesh region is acquired.

FIG. 6 is an explanatory diagram showing an example of a maximum main curvature line partial line and a minimum main curvature line partial line that constitute the target surface mesh region.
In FIG. 6, the target surface mesh area A51 on the curved surface F51 is shown. The target surface mesh area A51 is an area surrounded by the maximum main curvature line partial lines L511-1 and L511-2 and the minimum main curvature line partial lines L512-1 and L512-2. At the point P511, the maximum main curvature line partial line L511-1 and the minimum main curvature line partial line L512-2 are connected. At point P512, the minimum main curvature line partial line L512-1 and the maximum main curvature line partial line L511-1 are connected. At the point P513, the maximum main curvature line partial line L511-2 and the minimum main curvature line partial line L512-1 are connected. At the point P514, the minimum main curvature line partial line L512-2 and the maximum main curvature line partial line L511-2 are connected.

FIG. 7 is an explanatory diagram illustrating an example of a planar mesh region.
The planar mesh area A52 shown in FIG. 7 is associated with the target mesh area A51 shown in FIG. In particular, the maximum main curvature direction corresponding lines L521-1 and L521-2 are respectively associated with the maximum main curvature line partial lines L511-1 and L511-2. Further, the minimum main curvature direction corresponding lines L522-1, L522-2 are respectively associated with the minimum main curvature line partial lines L512-1, L512-2.

The connection relationship determining unit 122 connects the maximum main curvature direction corresponding line and the minimum main curvature direction corresponding line with the same orientation and connection relationship as the maximum main curvature line partial line and the minimum main curvature line partial line before mapping. In the example of FIG. 7, the maximum main curvature line partial line L511-1 and the minimum main curvature line partial line L512-2 are connected in FIG. Therefore, the connection relationship determining unit 122 connects the maximum main curvature direction corresponding line L521-1 and the minimum main curvature direction corresponding line L522-2. The maximum main curvature direction corresponding line L521-1 is a line obtained by mapping the maximum main curvature line partial line L511-1 to the plane F 52 by the corresponding line acquisition unit 121. Also, the minimum main curvature direction corresponding line L522-2 is a line obtained by mapping the minimum main curvature line partial line L512-2 to the plane F52 by the corresponding line acquisition unit 121.
At that time, in the connection relationship determining unit 122, the end portion on the point P521 side of the maximum main curvature direction corresponding line L521-1 corresponds to the end portion on the point P511 side of the maximum main curvature line partial line L511-1 in FIG. The direction of the maximum principal curvature direction corresponding line L521-1 is determined so as to be the end.

Similarly, the connection relationship determination unit 122 connects the connection relationships at the points P522, P523, and P524 so that the connection relationship corresponds to the connection relationship at the points P512, P513, and P514 in FIG. Further, the connection relationship determining unit 122 is configured such that the end on the point P522 side of the minimum main curvature direction corresponding line L522-1 corresponds to the end on the point P512 side of the minimum main curvature line partial line L512-1 in FIG. The direction of the minimum principal curvature direction corresponding line L522-1 is determined so as to be a part. Further, the connection relationship determining unit 122 is configured such that the end on the point P523 side of the maximum main curvature direction corresponding line L521-2 corresponds to the end on the point P513 side of the maximum main curvature line partial line L511-2 in FIG. The direction of the maximum principal curvature direction corresponding line L521-2 is determined so as to be a part. Further, the connection relationship determining unit 122 is configured such that the end on the point P524 side of the minimum main curvature direction corresponding line L522-2 corresponds to the end on the point P514 side of the minimum main curvature line partial line L512-2 in FIG. The direction of the minimum principal curvature direction corresponding line L522-2 is determined so as to be a part.
In this way, the connection relationship determining unit 122 supports the maximum principal curvature direction so that the orientation and connection relationship of the maximum main curvature line partial line and the minimum main curvature line partial line surrounding the target surface mesh region are expanded in a plane. The plane mesh region is obtained by determining the direction and connection relationship between the line and the minimum principal curvature direction corresponding line.
The processing performed by the connection relationship determination unit 122 corresponds to an example of processing in the connection relationship determination step.

The angle determination unit 123 determines an angle formed by the maximum main curvature direction corresponding line and the minimum main curvature direction corresponding line constituting the planar mesh.
Specifically, the angle determination unit 123 determines the angle formed by the maximum principal curvature direction corresponding line and the minimum main curvature direction corresponding line, the maximum main curvature line partial line corresponding to the maximum main curvature direction corresponding line, and the minimum main curvature direction corresponding line. The difference between the angle formed by the minimum main curvature line partial line corresponding to the curvature direction corresponding line is connected to the maximum main curvature direction corresponding line and the minimum main curvature direction corresponding line in the connection relationship determined by the connection relationship determining unit 122. In the area on the plane (plane mesh area) obtained in this way, a process for equalizing each connection location is performed. Thereby, the angle determination part 123 determines the angle which the largest main curvature direction corresponding line and the minimum main curvature direction corresponding line make.
As the angle formed by the two curves, the angle formed by the tangent lines of these two curves at the point where these two curves are connected can be used.

Here, the maximum main curvature line and the minimum main curvature line are orthogonal to each other. Therefore, the maximum main curvature line partial line and the minimum main curvature line partial line are orthogonal to each other. On the other hand, the curved surface of the target surface mesh region is usually not a developable surface. For this reason, in the plane mesh region, the angle between the maximum main curvature line and the minimum main curvature line in the target surface mesh region cannot be completely reproduced.

FIG. 8 shows that the maximum principal curvature direction correspondence line and the minimum principal curvature direction correspondence line are set so that the angle determination unit 123 completely reproduces the angle between the maximum principal curvature line and the minimum principal curvature line in the target surface mesh region. It is explanatory drawing which shows the example of the malfunction at the time of trying to determine the angle of.
Since the maximum main curvature line partial line and the minimum main curvature line partial line are orthogonal to each other, the angle determining unit 123 determines that the maximum main curvature direction corresponding line L521-1 and the minimum main curvature direction corresponding line L522-2 are point P 521. The angle formed by is determined to be a right angle. Similarly, the angle determining unit 123 determines the angle formed by the minimum main curvature direction corresponding line L522-1 and the maximum main curvature direction corresponding line L521-1 at the point P522 as a right angle. Further, the angle determination unit 123 determines the angle formed by the maximum principal curvature direction correspondence line L521-2 and the minimum principal curvature direction correspondence line L522-1 at the point P 523 as a right angle.

Then, as shown in the region A53, the end of the minimum main curvature direction corresponding line L522-2 and the end of the maximum main curvature direction corresponding line L521-2 do not overlap. As described above, generally, the angles formed by the maximum principal curvature direction corresponding line surrounding the planar mesh region and the minimum main curvature direction corresponding line are all the maximum main curvature line partial lines surrounding the original target surface mesh region. It is not possible to match the angle formed with the minimum main curvature line partial line.

Therefore, the angle determination unit 123 determines the angle formed between the maximum principal curvature direction corresponding line surrounding the planar mesh region and the minimum main curvature direction corresponding line, the maximum main curvature line partial line surrounding the original target surface mesh region, and the minimum main curvature. The difference from the angle formed with the line partial line is dispersed in the plane mesh region.
FIG. 9 is an explanatory diagram illustrating an example of an angle formed by the maximum main curvature direction corresponding line and the minimum main curvature direction corresponding line surrounding the planar mesh region.

Hereinafter, the connection point between the maximum principal curvature direction correspondence line and the minimum principal curvature direction correspondence line is referred to as a vertex of the planar mesh region or simply as a vertex. In addition, the angle formed by the maximum principal curvature direction corresponding line and the minimum main curvature direction corresponding line at the vertex of the planar mesh region is referred to as the vertex angle of the planar mesh region or simply the vertex angle.
FIG. 9 shows a planar mesh region A54 surrounded by maximum main curvature direction corresponding lines L531-1 and L531-2 and minimum main curvature direction corresponding lines L532-1 and L532-2.

Further, the maximum main curvature direction corresponding line L531-1 and the minimum main curvature direction corresponding line L532-2 are connected at the vertex P530 of the planar mesh region A54. The minimum main curvature direction corresponding line L532-1 and the maximum main curvature direction corresponding line L531-1 are connected at the vertex P531 of the planar mesh region A54. The maximum main curvature direction corresponding line L531-2 and the minimum main curvature direction corresponding line L532-1 are connected by the vertex P532 of the planar mesh region A54. The minimum main curvature direction corresponding line L532-2 and the maximum main curvature direction corresponding line L531-2 are connected by a vertex P533 of the planar mesh region A54. Vertices of planar mesh area A54 P530, P531, P532, the angle of the P533, respectively _{_{_{φ 0, φ 1, φ 2}}} , φ 3 and notation.

The vertices P531 and P530 are connected by a line segment L540. The vertices P532 and P531 are connected by a line segment L541. The vertices P533 and P532 are connected by a line segment L542. The vertices P530 and P533 are connected by a line segment L543.
The line segments L540, L541, L542, and L543 form a quadrangle. Accordingly, the vertices P530, P531, P532, and P533 are also quadrangular vertices.
The angles of the vertices P530, P531, P532, and P533 of the quadrangle are expressed as Ψ ₀ , Ψ ₁ , Ψ ₂ , and Ψ ₃ , respectively.

Here, when any one of φ ₀ , φ ₁ , φ ₂ , φ ₃ , ψ ₀ , ψ ₁ , ψ _2, and ψ ₃ is determined, another angle is also determined. For example, with Ψ ₀ as a parameter, Ψ ₁ (Ψ ₀ ), Ψ ₂ (Ψ ₀ ), Ψ ₃ (Ψ ₀ ), φ ₀ (Ψ ₀ ), φ ₁ (Ψ ₀ ), φ ₂ (Ψ ₀ ), It can be expressed as φ ₃ (Ψ ₀ ).
Further, the relationship between the vertex angles φ ₀ , φ ₁ , φ ₂ and φ _{3 of} the planar mesh region A54 and the square vertex angles Ψ ₀ , Ψ ₁ , Ψ ₂ and Ψ ₃ is expressed by Equation (3). Shown in

Here, [delta] _{0_1} is, the maximum principal curvature direction corresponding line L531-1 and the line segment L540 is a constant indicating the angle formed at the apex P530. positive and negative values of [delta] _{0_1} is line L540 for the maximum principal curvature direction corresponding line L531-1 is negative when a certain case in the clockwise side as viewed toward 9 to positive, counterclockwise side And In the example of FIG. 9, since the line segment L540 is in the counterclockwise side with respect to the maximum principal curvature direction corresponding line L531-1, δ _{0_1} has a negative value.

Furthermore, [delta] _{0_2} has a minimum principal curvature direction corresponding line L532-2 and the line segment L543 is a constant indicating the angle formed at the apex P530. positive and negative values of [delta] _{0_2} is line L543 for the minimum principal curvature direction corresponding line L532-2 is negative when there a case where the left-handed side as viewed toward 9 to positive, clockwise side And In the example of FIG. 9, since the line segment L540 is in the counterclockwise side with respect to the minimum principal curvature direction corresponding line L532-2, δ _{0_2} takes a positive value.

Further, δ _{1_1} is a constant indicating the angle formed between the minimum principal curvature direction corresponding line L532-1 and the line segment L541 at the vertex P531. The value of δ _{1_1} is positive when the line segment L541 is on the clockwise side as viewed in FIG. 9 with respect to the minimum principal curvature direction corresponding line L532-1, and is negative when the line segment L541 is on the counterclockwise side. And In the example of FIG. 9, since the line segment L541 is on the counterclockwise side with respect to the minimum main curvature direction corresponding line L532-1, δ _{1_1} takes a negative value.

Further, δ _{1_2} is a constant indicating the angle formed by the maximum principal curvature direction corresponding line L531-1 and the line segment L540 at the vertex P531. The sign of δ _{1_2} is positive when the line segment L540 is on the left-handed side as viewed in FIG. 9 with respect to the maximum principal curvature direction corresponding line L531-1, and is negative when it is on the right-handed side. And In the example of FIG. 9, since the line segment L540 is on the clockwise side with respect to the maximum principal curvature direction corresponding line L531-1, δ _{1_2} takes a negative value.

Further, δ _{2_1} is a constant indicating an angle formed by the vertex P532 between the maximum principal curvature direction corresponding line L531-2 and the line segment L542. The value of δ _{2_1} is positive when the line segment L542 is on the clockwise side as viewed in FIG. 9 with respect to the maximum principal curvature direction corresponding line L531-2, and negative when the line segment L542 is on the counterclockwise side. And In the example of FIG. 9, since the line segment L542 is on the counterclockwise side with respect to the maximum principal curvature direction corresponding line L531-2, δ _{2_1} takes a negative value.

Further, δ _{2_2} is a constant indicating the angle formed between the minimum principal curvature direction corresponding line L532-1 and the line segment L541 at the vertex P532. The sign of δ _{2_2} is positive when the line segment L541 is on the counterclockwise side as viewed in FIG. 9 with respect to the minimum principal curvature direction corresponding line L532-1, and negative when the segment is on the clockwise side. And In the example of FIG. 9, since the line segment L541 is on the clockwise side with respect to the minimum main curvature direction corresponding line L532-1, δ _{2_2} takes a negative value.

Furthermore, [delta] _{3_1} has a minimum principal curvature direction corresponding line L532-2 and the line segment L543 is a constant indicating the angle formed at the apex P533. The sign of δ _{3_1} is positive when the line segment L543 is in the clockwise direction as viewed in FIG. 9 with respect to the minimum principal curvature direction corresponding line L532-2 and negative in the case of the counterclockwise side. And In the example of FIG. 9, since the line segment L543 is on the clockwise side with respect to the minimum main curvature direction corresponding line L532-2, δ _{3_1} takes a positive value.

Further, δ _{3_2} is a constant indicating the angle formed by the maximum principal curvature direction corresponding line L531-2 and the line segment L542 at the vertex P533. The sign of δ _{3_2} is positive when the line segment L542 is on the counterclockwise side as viewed in FIG. 9 with respect to the maximum principal curvature direction corresponding line L531-2 and negative when it is on the clockwise side. And In the example of FIG. 9, since the line segment L542 is on the clockwise side with respect to the maximum principal curvature direction corresponding line L531-2, δ _{3_2} takes a negative value.

The angle determination unit 123 solves the optimization problem that minimizes the value of the optimization function F (Ψ ₀ ) expressed by, for example, Expression (4). Thereby, the angle determination unit 123 calculates the angle between the maximum curvature line partial line and the minimum curvature line partial line surrounding the target surface mesh area, and the maximum curvature direction corresponding line and the minimum curvature direction corresponding line surrounding the planar mesh area. The difference from the angle formed is equalized in the planar mesh area.

The right side of the equation (4) includes the angle between the maximum curvature line partial line and the minimum curvature line partial line surrounding the plane mesh area, the maximum curvature line partial line and the minimum curvature line partial line surrounding the target plane mesh area, and Is the sum of the squares of the differences from each of the angles (both are 90 °).
The angle determination unit 123 obtains Ψ ₀ that satisfies Expression (5) using, for example, the Newton method.

Here, “′” indicates a first derivative. That is, F ′ (Ψ ₀ ) is a function obtained by first-order differentiation of the optimization function F (Ψ ₀ ) with Ψ ₀ . The angle determination unit 123 obtains Ψ ₀ that satisfies Expression (5), whereby the angle formed by the maximum main curvature direction corresponding line and the minimum main curvature direction corresponding line and the maximum main curvature corresponding to the maximum main curvature direction corresponding line. The maximum principal curvature direction correspondence line and the minimum principal curvature direction correspondence line so that the sum of the squares of the differences between the angle formed by the line partial line and the minimum principal curvature direction partial line corresponding to the minimum principal curvature direction correspondence line is minimized. Determine the angle between.
Note that the number of vertices of the corresponding planar mesh region may be other than 4 when the umbilical point is included in the target surface mesh region and in the vicinity of the edge (boundary) of the formation target surface. In this case, the angle determination unit 123 obtains the angle of each vertex using an expression that generalizes Expression (5).

FIG. 10 is an explanatory diagram illustrating an example in which a planar mesh region is approximated by an N-gon (N is the number of vertices of the planar mesh region).
N-3 diagonal lines are drawn between the vertex V _N-1 and the vertexes V ₁ , V ₂ ,..., V _N-3 shown in FIG. As a result, the N-gon is divided into N-2 triangles.
The angle determination unit 123 is known about the length of each side of the N-gon in FIG. Thus, α _i and β _i (i = 0, 1,... N−4) can be obtained from θ _i using the cosine theorem. Specifically, the angle determination unit 123 obtains the angle of each vertex of the N-gon from Equation (6).

Here, ψ _i (i = 0,..., N−1) represents the angle of each vertex of the N-gon.
Note that the value of θ _i can be negative. In this case, the value of α _{i and} the value of β _i are determined as in equation (7).

Also, the value of θ _i can be greater than π (180 °). In this case, the value of α _{i and} the value of β _i are determined as in equation (8).

Note that θ _N-3 is not a variable. The sign of θ _N−3 is determined by comparison with the target angle.
The angle determination unit 123 obtains the angle of the line segment at each vertex by connecting the vertices with the line segment in the target surface mesh region, for example. Then, the angle determination unit 123 sets the obtained angle as the target angle Ω ₀ ... Ω _N−1 and solves the optimization problem that minimizes the value of the objective function shown in Equation (9).

Thereby, the angle determination unit 123 calculates the angle between the maximum curvature line partial line and the minimum curvature line partial line surrounding the target surface mesh area, and the maximum curvature direction corresponding line and the minimum curvature direction corresponding line surrounding the planar mesh area. Equalize the difference from the angle you make.
In order to minimize the value of the function shown in Expression (9), the angle determination unit 123 obtains values of θ ₀ , θ ₁ ,..., Θ _N−4 that satisfy Expression (10).

Here, it is set as equation (11).

Then, the equation of Newton's method is shown as equation (12).

The angle determination unit 123 solves the equation (12) using Newton's method, and the angle formed by the maximum curvature line partial line and the minimum curvature line partial line surrounding the target mesh area and the maximum curvature direction surrounding the planar mesh area. The difference between the angle between the corresponding line and the minimum curvature direction corresponding line is equalized.

When the plane mesh region includes the maximum principal curvature direction corresponding line, the minimum main curvature direction corresponding line, and the line corresponding to the edge of the formation target surface, the angle determination unit 123 sets the maximum main curvature direction corresponding line and the formation purpose. The angle between the line corresponding to the edge of the surface and the angle between the line corresponding to the maximum principal curvature direction and the line corresponding to the edge of the formation target surface are also determined. As the determination method, the same method as described above can be used.

Note that the method by which the angle determination unit 123 determines the angle formed by the line surrounding the planar mesh region is not limited to the method described above. For example, in the example of FIG. 9, the angle determination unit 123 may determine the angle formed by the line surrounding the planar mesh region by determining the angle φ ₁ to 90 degrees. Thus, the angle determination unit 123 may determine one or more of the angles formed by the lines surrounding the planar mesh region as a predetermined angle.
The process performed by the angle determination unit 123 corresponds to an example of the process in the angle determination step.

The shape processing unit 130 is formed by joining regions on the plane (planar mesh regions) according to the arrangement in the direction along the maximum principal curvature line of the regions (target surface mesh regions) on the formation target surface, The material is processed into a shape in which the regions on the plane are joined together in accordance with the arrangement in the direction along the minimum principal curvature line of each region on the surface.
For example, the shape processing unit 130 generates a first member obtained by processing the material into a shape in which the regions on the plane are joined according to the arrangement in the direction along the maximum principal curvature line of each region on the formation target surface. In addition, the shape processing unit 130 generates a second member obtained by processing the material into a shape in which the regions on the plane are joined according to the arrangement in the direction along the minimum main curvature line of each region on the formation target surface.
A member here is a thing before a combination obtained by changing a raw material, such as cutting a raw material. The formation target surface is formed by joining the members.

FIG. 11 is an explanatory diagram illustrating an example of a development view acquired by the shape processing unit 130. FIG. 11A shows an example of the formation target surface. Part (B) of FIG. 11 shows an example of a development view obtained by joining the planar mesh regions according to the arrangement in the direction along the maximum principal curvature line. (C) part of FIG. 11 shows the example of the expanded view obtained by connecting a planar mesh area | region according to the arrangement in the direction along the minimum principal curvature.
The thing obtained by processing a raw material according to the developed view of part (B) in FIG. 11 corresponds to an example of the first member.
Moreover, the thing obtained by processing a raw material according to the expanded view of the (C) part of FIG. 11 corresponds to an example of the second member.

In part (A) of FIG. 11, a maximum main curvature line L611, a minimum main curvature line L621, maximum main curvature line partial lines L631 to L635, and minimum main curvature line partial lines L641 to L645 are shown. Yes.
Further, a target mesh area A611 is formed surrounded by the maximum main curvature line partial lines L631 and L633 and the minimum main curvature line partial lines L641 and L642. A target mesh area A612 is formed by being surrounded by the maximum main curvature line partial lines L632 and L634 and the minimum main curvature line partial lines L642 and L643. A target mesh area A613 is formed surrounded by the maximum main curvature line partial lines L634 and L635 and the minimum main curvature line partial lines L644 and L645.

The maximum main curvature direction corresponding lines L671, L672, L673, L674, and L675 shown in the portion (B) of FIG. 11 are expanded on the plane of the maximum main curvature line partial lines L631, L632, L633, L634, and L635, respectively. This is the line obtained. The minimum main curvature direction corresponding lines L681, L682, L683, L684, and L685 are lines obtained by expanding the minimum main curvature line partial lines L641, L642, L643, L644, and L645 on a plane, respectively. From the correspondence between the maximum main curvature line partial line and the maximum main curvature direction corresponding line and the correspondence between the minimum main curvature line partial line and the minimum main curvature direction corresponding line, the planar mesh regions A621, A622, A623 are: , Are respectively associated with the target surface mesh areas A611, A612, and A613.

The planar mesh region of the part (B) in FIG. 11 is arranged by joining in accordance with the alignment in the direction along the maximum principal curvature line of the target surface mesh area in the formation target surface of the part (A) in FIG.
For example, in the portion (A) of FIG. 11, the target surface mesh regions A611 and A612 are arranged in contact with each other along the maximum principal curvature line L611. Correspondingly, the planar mesh regions A621 and A622 are arranged in contact with each other in the portion (B) of FIG.

Further, in the portion (B) of FIG. 11, the planar mesh region is in contact with the same line corresponding to the minimum principal curvature direction. For example, each of the planar mesh regions A621 and A622 includes a minimum main curvature direction corresponding line L682, and is in contact with the minimum main curvature direction corresponding line L682.
In this way, by connecting and joining the planar mesh regions with the same minimum principal curvature line corresponding line, the planar mesh regions can be joined together without gaps, and a development view can be configured. Therefore, it is not necessary to deform the plane mesh regions for joining, and in this respect, a development view with a small distortion from the shape of the formation target surface can be obtained.

Further, in the development view of the portion (B) in FIG. 11, the portions to be joined when assembling the formation target surface from the development view are configured by the same maximum principal curvature direction corresponding line. For example, in the formation target surface of the portion (A) in FIG. 11, the target surface mesh regions A612 and A613 are in contact with each other at the maximum principal curvature line partial line L634. Correspondingly, the planar mesh regions A622 and A623 in the portion (B) of FIG. 11 are connected. Each of the planar mesh regions A622 and A623 is configured to include a maximum principal curvature direction corresponding line L674. When assembling the formation target surface from the development view of the portion (B) in FIG. 11, the target surface mesh regions A612 and A613 are joined and connected by the maximum principal curvature direction corresponding line L674.
In this way, the formation target surface is assembled by connecting the portions shown in the development view with the same maximum principal curvature direction corresponding line, so that it is not necessary to deform the portion when assembling the development view. When assembling the development view, it is not necessary to make adjustments for joining the parts well together, and the assembly work of the development view is easy.

In part (C) of FIG. 11, the same planar mesh regions as in part (B) of FIG. 11 are arranged in a different arrangement from the case of part (B) of FIG. 11. 11B, the same reference numerals (A621... A623, L671... L675, L681... L685) are assigned to the portions indicated by the reference numerals in FIG.
The planar mesh region in the part (C) of FIG. 11 is an arrangement in which the target mesh region in the formation target surface of the part (A) in FIG. 11 is connected according to the arrangement in the direction along the minimum principal curvature line.
For example, in the part (A) of FIG. 11, the target surface mesh regions A612 and A613 are aligned in the direction along the minimum main curvature line L621 and are in contact with each other at the maximum main curvature line partial line L634. Correspondingly, in the portion (C) of FIG. 11, the planar mesh regions A622 and A623 are arranged in contact with each other at the maximum principal curvature direction corresponding line L674.

Further, in the portion (C) of FIG. 11, the planar mesh region is in contact with the same line corresponding to the maximum principal curvature direction. For example, each of the planar mesh regions A622 and A623 includes a maximum principal curvature direction corresponding line L674 and is in contact with the maximum main curvature direction correspondence line L674.
In this way, by connecting and connecting the planar mesh regions with the same maximum principal curvature line-corresponding line, it is possible to connect the planar mesh regions without any gaps to form a development view. Therefore, it is not necessary to deform the plane mesh regions for joining, and in this respect, a development view with a small distortion from the shape of the formation target surface can be obtained.

Further, in the development view of the portion (C) in FIG. 11, the portions that are to be joined when assembling the formation target surface from the development view are configured by the same minimum principal curvature direction corresponding line. For example, in the formation target surface of the portion (A) in FIG. 11, the target surface mesh regions A611 and A612 are in contact with each other at the minimum principal curvature line partial line L642. Correspondingly, the planar mesh areas A621 and A622 in the part (C) of FIG. 11 are connected. The planar mesh regions A621 and A622 are each configured to include a minimum principal curvature direction corresponding line L682. When assembling the formation target surface from the development view of the part (C) in FIG. 11, the target surface mesh regions A611 and A612 are connected and connected by the minimum principal curvature direction corresponding line L682.
In this way, since the formation target surface is assembled by joining the parts shown in the development view with the same line corresponding to the minimum principal curvature direction, it is not necessary to deform the part when assembling the development view. When assembling the development view, it is not necessary to make adjustments for joining the parts well together, and the assembly work of the development view is easy.

Further, the shape obtained by assembling the development view of the part (B) in FIG. 11 and the shape obtained by assembling the development view of the part (C) in FIG. 11 are the same in which the same plane mesh region is arranged in the same manner. It is the shape. Thereby, the curved surface obtained by assembling the development view of the part (B) of FIG. 11 and the curved surface obtained by assembling the development view of the part (C) of FIG. 11 can be easily superimposed.
Here, the maximum main curvature line and the minimum main curvature line are orthogonal to each other. Moreover, the connection part (seam | joint) in the shape obtained by assembling the expanded view of the (B) part of FIG. 11 respond | corresponds to the largest principal curvature line. Moreover, the connection part in the shape obtained by assembling the development view of the part (C) in FIG. 11 corresponds to the minimum principal curvature line. Therefore, the connection portion in the shape obtained by assembling the development view of the portion (B) in FIG. 11 and the connection portion in the shape obtained by assembling the development view of the portion (C) in FIG. Accordingly, the object obtained by assembling the development view of the part (B) of FIG. 11 and the object obtained by assembling the development view of the part (C) of FIG. A shape can be obtained.

The features described with reference to part (B) of FIG. 11 are not limited to the development shown in part (B) of FIG. 11, but are arranged in a direction along the maximum principal curvature line of the target surface mesh area on the formation target surface. This applies to the developed view obtained by joining the planar mesh regions according to Further, the feature described with reference to part (C) of FIG. 11 is not limited to the development view shown in part (C) of FIG. 11, but the direction along the minimum principal curvature line of the target surface mesh area on the formation target surface. This applies to a developed view obtained by joining the planar mesh regions according to the arrangement in FIG.

As described with reference to FIG. 11, the shape processing unit 130 connects and connects two planar mesh regions with the same minimum principal curvature line corresponding line. By repeating this process, the shape processing unit 130 acquires a shape obtained by joining the planar mesh regions along the line in the direction along the maximum principal curvature line. Except for the case where the minimum main curvature line corresponding line is a mapping of the edge of the formation target surface, there are always two planar mesh regions including the same minimum main curvature line corresponding line. Therefore, the shape processing unit 130 connects the two planar mesh regions so that the same minimum principal curvature line-corresponding line touches in the same direction.
Similarly, the shape processing unit 130 joins two planar mesh regions in contact with the same maximum principal curvature line-corresponding line. By repeating this processing, the shape processing unit 130 acquires a shape obtained by joining the planar mesh regions along the direction along the minimum principal curvature line. Except for the case where the maximum main curvature line corresponding line is a mapping of the edge of the formation target surface, there are always two planar mesh regions including the same maximum main curvature line corresponding line. Therefore, the shape processing unit 130 connects the two planar mesh regions so that the same maximum principal curvature line corresponding line contacts in the same direction.
The shape processing unit 130 has a shape in which the planar mesh regions are joined along the direction along the maximum principal curvature line, and a shape in which the planar mesh regions are joined along the direction along the minimum principal curvature line. Any one of them may be acquired. Alternatively, the shape processing unit 130 joins the planar mesh regions joined in the direction along the maximum principal curvature line and joined the planar mesh regions in the direction along the minimum principal curvature line. You may make it acquire both shapes.

For example, when the on-planar region acquisition unit 120 forms the planar mesh region, an identification number is assigned to the planar mesh region so that the shape processing unit 130 can perform the process of joining the planar mesh regions in this way. The on-plane area acquisition unit 120 also assigns an identification number to each of the maximum main curvature line corresponding line and the minimum main curvature line corresponding line constituting the plane mesh area. Then, the on-planar region acquisition unit 120 generates information that combines the identification number of the planar mesh region and the identification numbers of the maximum main curvature line corresponding line and the minimum main curvature line corresponding to the planar mesh region. The on-plane area acquisition unit 120 generates information that combines the identification number of the maximum main curvature line corresponding line and the identification numbers of the two planar mesh areas including the maximum main curvature line corresponding line. The on-plane area acquisition unit 120 generates information that combines the identification number of the minimum main curvature line corresponding line and the identification numbers of the two planar mesh areas including the minimum main curvature line corresponding line. The shape processing unit 130 refers to the information generated by the on-plane region acquisition unit 120, identifies two planar mesh regions including the same minimum principal curvature line corresponding line, and connects the identified planar mesh regions. Similarly, the shape processing unit 130 refers to the information generated by the on-planar region acquisition unit 120, identifies two planar mesh regions including the same maximum principal curvature line corresponding line, and connects the identified planar mesh regions. Match.
The processing performed by the shape processing unit 130 corresponds to an example of processing in the shape processing step.

The formation target surface forming unit 140 combines the members obtained by processing the material by the shape processing unit 130 into a surface shape for the formation purpose. For example, the formation target surface forming unit 140 forms the surface shape for the formation purpose by alternately combining the first member and the second member generated by the shape processing unit 130.
FIG. 12 is an explanatory diagram illustrating an example of the outer shape of an object obtained by the combination process performed by the formation target surface forming unit 140. In the areas A711 and A712 of FIG. 12, the first member appears.
On the other hand, in the areas A721 and A722, the second member appears. As described above, the shape processing unit 130 alternately combines the first member and the second member, and in the obtained product, the first member and the second member are alternately arranged.

As described with reference to FIG. 11, the shape obtained by assembling the development view of the first member and the shape obtained by assembling the development view of the second member are the same shape (the same planar mesh region is deformed). (Shapes arranged in the same order without). Therefore, when the formation target surface forming portion 140 combines the first member and the second member, the other portions other than the gap due to the thickness of the member can be combined without generating a gap. Thereby, a shape close to the shape of the formation target surface can be obtained. In addition, a target surface shape with relatively high strength can be obtained.
Moreover, the thing obtained by the combination which the formation target surface formation part 140 performs has a design property in the point that the 1st member and the 2nd member appear alternately in a line like the example of FIG.
The processing performed by the forming target surface forming unit 140 corresponds to an example of processing in the forming target surface forming step.

Next, the operation of the target surface shape object manufacturing apparatus 100 will be described with reference to FIG.
FIG. 13 is a flowchart illustrating an example of a procedure of processing performed by the target surface shape object manufacturing apparatus 100. However, all or part of the processing in FIG. 13 may be performed by a person instead of the target surface shape object manufacturing apparatus 100.
In the process of FIG. 13, the target surface curvature line acquisition unit 110 acquires a plurality of maximum main curvature lines and minimum main curvature lines of the formation target surface (Step S101). Step S101 corresponds to an example of a target surface curvature line acquisition step.

Next, the corresponding line acquisition unit 121 acquires a maximum main curvature direction corresponding line and a minimum main curvature corresponding line (step S102). Step S102 corresponds to an example of a corresponding line acquisition step.
Next, the connection relationship determining unit 122 determines the connection relationship between the maximum main curvature direction corresponding line and the minimum main curvature direction corresponding line (step S103). Step S103 corresponds to an example of a connection relationship determination step.

Next, the angle determination part 123 determines the angle of the connection part of the largest main curvature direction corresponding line and the minimum main curvature direction corresponding line. (Step S104). Step S104 corresponds to an example of an angle determination step. Steps S102 to S104 correspond to an example of a planar area acquisition step.
Next, the shape processing unit 130 processes the material into a shape obtained by joining the planar mesh regions obtained in step S104 (step S105). Specifically, the shape processing unit 130 obtains a shape obtained by joining the planar mesh regions in accordance with the alignment in the direction along the maximum principal curvature line of the target surface mesh region on the formation target surface. In addition, the shape processing unit 130 obtains a shape obtained by joining the planar mesh regions in accordance with the arrangement in the direction along the minimum principal curvature line of the target surface mesh region on the formation target surface. Then, the shape processing unit 130 processes the material into the obtained shape.
Step S105 corresponds to an example of a shape processing step.

Hereinafter, a member obtained by processing a material into a shape in which plane mesh regions are joined in accordance with the alignment in the direction along the maximum principal curvature line of the target surface mesh region on the formation target surface is referred to as a first member. In addition, a member obtained by processing a material into a shape obtained by joining the planar mesh regions in accordance with the alignment in the direction along the minimum principal curvature line of the target surface mesh region on the formation target surface is referred to as a second member.

Next, the formation target surface forming unit 140 combines the members obtained by processing the material in step S105 to form the formation target surface shape (step S106). Step S106 corresponds to an example of a formation target surface forming step.
After step S106, the process of FIG. 13 is terminated.

In step S106, the formation target surface forming unit 140 may be formed in the shape of the formation target surface by combining the first member and the second member. Then, the formation target surface forming unit 140 may superimpose an object obtained by combining the first member and an object obtained by combining the second member.

In step S105, the shape processing unit 130 may obtain only one of the first member and the second member. In step S <b> 106, the formation target surface forming unit 140 may combine either one of the first member and the second member to form the formation target surface.

As described above, the target surface curvature line acquisition unit 110 obtains a plurality of maximum main curvature lines and a plurality of minimum main curvature lines on the formation target surface. Further, the on-plane area acquisition unit 120 obtains an area on the plane (plane mesh area) associated with this area for each of the target surface mesh areas. In addition, the shape processing unit 130 forms the planar mesh region according to the shape in which the planar mesh regions are joined according to the arrangement of the target surface mesh regions in the direction along the maximum principal curvature line, or the arrangement in the direction along the minimum principal curvature line. Process materials into connected shapes. Then, the formation target surface forming unit 140 combines the members obtained by processing the material by the shape processing unit 130 into the surface shape of the formation target.
In addition, the corresponding line acquisition unit 121 of the on-plane area acquisition unit 120 obtains a maximum main curvature direction corresponding line and a minimum main curvature direction corresponding line. As described above, the maximum principal curvature direction corresponding line is a line obtained by mapping the developable surface including the maximum main curvature line partial line into a plane without expansion and contraction. The minimum main curvature direction corresponding line is a line obtained by mapping a developable surface including the minimum main curvature line partial line to a plane without expansion and contraction.
In addition, the connection relationship determination unit 122 of the on-plane region acquisition unit 120 determines the maximum main curvature line partial line and the minimum main curvature line according to the connection relationship between the maximum main curvature line partial line and the minimum main curvature line partial line forming the target surface mesh region. The connection relationship between the maximum main curvature direction corresponding line and the minimum main curvature direction corresponding line associated with the curvature line partial line is determined.

The members obtained by processing the material by the shape processing unit 130 have the same length of curves (edges of the members) in contact with the formation target surface forming unit 140 when the members are combined. For this reason, the edge of the target shape object obtained by combining members becomes smooth. Therefore, no step is generated at the edge of the target shape object obtained by combining the members.
Here, the material processed by the target surface shape object manufacturing apparatus 100 is not limited to a steel plate, but may be any material that can perform shape processing and processing from a flat surface to a curved surface. For example, the target surface shape object manufacturing apparatus 100 may process cloth or paper. Or you may make it the target surface shape thing manufacturing apparatus 100 process the wood which can be bent, such as a bark of a tree, for example. Alternatively, the target surface shape object manufacturing apparatus 100 may process a metal plate other than a steel plate such as a tin plate.
Thus, in the target surface shape object manufacturing apparatus 100, materials other than a steel plate can be processed into a curved surface shape with high accuracy.

In addition, when the formation target surface forming unit 140 combines the members, there is no gap in the members. In this respect, a target surface shape having a relatively high strength can be obtained. Further, since no gap is generated in the member, it is not necessary to perform a process of filling the gap when the members are combined. In this respect, the process of combining the members is simple, and the load on the formation target surface forming unit 140 can be small. For example, when the formation target surface forming unit 140 bonds members together, only the boundary between the members may be bonded. In addition, the formation target surface forming unit 140 can combine the members with the shape of the formation target surface without having to perform processing such as bending.

Further, in the shape of the formation target surface obtained by the shape processing unit 130, the planar mesh regions are connected by the same corresponding line (maximum principal curvature direction correspondence line or minimum principal curvature direction correspondence line). And connected without overlap. In this respect, the shape of the formation target surface can be realized with high accuracy. In this respect, the target surface shape object manufacturing apparatus 100 can accurately process a material other than a steel plate into a curved surface shape.

Further, in the target surface shape object manufacturing apparatus 100, the formation target surface can be realized with higher precision as the target surface mesh region is set finer. Therefore, design according to the required accuracy is possible. When the accuracy for realizing the target surface shape may be low, the width of at least one of the maximum main curvature line and the minimum main curvature line obtained by the target surface curvature line acquisition unit 110 is increased to manufacture the target surface shape object. The load of processing performed by the apparatus 100 can be reduced. On the other hand, by reducing the width of at least one of the maximum main curvature line and the minimum main curvature line obtained by the target surface curvature line acquisition unit 110, the accuracy of realizing the target surface shape can be improved.

Further, when the planar mesh region is configured by being surrounded by two lines corresponding to the maximum principal curvature direction and two lines corresponding to the minimum principal curvature direction, refer to FIG. 9 and Expressions (3) to (5). As described above, the angle determination unit 123 can obtain the angle between the maximum principal curvature direction corresponding line and the minimum main curvature direction corresponding line by minimizing the objective function of one variable. In this respect, the calculation of the angle determination unit 123 is easy and the processing load of the angle determination unit 123 can be reduced. Further, the time required for the angle determination unit 123 to obtain the angle can be short.

Further, the angle determination unit 123 of the corresponding line acquisition unit 121 in the plane mesh region obtained by connecting the maximum main curvature direction corresponding line and the minimum main curvature direction corresponding line in the connection relationship determined by the connection relationship determination unit 122, The angle formed by the maximum main curvature direction corresponding line and the minimum main curvature direction corresponding line at this connection location, the maximum main curvature line partial line corresponding to the maximum main curvature direction corresponding line, and the minimum main curvature direction corresponding line The maximum main curvature direction corresponding line and the minimum main curvature direction connected by the connection relationship determined by the connection relationship determining unit 122 by equalizing the difference between the angle with the minimum main curvature line partial line corresponding to Determine the angle between the corresponding lines.
Thereby, it is possible to avoid the deviation between the angle on the formation target surface and the angle in the development view from being concentrated on one place, and the accuracy of realizing the target surface shape can be improved.

Further, the developable surface used by the corresponding line acquisition unit 121 includes a normal vector of the formation target surface at this point and a tangent vector of the maximum main curvature line partial line at this point at each point on the maximum main curvature line partial line. The vector of the outer product of the normal vector of the formation target surface at this point and the tangent vector of the minimum main curvature line partial line at this point at each point on the surface including the vector of the outer product and the minimum main curvature line partial line It is a surface including.
Thereby, the corresponding line acquisition unit 121 includes the normal vector of the formation target surface and the maximum main curvature line partial line or the minimum main curvature line partial line along each of the maximum main curvature line partial line and the minimum main curvature line partial line. A developable surface can be obtained by a simple operation of obtaining an outer product with a tangent vector.

Further, the formation target surface forming unit 140 may generate a plurality of objects having the shape of the formation target surface and superimpose the obtained objects. Thereby, the thickness of the target shape object obtained can be increased and intensity | strength can be raised.
At that time, the target surface curvature line acquisition unit 110 may change the position of the curvature line (for example, shift the phase) so that the position of the connecting portion of the member differs for each object to be superimposed. Thereby, the intensity | strength of the target surface shape thing obtained can further be raised.

In addition, the shape processing unit 130 generates a first member obtained by processing the material into a shape in which the planar mesh regions are joined according to the arrangement of the target surface mesh regions in the direction along the maximum principal curvature line.
In addition, the shape processing unit 130 generates a second member obtained by processing the material into a shape in which the planar mesh regions are joined according to the arrangement of the target surface mesh regions in the direction along the minimum principal curvature line.
And the formation target surface formation part 140 makes the surface shape of a formation purpose by combining a 1st member and a 2nd member alternately (namely, by knitting a 1st member and a 2nd member).
Thus, the formation target surface formation part 140 knits a member and manufactures a target surface shape thing, and the combination of a member does not collapse easily. In this respect, a target surface shape having a relatively high strength can be obtained. In this method, in principle, the target surface is generated by using an adhesive, but if the curvature of the target surface is gentle, it can be generated without bonding. In addition, the design is high in that the first member and the second member appear alternately in the outer shape of the target shape object.
In addition, the formation target surface forming unit 140 only needs to knit the first member and the second member so that no gap is generated. In this respect, the process of combining the members is simple, and the load on the formation target surface forming unit 140 is reduced. Is small. For example, the formation target surface forming unit 140 can knit the member into the shape of the formation target surface without having to perform a process such as bending.

The formation target surface forming unit 140 may be formed in the shape of the formation target surface by combining the first member and the second member. Then, the formation target surface forming unit 140 may superimpose an object obtained by combining the first member and an object obtained by combining the second member.
In this case, in the target shape object obtained, the position of the connection part of the member in the object obtained by combining the first member and the position of the connection part of the member in the object obtained by combining the second member are orthogonal to each other. To do. Thereby, the intensity | strength of the target surface shape thing obtained can be raised.
In addition, when a part or all of the processing performed by the target surface shape object manufacturing apparatus 100 is performed by a person instead of the target surface shape object manufacturing apparatus 100, the same effect as the case where the target surface shape object manufacturing apparatus 100 performs processing is performed. Can be obtained.

<Second Embodiment>
FIG. 14 is a schematic block diagram showing a functional configuration of a shape acquisition apparatus according to the second embodiment of the present invention. As illustrated in FIG. 14, the shape acquisition device 200 includes a target surface curvature line acquisition unit 110, a planar area acquisition unit 120, and a shape acquisition unit 230. The on-plane area acquisition unit 120 includes a corresponding line acquisition unit 121, a connection relationship determination unit 122, and an angle determination unit 123.
14, parts having the same configuration corresponding to the parts in FIG. 1 are denoted by the same reference numerals (110, 120... 123), and description thereof is omitted. The shape acquisition device 200 is different from the target surface shape object manufacturing device 100 (FIG. 1) in that a shape acquisition unit 230 is provided instead of the shape processing unit 130 and the formation target surface formation unit 140.

The shape acquisition unit 230 has a shape obtained by joining the plane mesh regions according to the sequence of the target surface mesh regions in the direction along the maximum principal curvature line, or a plane according to the sequence of the target surface mesh regions in the direction along the minimum principal curvature line. A shape obtained by joining mesh regions is obtained. Specifically, the shape acquisition unit 230 is the member of the process for obtaining the shape of the member and the process for processing the material into the obtained shape described for the shape processing unit 130 of the target surface shape object manufacturing apparatus 100. Processing to obtain the shape is performed.

Next, the operation of the shape acquisition apparatus 200 will be described with reference to FIG.
FIG. 15 is a flowchart illustrating an example of a procedure of processing performed by the shape acquisition device 200. However, all or part of the processing in FIG. 15 may be performed by a person instead of the shape acquisition device 200.
Steps S201 to S204 in FIG. 15 are the same as steps S101 to S104 in FIG.

After step S204, the shape acquisition unit 230 obtains a shape obtained by connecting the planar mesh regions obtained in step S104 (step S205). Specifically, the shape processing unit 130 includes a shape obtained by joining the planar mesh regions according to the arrangement of the target surface mesh regions in the direction along the maximum principal curvature line, and the target surface mesh in the direction along the minimum principal curvature line. One or both of the shapes obtained by joining the planar mesh regions are obtained according to the region arrangement.
After step S205, the process of FIG.

As described above, the target surface curvature line acquisition unit 110 obtains a plurality of maximum main curvature lines and a plurality of minimum main curvature lines on the formation target surface. Further, the on-plane area acquisition unit 120 obtains an area on the plane (plane mesh area) associated with this area for each of the target surface mesh areas. Further, the shape acquisition unit 230 forms a shape obtained by joining the planar mesh regions according to the arrangement of the target surface mesh regions in the direction along the maximum principal curvature line, or the planar mesh region according to the arrangement in the direction along the minimum principal curvature line. Get the connected shape. The shape acquisition unit 230 joins the planar mesh regions according to the alignment along the minimum principal curvature line and the shape obtained by joining the planar mesh regions according to the alignment along the target principal mesh region in the direction along the maximum principal curvature line. You may make it acquire both of the shape.
In addition, the corresponding line acquisition unit 121 of the on-plane area acquisition unit 120 obtains a maximum main curvature direction corresponding line and a minimum main curvature direction corresponding line. As described above, the maximum principal curvature direction corresponding line is a line obtained by mapping the developable surface including the maximum main curvature line partial line into a plane without expansion and contraction. The minimum main curvature direction corresponding line is a line obtained by mapping a developable surface including the minimum main curvature line partial line to a plane without expansion and contraction.
In addition, the connection relationship determination unit 122 of the on-plane region acquisition unit 120 determines the maximum main curvature line partial line and the minimum main curvature line according to the connection relationship between the maximum main curvature line partial line and the minimum main curvature line partial line forming the target surface mesh region. The connection relationship between the maximum main curvature direction corresponding line and the minimum main curvature direction corresponding line associated with the curvature line partial line is determined.
Further, the angle determination unit 123 of the corresponding line acquisition unit 121 in the plane mesh region obtained by connecting the maximum main curvature direction corresponding line and the minimum main curvature direction corresponding line in the connection relationship determined by the connection relationship determination unit 122, The angle formed by the maximum main curvature direction corresponding line and the minimum main curvature direction corresponding line at this connection location, the maximum main curvature line partial line corresponding to the maximum main curvature direction corresponding line, and the minimum main curvature direction corresponding line The maximum main curvature direction corresponding line and the minimum main curvature direction connected by the connection relationship determined by the connection relationship determining unit 122 by equalizing the difference between the angle with the minimum main curvature line partial line corresponding to Determine the angle between the corresponding lines.

In the shape of the member required by the shape acquisition unit 230, the lengths of the curves (edges of the member) in contact with the members are equal. For this reason, a level | step difference cannot be performed in the boundary (edge) of the thing obtained by combining a member.
Further, when the members having the shapes obtained by the shape acquisition unit 230 are combined, no gaps are generated in the members. In this respect, a target surface shape having a relatively high strength can be obtained. Further, since no gap is generated in the member, it is not necessary to perform a process of filling the gap when the members are combined. In this respect, the process of combining the members is simple, and the load of this process can be reduced. For example, when the members having the shape obtained by the shape acquisition unit 230 are bonded to each other, only the boundary between the members may be bonded. Further, the member can be combined with the shape of the formation target surface without the need to perform a process such as bending.

Further, in the shape of the formation target surface obtained by the shape acquisition unit 230, the planar mesh regions are connected by the same corresponding line (maximum principal curvature direction correspondence line or minimum principal curvature direction correspondence line). And connected without overlap. In this respect, the shape of the formation target surface can be realized with high accuracy.

Moreover, in the shape acquisition apparatus 200, the formation target surface can be realized with higher precision as the target surface mesh region is set more finely. Therefore, design according to the required accuracy is possible. When the accuracy for realizing the target surface shape may be low, the shape acquisition device 200 increases the width of at least one of the maximum main curvature line and the minimum main curvature line obtained by the target surface curvature line acquisition unit 110 and The load of processing to be performed can be reduced. On the other hand, by reducing the width of at least one of the maximum main curvature line and the minimum main curvature line obtained by the target surface curvature line acquisition unit 110, the accuracy of realizing the target surface shape can be improved.

From the viewpoint of increasing the strength of the target shape object, when the shape processing unit 130 processes the material to form the member, the smaller the cut into the member, the better. The shallow cut here means that the cut length is short.
Therefore, when the target surface curvature line acquisition unit 110 obtains a curvature line, the calculation of the curvature line may be stopped when it is detected that the distance between the same kind of curvature lines is smaller than the distance threshold. Accordingly, the number of curvature lines acquired by the target surface curvature line acquisition unit 110 may be reduced, and the length of the curvature line acquired by the target surface curvature line acquisition unit 110 may be shortened.

By reducing the number of curvature lines acquired by the target surface curvature line acquisition unit 110, the number of curvature line partial lines is reduced, and the number of curvature line corresponding lines is also reduced. The curvature line corresponding line here is a general term for the maximum main curvature line corresponding line and the minimum main curvature line corresponding line.
Further, the length of the curvature line acquired by the target surface curvature line acquisition unit 110 is shortened, so that the number of intersections between the maximum main curvature line and the minimum main curvature line is reduced, and the number of curvature line partial lines is reduced. . By reducing the number of curvature line partial lines, the number of curvature line corresponding lines is also reduced.
By reducing the number of lines corresponding to the curvature line, when the shape processing unit 130 processes the material to form the member, the cut into the member is reduced, or the cut into the member is shallow.

FIG. 16 is a diagram illustrating an example in which calculation of the curvature line is stopped when the target surface curvature line acquisition unit 110 detects that the distance between the same type of curvature lines is smaller than the distance threshold. The distance threshold is a threshold given in advance as a constant, for example.
Both the line L811 and the line L813 are minimum main curvature lines, and the line L812 is a maximum main curvature line. The target surface curvature line acquisition unit 110 obtains the coordinates of the points on the line L813 in order from the point P811 in a state where the coordinates of the lines L811 and L812 have been calculated. As the line L813 extends, the end portion first approaches the line L812. The line L812 is the minimum main curvature line, whereas the line L812 is the maximum main curvature line, and the types of the curvature lines are different. Therefore, the target surface curvature line acquisition unit 110 continues the process of calculating the coordinates of the line L813.
Thereafter, the end portion approaches the line L811 as the line L813 extends, and the distance D81 between the point P812 and the line L811 is smaller than the distance threshold value. Since both the line L811 and the line L813 are the minimum main curvature lines and the same kind of curvature lines, the target surface curvature line acquisition unit 110 ends the calculation of the coordinates of the line L813 up to the point P812.
As described above, when the target surface curvature line acquisition unit 110 stops the process of obtaining the curvature line, as described above, when the shape processing unit 130 processes the material to form the member, there is less cutting into the member. Or the depth of cut into the member becomes shallower. The process for obtaining the curvature line here is a process for obtaining the coordinates of the curvature line, and specifically, a process for obtaining the coordinates of the points on the curvature line.
When the target surface curvature line acquisition unit 110 detects that the distance between the same kind of curvature lines is smaller than the distance threshold, the calculation of the curvature line is stopped in either the first embodiment or the second embodiment. Is also applicable.

The target surface curvature line acquisition unit 110 may stop the process of obtaining a curvature line for a region having a small Gaussian curvature. A small Gaussian curvature indicates that at least one of the maximum main curvature and the minimum main curvature is close to zero. In this case, the material can be formed in the shape of the formation target surface relatively accurately without making a cut in the material.

FIG. 17 is a diagram illustrating an example in which the target surface curvature line acquisition unit 110 stops calculating the curvature line for a region where the magnitude of the Gaussian curvature is smaller than the curvature threshold. The curvature threshold is a threshold given in advance as a constant, for example.
Region A821 is a region in which the Gaussian curvature is smaller than the curvature threshold. When obtaining the coordinates of the points on the curvature line in order, the target surface curvature line acquisition unit 110 arrives at the region A821 and detects that the magnitude of the Gaussian curvature is smaller than the curvature threshold value. Cancel. As a result, the target surface curvature line acquisition unit 110 does not obtain a curvature line for the region A821.
As described above, the shape processing unit 130 processes the material in the same manner as when the distance between the curvature lines of the same type becomes smaller than the distance threshold by stopping the process of obtaining the curvature line by the target surface curvature line acquisition unit 110. Thus, when forming the member, the cut into the member is reduced, or the cut into the member is shallow.
The fact that the target surface curvature line acquisition unit 110 detects that the Gaussian curvature is smaller than the curvature threshold is applicable to both the first embodiment and the second embodiment.

When the target surface curvature line acquisition unit 110 detects that the distance between the same type of curvature lines is smaller than the distance threshold and stops obtaining the curvature line, it detects that the Gaussian curvature is smaller than the curvature threshold and detects the curvature line In any case where the acquisition is stopped, the end of the curvature line may not overlap the edge of the formation target surface and any other curvature line. In this case, this end does not form a target surface mesh region. Therefore, the target surface curvature line acquisition unit 110 may delete a portion from this end to the intersection with another curvature line.

FIG. 18 is a diagram illustrating an example in which the end portion of the curvature line does not overlap the edge of the formation target surface and any other curvature line.
In any of the lines L831 and L832, a portion surrounded by a chain line does not form a target surface mesh region.

FIG. 19 is a diagram illustrating an example in which the target surface curvature line acquisition unit 110 deletes a portion from the end of the curvature line to the intersection with another curvature line.
FIG. 19 shows an example in which the target surface curvature line acquisition unit 110 deletes the portion from the end of the curvature line to the intersection with another curvature line from the state shown in FIG.
In each of the lines L831 and L832, a portion surrounded by a chain line is removed.
It can be applied to both the first embodiment and the second embodiment that the target surface curvature line acquisition unit 110 deletes a portion from the end of the curvature line to the intersection with another curvature line.

FIG. 20 is a flowchart illustrating an example of a processing procedure in which the target surface curvature line acquisition unit 110 obtains a curvature line.
The target surface curvature line acquisition unit 110 determines the position of the start point of the curvature line, and calculates the coordinates of the start point (step S301).
Next, the target surface curvature line acquisition unit 110 calculates the coordinates of the next point after the points for which the coordinates have been calculated among the points on the calculated curvature line (step S302).

Then, the target surface curvature line acquisition unit 110 determines whether or not the current point has reached the boundary of the formation target surface (step S303). If it is determined that the boundary has been reached (step S303: YES), the processing in FIG. On the other hand, if it is determined that the boundary has not yet been reached (step S303: NO), the target surface curvature line acquisition unit 110 calculates a Gaussian curvature at the current point (step S304).
Then, the target surface curvature line acquisition unit 110 determines whether or not the Gaussian curvature at the current point is smaller than the curvature threshold (step S305).

When it is determined that the Gaussian curvature at the current point is smaller than the curvature threshold (step S305: YES), the processing in FIG.
On the other hand, when it is determined that the Gaussian curvature at the current point is greater than or equal to the curvature threshold value (step S305: NO), the target surface curvature line acquisition unit 110 calculates the current point and the calculated same type of curvature line. Is calculated (step S306).

Then, the target surface curvature line acquisition unit 110 determines whether or not the distance between the current point and the calculated same kind of curvature line is smaller than the distance threshold (step S307).
When it is determined that the distance between the current point and the calculated curvature line of the same kind is greater than or equal to the distance threshold (step S307: NO), the process returns to step S302.
On the other hand, when it is determined that the distance between the current point and the calculated curvature line of the same kind is smaller than the distance threshold (step S307: NO), the processing in FIG.

In FIG. 20, when the target surface curvature line acquisition unit 110 detects that the distance between the same type of curvature lines is smaller than the distance threshold, the curvature being calculated in both cases where the Gaussian curvature is detected to be smaller than the curvature threshold. The example in the case of complete | finishing the process which calculates | requires a line is shown. However, when the target surface curvature line acquisition unit 110 detects that the distance between the same kind of curvature lines is smaller than the distance threshold, the calculation of the curvature line being calculated is stopped, and it is detected that the Gaussian curvature is smaller than the curvature threshold. In this case, only one of the cancellation of the calculation of the curvature line being calculated may be performed.

The shape acquisition unit 230 may obtain a plurality of development views of the formation target surface by shifting the cut positions.
FIG. 21 is a diagram illustrating an example of a plurality of development views with different cut positions.
Each of (A) part, (B) part, and (C) part of FIG. 21 shows a maximum main curvature line and a minimum main curvature line on the formation target surface. The positions of the maximum main curvature line and the minimum main curvature line are different between the part (B) and the part (C). In the (B) portion and the (C) portion, different combinations are selected from the maximum main curvature line and the minimum main curvature line shown in the (A) portion.

21 (D), (E), (F), and (G) are respectively developed views of the formation target surface. The developed view shown in part (D) and the developed view shown in part (F) are both developed views obtained by joining the planar mesh regions along the minimum principal curvature line direction. The developed view shown in part (D) is generated based on the maximum main curvature line and the minimum main curvature line shown in part (B). On the other hand, the developed view shown in the (F) part is generated based on the maximum main curvature line and the minimum main curvature line shown in the (C) part. Since the maximum main curvature line and the minimum main curvature line that are the basis are different, in the development view shown in part (D) of FIG. 21 and the development view shown in part (F), the position of the cut Is different.

Similarly, the developed view shown in the (E) portion and the developed view shown in the (G) portion are both developed views obtained by joining the planar mesh regions along the maximum principal curvature line direction. . The developed view shown in part (E) is generated based on the maximum main curvature line and the minimum main curvature line shown in part (B). On the other hand, the developed view shown in the (G) portion is generated based on the maximum main curvature line and the minimum main curvature line shown in the (C) portion. Since the maximum main curvature line and the minimum main curvature line that are the basis are different, in the development view shown in part (E) of FIG. 21 and the development view shown in part (G), the position of the cut Is different.

By obtaining development views with different incision positions in this way, target surface shapes are formed from the respective development views and overlapped, or the formed target surface mesh regions of the first member and the second member are alternately arranged. Stacking is also possible, and strength can be obtained in that the positions of the cuts are different.
The same applies to the target surface shape object manufacturing apparatus of the first embodiment.
As described with reference to FIG. 3, the target surface curvature line acquisition unit 110 identifies a plurality of calculation start points on the formation target surface, and a plurality of maximum main curvature lines and a plurality of points from the plurality of specified calculation start positions. Find the minimum principal curvature line.
In the example of FIG. 21, the target surface curvature line acquisition unit 110 obtains the maximum main curvature line and the minimum main curvature line of the formation target surface shown in part (A). Thereafter, the target surface curvature line acquisition unit 110 removes the maximum main curvature line and a part of the minimum main curvature line shown in the (A) part so as to become the (B) part, and the (D) part and the (E) part. Find each development. Moreover, the target surface curvature line acquisition part 110 remove | excludes a part of the maximum main curvature line and minimum main curvature line shown by the (A) part so that it may become a (C) part, (F) part, (G) part Each development can be obtained.
As another method, in the example of FIG. 21, the target surface curvature line acquisition unit 110 obtains the maximum main curvature line and the minimum main curvature line shown in the (B) portion, and then the maximum main curvature shown in the (C) portion. A curvature line and a minimum main curvature line are obtained. Therefore, the target surface curvature line acquisition unit 110 specifies the calculation start position twice. The target surface curvature line acquisition unit 110 obtains the maximum main curvature line and the minimum main curvature line shown in the part (B) from the plurality of calculation start positions specified for the first time. And the target surface curvature line acquisition part 110 calculates | requires the maximum main curvature line and minimum main curvature line shown by the (C) part from the several calculation start position specified for the 2nd time. In this way, the target surface curvature line acquisition unit 110 performs processing for obtaining a plurality of maximum main curvature lines and a plurality of minimum main curvature lines from a plurality of calculation start positions specified on the formation target surface while changing the calculation start positions. You can do more than one.

FIG. 22 is a schematic block diagram illustrating a configuration of a computer according to at least one embodiment.
The computer includes a CPU, a main storage device, an auxiliary storage device, and an interface.
The above-described target surface shape acquisition device is mounted on a computer. The operation of each processing unit described above is stored in the auxiliary storage device in the form of a program. The CPU reads the program from the auxiliary storage device, develops it in the main storage device, and executes the above processing according to the program. Further, the CPU secures a storage area corresponding to each storage unit described above in the main storage device according to the program.

As described above, the target surface curvature line acquisition unit 110 obtains a plurality of maximum main curvature lines and a plurality of minimum main curvature lines on the formation target surface. The on-plane area acquisition unit 120 obtains data indicating the shape of the area on the corresponding plane for each area in which the formation target surface is divided by the maximum main curvature line and the minimum main curvature line. Thereby, the error which arises when forming the shape of the part of the surface of the formation object on a plane can be distributed.

In addition, the corresponding line acquisition unit 121 obtains a maximum main curvature direction corresponding line and a minimum main curvature direction corresponding line obtained by mapping a plane including the curvature line partial line into a plane.
The connection relation determining unit 122 corresponds to the maximum main curvature line partial line and the minimum main curvature line partial line according to the connection relation of the maximum main curvature line partial line and the minimum main curvature line partial line forming the region of the formation target surface. The connection relationship between the maximum main curvature direction corresponding line and the minimum main curvature direction corresponding line is determined.
Thereby, the connection relationship between the maximum curvature line corresponding line and the minimum curvature line corresponding line on the formation target surface can be reflected in the connection relationship between the maximum main curvature direction corresponding line and the minimum main curvature direction corresponding line on the plane. it can.

The angle determination unit 123 calculates the angle between the maximum principal curvature direction corresponding line and the minimum main curvature direction corresponding line calculated based on the divided area on the plane corresponding to the formation target surface and the corresponding divided area on the plane, and the maximum main curvature direction. The maximum main curvature so that the sum of the squares of the differences between the maximum main curvature line partial line corresponding to the curvature direction corresponding line and the minimum main curvature line partial line corresponding to the minimum main curvature direction corresponding line is minimized. An angle formed by the direction corresponding line and the minimum principal curvature direction corresponding line is determined.
Thereby, the error with the target surface mesh area | region in a plane mesh area | region can be disperse | distributed to each corner, and it can avoid that the distortion by an error concentrates on one place.

The surface including the maximum principal curvature line partial line includes a vector of the outer product of the normal vector of the formation target surface at a point on the maximum principal curvature line partial line and the tangent vector of the maximum principal curvature line partial line at this point. The surface that includes the minimum principal curvature line partial line is the vector of the outer product of the normal vector of the target surface at the point on the minimum principal curvature line partial line and the tangent vector of the minimum principal curvature line partial line at this point. It is a surface including.
By developing this surface in a plane, a maximum main curvature direction corresponding line and a minimum main curvature direction corresponding line corresponding to the maximum main curvature line partial line and the minimum main curvature line partial line are obtained.

Further, the target surface curvature line acquisition unit 110 performs a plurality of processes for obtaining a plurality of maximum main curvature lines and a plurality of minimum main curvature lines from a plurality of calculation start positions specified on the formation target surface while changing the calculation start positions. Do.
The on-plane area acquisition unit 120 shows the shape of the area on the plane constituted by the maximum main curvature direction corresponding line and the minimum main curvature direction corresponding line corresponding to the plurality of maximum main curvature lines and the plurality of minimum main curvature lines. Ask for data.
Thereby, a plurality of development views in which the positions of the cuts are shifted are obtained. For example, a relatively strong target surface shape object can be generated by forming and superimposing the target surface shape from each of the developed views in which the positions of the cuts are shifted.

The target surface curvature line acquisition unit 110
A process of determining a start point for obtaining a target main curvature line that is either the maximum main curvature line or the minimum main curvature line on the formation target surface, and sequentially obtaining points that follow the start point constituting the target main curvature line, It reaches the boundary of the formation target surface, reaches a region where the Gaussian curvature is equal to or less than the curvature threshold, or the acquired main main curvature line and minimum main curvature line with the target main curvature line and the same type of curvature line Repeat until the distance reaches a point below the distance threshold.
Thereby, the cut in the developed view obtained decreases, and a stronger target surface shape can be obtained.

The on-plane area acquisition unit 120 is configured to connect the areas on the plane according to the arrangement in the direction along the maximum principal curvature line of the areas on the formation target surface, and the minimum main curvature of each area on the formation target surface. According to the arrangement in the direction along the line, at least one of the data of the shape obtained by joining the areas on the plane is obtained.
As a result, a band-shaped component can be obtained, and the shape of the formation target surface can be configured by a relatively simple process of joining the band-shaped components together.

Further, the shape processing unit 130 is formed by joining the regions on the plane according to the arrangement in the direction along the maximum main curvature line of the region on the formation target surface, or along the minimum main curvature line of the region on the formation target surface. According to the arrangement in the selected direction, the material is processed into a shape in which the areas on the plane are connected.
The formation target surface forming unit 140 combines the materials processed by the shape processing unit 130 into the surface shape of the formation target.
Thereby, the target surface shape object manufacturing apparatus 100 can process the material into the surface shape of the formation purpose. In addition, it is possible to avoid the strain from being concentrated at one place in the target shape object by connecting the regions on the plane.

The shape processing unit 130 includes a first member that has processed the material into a shape in which the regions on the plane are joined together according to the arrangement in the direction along the maximum principal curvature line of each region on the formation target surface, and each region on the formation target surface. In accordance with the arrangement in the direction along the minimum principal curvature line, a second member obtained by processing the material into a shape obtained by joining the regions on the plane is generated. The formation target surface forming unit 140 combines the first member and the second member in a staggered manner to obtain a surface shape for the formation purpose.
Accordingly, the shape processing unit 130 can obtain a formation target surface by a relatively simple process of alternately combining the first member and the second member.

A program for realizing all or part of the functions and operations performed by the target shape object manufacturing apparatus 100 or the shape acquisition apparatus 200 is recorded on a computer-readable recording medium, and the program recorded on the recording medium May be read by a computer system and executed to execute the processing of each unit. The “computer system” here includes an OS and hardware such as peripheral devices.
“Computer-readable recording medium” refers to a portable medium such as a flexible disk, a magneto-optical disk, a ROM, and a CD-ROM, and a storage device such as a hard disk built in a computer system. The program may be a program for realizing a part of the functions described above, and may be a program capable of realizing the functions described above in combination with a program already recorded in a computer system.

As described above, the embodiment of the present invention has been described in detail with reference to the drawings. However, the specific configuration is not limited to this embodiment, and includes design changes and the like without departing from the gist of the present invention.

An embodiment of the present invention includes a target surface curvature line acquisition unit that obtains a plurality of maximum main curvature lines and a plurality of minimum main curvature lines on a formation target surface, and the formation target surface is the maximum main curvature line and the minimum main curvature line. The present invention relates to a shape acquisition device including an on-plane area acquisition unit that obtains data indicating the shape of a corresponding area on a plane for each divided area.
According to this embodiment, it is possible to disperse errors that occur when forming the shape of the component of the surface to be formed on a plane.

DESCRIPTION OF SYMBOLS 100 Target surface shape thing manufacturing apparatus 110 Target surface curvature line acquisition part 120 Plane top area | region acquisition part 121 Corresponding line acquisition part 122 Connection relation determination part 123 Angle determination part 130 Shape processing part 140 Formation target surface formation part 200 Shape acquisition apparatus 230 Shape Acquisition department

Claims

A target surface curvature line acquisition unit for obtaining a plurality of maximum principal curvature lines and a plurality of minimum principal curvature lines on the formation target surface;
On-plane area acquisition unit for obtaining data indicating the shape of the area on the corresponding plane for each area where the formation target surface is divided by the maximum main curvature line and the minimum main curvature line;
A shape acquisition device comprising:
The area acquisition unit on the plane is
On the plane corresponding to the maximum main curvature line partial line, obtained by mapping a plane including the maximum main curvature line partial line, wherein the maximum main curvature line is a line divided by the minimum main curvature line. And a plane including a plane including a minimum main curvature line partial line in which the minimum main curvature line is a line delimited by the maximum main curvature line. A corresponding line acquisition unit for obtaining a minimum main curvature direction corresponding line that is a line on a plane corresponding to the minimum main curvature line partial line;
The maximum corresponding to the maximum main curvature line partial line and the minimum main curvature line partial line according to the connection relation of the maximum main curvature line partial line and the minimum main curvature line partial line forming the region of the formation target surface. A connection relationship determining unit for determining a connection relationship between the main curvature direction corresponding line and the minimum main curvature direction corresponding line;
The shape acquisition apparatus according to claim 1.
The area acquisition unit on the plane is
An angle formed by the maximum main curvature direction corresponding line and the minimum main curvature direction corresponding line, calculated based on the divided area on the formation target surface and the corresponding planar divided area, and the maximum main curvature direction corresponding line Corresponding to the maximum principal curvature direction so that the sum of the squares of the differences between the maximum principal curvature line partial line corresponding to and the minimum principal curvature line partial line corresponding to the minimum principal curvature direction corresponding line is minimized. The shape acquisition apparatus according to claim 2, further comprising an angle determination unit that determines an angle formed by a line and the minimum principal curvature direction corresponding line.
The surface including the maximum principal curvature line partial line includes a vector of outer products of a normal vector of the formation target surface at a point on the maximum principal curvature line partial line and a tangent vector of the maximum principal curvature line partial line at the point. A plane including the minimum principal curvature line partial line is a cross product of a normal vector of the formation target surface at a point on the minimum principal curvature line partial line and a tangent vector of the minimum principal curvature line partial line at the point The shape acquisition apparatus according to claim 2, wherein the shape acquisition apparatus is a plane including a vector.
The target surface curvature line acquisition unit performs a plurality of processes for obtaining the plurality of maximum main curvature lines and a plurality of minimum main curvature lines from a plurality of calculation start positions specified on the formation target surface while changing the calculation start positions. Done
The area acquisition unit on the plane is an area on the plane constituted by the maximum main curvature direction corresponding line and the minimum main curvature direction corresponding line corresponding to the plurality of maximum main curvature lines and the plurality of minimum main curvature lines. Find data showing the shape,
The shape acquisition apparatus as described in any one of Claim 2 to 4.
The target surface curvature line acquisition unit
Determining a starting point for obtaining a target main curvature line that is either a maximum main curvature line or a minimum main curvature line on the formation target surface;
The process of obtaining the points following the start point constituting the target main curvature line in order, the boundary of the formation target surface is reached, the region where the Gaussian curvature is equal to or less than the curvature threshold, or the acquired maximum principal curvature The shape acquisition device according to any one of claims 1 to 5, wherein the shape acquisition device repeats until a distance between the target main curvature line and the same type of curvature line among the lines and the minimum main curvature line reaches a point that is equal to or less than a distance threshold value.
The on-plane area acquisition unit is configured to connect the areas on the plane according to the arrangement in the direction along the maximum principal curvature line of the area on the formation target surface, and the data on the formation target surface. According to the arrangement in the direction along the minimum principal curvature line of each region, obtain at least one of the data of the shape obtained by joining the regions on the plane,
The shape acquisition apparatus as described in any one of Claim 1 to 6.
The shape acquisition device according to claim 7,
According to the arrangement in the direction along the maximum principal curvature line of the region on the formation target surface, the shape in which the regions on the plane are joined together, or along the minimum principal curvature line of the region on the formation target surface In accordance with the arrangement in the direction, a shape processing unit that processes the material into a shape that joins the regions on the plane, and
A forming target surface forming portion that combines the material processed by the shape processing portion into a forming target surface shape;
A target surface shape manufacturing apparatus comprising:
The shape processing portion includes a first member that processes a material into a shape in which the regions on the plane are joined together in accordance with the arrangement in the direction along the maximum principal curvature line of the regions on the formation target surface, and the formation According to the arrangement in the direction along the minimum principal curvature line of each region on the target surface, to generate a second member processed material in a shape that joins the regions on the plane,
The formation target surface forming portion is configured by alternately combining the first member and the second member into a formation target surface shape.
The target surface shape thing manufacturing apparatus of Claim 8.
Determine the starting point for finding the target main curvature line that is either the maximum main curvature line or the minimum main curvature line on the formation target surface,
The process of obtaining the points following the start point constituting the target main curvature line in order, the boundary of the formation target surface is reached, the region where the Gaussian curvature is equal to or less than the curvature threshold, or the acquired maximum principal curvature It repeats until the distance between the target main curvature line and the same kind of curvature line among the lines and the minimum main curvature line reaches a point that is equal to or less than the distance threshold,
The process of determining the start point and the process of obtaining a point on the target main curvature line are repeated to obtain a plurality of the maximum main curvature lines and a plurality of the minimum main curvature lines,
For each region where the formation target surface is divided by the maximum main curvature line and the minimum main curvature line, obtain data indicating the shape of the region on the corresponding plane,
According to the arrangement in the direction along the maximum principal curvature line of the region on the formation target surface, the shape in which the regions on the plane are joined together, or along the minimum principal curvature line of the region on the formation target surface According to the arrangement in the direction, the material is processed into a shape that joins the areas on the plane,
A method for producing a target surface shape product, which comprises forming processed surface shapes by combining processed materials.
Processing the material
Generating a first member obtained by processing a material into a shape in which the regions on the plane are joined according to the arrangement in the direction along the maximum principal curvature line of the regions on the formation target surface;
Generating a second member obtained by processing a material into a shape obtained by joining the regions on the plane according to the arrangement in the direction along the minimum principal curvature line of the regions on the formation target surface,
Making the surface shape for the purpose of formation includes making the surface shape for the purpose of formation by alternately combining the first member and the second member,
The method for manufacturing a target shape object according to claim 10.
On the computer,
Obtaining a plurality of maximum principal curvature lines and a plurality of minimum principal curvature lines on the formation target surface;
A program for obtaining data indicating a shape of a region on a plane associated with the region for a region in which the formation target surface is divided by the maximum main curvature line and the minimum main curvature line.