JPH1115994A - Method for creating curved surface - Google Patents

Abstract

PROBLEM TO BE SOLVED: To obtain such a transformational curved surface as to have smooth continuity by creating a transformational curved surface which includes points of designated moving destinations and includes a smooth interpolation curved line that contacts the original curved surface with a border of a transformation area. SOLUTION: A border of a designated transformational area is set as graphic data that is represented by more than one parameter coordinate position on a main storage. When the point of the moving destination is indicated in accordance with each passing point group on the original curved surface, a curved surface creating part 101 sets the three-dimensional space coordinate point on the main storage. Next, it creates an interpolation line group that smoothly connects a point group of moving destinations and a part except the transformational area of the original curved surface. Then, an interpolation surface is created which interpolates a created interpolation line group and the part except a transformational area of the original curved surface in the form of having smooth continuity. The shape of a created interpolation surface is shown on a display 104 through a display controlling part 103. Next, numeric data showing the shape change of a created transformational curved surface is shown on the display 104 and the transformational curved surface is visually evaluated.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for creating a curved surface using a computer, and more particularly, to a CAD (Compupu).
ter Aided Design) / CAM (Com
puter Aided Manufacturin
g) / CAE (Computer Aided Eng)
inering) / CAGD (Computer A)
ided Geometric Design) / CG
The present invention relates to a method for creating a curved surface that locally deforms an original curved surface shape into a desired curved surface in (Computer Graphics).

[0002]

2. Description of the Related Art In a conventional field such as CAGD, as a method of transforming a three-dimensional original curved surface into a curved surface suitable for the purpose,
There is a method in which a basic curved surface such as a sphere or a cone is set at the position of a curved surface to be deformed, and a deformed curved surface is generated by combining data of these curved surfaces.

[0003] As disclosed in Japanese Patent Publication No. 7-120437, a deformation area including an action point with respect to an original curved surface is designated, and each position of the curved surface is determined based on the position of each deformation point in the deformation area. There is a method in which a vector field function representing a relative deformation rate of the target is obtained, a deformation vector representing a deformation amount and a direction is specified for an action point, and a vector obtained by multiplying the deformation vector and the vector field function is used as a base of the deformation surface.

[0004]

In the conventional method of generating a deformed surface by combining basic surface data, the method of connecting curved surfaces becomes unnatural, and it is difficult to express a smooth surface. Not suitable.

In the method described in Japanese Patent Publication No. 7-120439, it is difficult to maintain natural smoothness in the connection between the deformed curved surface and the original curved surface outside the deformed area. Further, there is a problem that only one action point is specified, and it is not possible to cope with the deformation of the curved surface when the action point is on the boundary line of the original curved surface.

Furthermore, after a deformed surface is created by the above-described method, there is a problem that there is no means for evaluating whether the created deformed surface satisfies the user.

It is an object of the present invention to provide a method for creating a curved surface that enables continuous creation of a deformed surface and evaluation of the deformed surface.

It is another object of the present invention to provide a method for creating a curved surface that provides a smooth continuity in the connection between the deformed curved surface and the original curved surface outside the deformed area.

It is still another object of the present invention to provide a method for creating a curved surface when there are two or more action points to be designated or when there are action points on the boundary of the original curved surface.

[0010]

SUMMARY OF THE INVENTION According to the present invention, there is provided a step of interpolating a specified three-dimensional space coordinate point outside an original surface to generate a deformed surface that is in contact with the original surface, and displaying the shape of the deformed surface. Displaying on a device, visually displaying numerical data indicating a change in the shape of the deformed surface on a display device, and a curved surface creating method for sequentially repeating the above steps until instructed to determine the deformed surface. Features.

Further, according to the present invention, at least one passing point is designated on the original curved surface, a deformation region on the original curved surface surrounding the passing point is designated, and the deformation area outside the original curved surface is designated corresponding to each passing point on the original curved surface. When a three-dimensional space coordinate point of the movement destination is specified in, a smooth interpolation curve that touches the original curved surface at the boundary of the deformation area by interpolating the specified movement destination point is interpolated, and a plurality of interpolation curves are interpolated. The method is characterized by generating a deformed curved surface and displaying the shape of the deformed curved surface on a display device. Note that one of the passing points on the original curved surface may exist on the boundary line or the vertex of the deformation area.

The computer program embodied on a computer-readable storage medium is:
The method includes each step of the curved surface creation method.

[0013]

DESCRIPTION OF THE PREFERRED EMBODIMENTS One embodiment of the present invention will be described below in detail with reference to the drawings.

FIG. 1 is a configuration diagram of an information processing apparatus according to the present embodiment. The processing device 100 includes a display control unit 103, a curved surface creating unit 101, a main storage device for storing curved surface data 110, an input control unit 108, and an output control unit 109. The display device 104 is connected to the processing device 100,
It is a device that displays the shape of a curved surface. Keyboard 105
Is a device that is connected to the processing device 100 and inputs numerical data such as coordinate values representing coordinate positions in a three-dimensional space.
The mouse 106 is an input device that is connected to the processing device 100 and indicates a point on a curved surface displayed on the display device 104, a symbol to be displayed, and the like. The printer 107 is a device that is connected to the processing device 100 and outputs a hard copy or the like having a curved surface shape displayed on the display device 104. The curved surface creating unit 101 reads the curved surface data 110 on the main storage device, displays the curved surface data 110 on the display device 104 in the form of a curved surface via the display control unit 103, and displays the keyboard 105 or the mouse 106
When a point on the original curved surface and its destination point are designated via the input control unit 108, data of a deformed curved surface that passes through the destination point is created and displayed on the display device 104,
A processing unit that outputs the completed deformed surface to the printer 107 via the output control unit 109. The curved surface creation unit 101
This is realized by executing a program stored in the main storage device of the processing device 100. Display control unit 103,
The input control unit 108 and the output control unit 109 are a hardware mechanism and a processing device 100 that control connected devices, respectively.
By executing a control program stored in the main storage device. The program of the curved surface creation unit 101 can be stored on a storage medium readable by the processing device 100 and can be read into the main storage device of the processing device 100 via an external storage device (not shown) connected to the processing device 100. is there.

FIG. 2 is a flowchart showing the flow of the process of the curved surface creating unit 101. The curved surface creation unit 101 displays the shape data of the original curved surface group on the main storage device in the form of a graphic on the display device 104 via the display control unit 103 (step 11). Here, the original surface data is data represented by a surface S (u, v) in a parametric expression. S
(U, v) includes a second-order curved surface such as a plane, an elliptical surface, a second-order conical surface, and a columnar surface. The curved surface of the parametric expression is composed of a plurality of quadrilateral surface elements (patches) arranged in a grid as shown in FIG.
And the position P (u, v) of a point on this curved surface is represented by U
This is referred to as a parameter coordinate position with respect to the coordinate axes in the direction and the V direction. The parameter coordinate position P (u, v) is converted into a coordinate position E (x,
y, z).

E (x, y, z) = R (P (u, v)).

FIG. 4 is a diagram showing an example of a shape figure of an original curved surface group displayed on the display device 104. An identifier such as a curved surface number 42 for identifying each original curved surface is displayed on the shape figure of the original curved surface 41, and a symbol is provided at a point at each of the four corners of the patch or at a lattice point obtained by further subdividing the patch into a lattice-shaped surface element. 4
3 is displayed. When the operator designates any one of the curved surface number 42, the symbol 43, and the original curved surface 41 via the mouse 106, the operator can select the original curved surface 41 or input a coordinate position on the original curved surface 41.

When an original surface S1 to be deformed is selected from the group of original surfaces to be displayed via the keyboard 105 or the mouse 106, the surface creating unit 101 selects the surface number 42 of the selected original surface S1. Is set in the main memory (step 12). Next, when a group of passing points SPi (i = 0, 1,...) On the original curved surface S1 is selected via the mouse 106 or the keyboard 105, the respective parameter coordinate positions are set on the main memory (step). 13). An arbitrary point other than the symbol 43 attached to a point on the original curved surface S1 can be designated via the mouse 106 as the passing point group SPi. The original curved surface S1 is input via the keyboard 105.
The above arbitrary parameter coordinate position may be input by a numerical value. Next, when a deformation area including the passing point group SPi is designated on the original curved surface S1 via the keyboard 105 or the mouse 106, the boundary C (t) of the designated deformation area is set to 1
It is set on the main memory as graphic data represented by one or more parameter coordinate positions (step 14).

FIG. 5 is a diagram for explaining a method of specifying a deformation area. 51 indicates an original curved surface S1, and 52 indicates a deformation area. Reference numeral 53 denotes a point for defining the deformation area, and reference numeral 54 denotes a boundary of the deformation area. FIG. 5A shows an example in which the deformation area 52 is a rectangle. The deformation area 52 is defined by designating two points 53 on the opposite corners. FIG.
(B) is a case where the deformation area 52 is a polygon, and the deformation area 52 is defined by designating a point 53 that is a vertex of the polygon. Alternatively, a free closed curve can be drawn on the original curved surface S1 via the mouse 106, and the closed curve can be interpolated by a polygon.

FIG. 6 is a diagram for explaining the relationship between the deformation area and the passing point group SPi. FIG. 6A shows the passing point group SPi.
Shows an example of a deformation region 52 that can be defined when all the data are inside the original curved surface S1. FIG. 6B shows an example of the deformation area 52 that can be defined when SPi indicating a point on the boundary of the original curved surface exists in the passing point group SPi. FIG. 6 (C)
Is a deformation area 52 that can be defined when SPi indicating the vertex (point at the corner) of the original curved surface exists in the passing point group SPi.
Here is an example.

Next, the keyboard 105 or the mouse 106
When the point MPi of the movement destination is designated corresponding to each passing point group SPi on the original curved surface S1 via the
Sets the three-dimensional space coordinate point in the main memory (step 15). When the operator indicates the destination point MPi, a three-dimensional space coordinate point or a curve L (t) in the three-dimensional space is displayed on the display device 104 in advance and is displayed via the mouse 106. Point or curve L (t)
By indicating the upper point, the point MPi can be visually indicated.

FIG. 7 is a diagram for explaining a method of designating a destination point MPi. The three-dimensional coordinate position MEi (x, y, z) of the destination point MPi is set by indicating a previously displayed three-dimensional space coordinate point 71 or a point on the curve 72 in the three-dimensional space. Alternatively, each coordinate value of the three-dimensional coordinate position MEi (x, y, z) may be directly input via the keyboard 105, or a vector amount Vi (x, y, z) representing the movement amount of the point SPi may be input. Good. Point MP
The position vector of i is calculated by the following equation.

Position vector of point MPi = position vector of point SPi + Vi (x, y, z). When the destination point group MPi is set in this way, an interpolation line group CVi that smoothly connects the destination point group MPi and a portion of the original curved surface S1 outside the deformation area is generated (step 16).

For example, with the V direction fixed, the point group of the destination arranged in the U direction is represented by MPij (j = 0, 1,... N).
Is expressed as Here, for the interpolation line CVi along the U direction, if a point MPij (j = 0) on one boundary line of the deformation region is set as a start point and a point MPij (j = n) on the other boundary line is set as an end point, MPij ( j = 0) and MPij (j =
Since n) is either a point on the original surface S1 or a point outside the original surface S1 specified by the user, its three-dimensional spatial position coordinates are clear. Therefore, a spline function Qj (j = 0, 1,... N-
The interpolation line CV along the U direction is obtained by the following equation using 1).
i can be obtained.

[0025]

(Equation 1)

Where MPij (j = 0) and MPij
Of (j = n), the point on the original curved surface S1 is CVi
Is 0. Further, if necessary, the Nth derivative of CVi must maintain continuity (for example, in order for the curvature of the curve CVi to be continuous, the N = second derivative must be continuous). Similarly, MPi when j is fixed
(I = 0, 1,... M), an interpolation line CVj along the V direction can be obtained.

FIG. 8 is a diagram showing an example of the interpolation line CVi. FIG. 8A is a diagram illustrating an example of the interpolation line CVi when all the points SPi exist inside the boundary of the original curved surface S1. In this example, when the original curved surface S1 is a plane, the deformation area 52 passes through the destination point MPi corresponding to the passing point SPi.
The interpolation line CVi that is in contact with the original curved surface S1 on the boundary line is generated. FIG. 8B shows that the original curved surface S is included in the passing point group SPi.
FIG. 9 is a diagram illustrating an example of an interpolation line CVi when there is an SPi located at a point on the boundary line of No. 1; In this example, the original curved surface S1
Is a plane, the interpolation line C that passes through the destination point MPi corresponding to the point SPi located at the point on the boundary line of the original curved surface S1 and is in contact with the original curved surface S1 on the boundary line of the deformation region 52 that is the opposite side.
Vi is being generated. The interpolation line CVi is generated for all the destination points MPi in the U direction and the V direction, respectively. FIG. 9 shows the interpolation line group CV generated in this manner.
It is a figure showing the example of i.

Next, the generated interpolation line group CVi and the original curved surface S1
Then, an interpolated surface S2 is generated by interpolating the portion outside the deformation region in such a manner as to have smooth continuity (step 17).

The interpolation line group CVi is represented by CVjk (j = 0, 1,
.. N; k = 0, 1,... M). Here, CVjk (j = 0; k), CVjk (j = n; k), C
Vjk (j; k = 0) and CVjk (j; k = m) are curves sharing the boundary of the deformation region or curves corresponding to the boundary. Therefore, a spline function Bjk (j = 0, 1,... N-1; k = 0, 1) for smoothly interpolating CVjk
.. M-1), the interpolation plane S2 can be obtained by the following equation.

[0030]

(Equation 2)

However, in a portion where the boundary of the deformation area coincides with the original curved surface S1, the partial differential of S2 in the direction orthogonal to the boundary is zero. If necessary, the Nth partial derivative of S2 must maintain continuity.

Next, the shape of the created interpolation plane S2 is displayed on the display device 104 via the display control unit 103 (step 18). At this time, the shape of the interpolation surface S2 in which the display color is changed is displayed so as to overlap the shape of the original curved surface S1.

Next, numerical data indicating a change in the shape of the created deformed surface S2 is displayed on the display device 104, and the deformed surface S2 is visually evaluated. First, candidates for the confirmation means for the deformed curved surface S2 are displayed on the display device 104, and wait for selection by the operator (step 19). As candidates for the confirmation means, for example, contour line data of the deformed curved surface S2, curvature radius line, normal line,
There is an amount of difference from the original curved surface S1 due to deformation, and the like. When the confirmation means is selected via the keyboard 105 or the mouse 106, confirmation data of the deformed curved surface S2 is displayed on the display device 104 (step 20).

FIG. 10 is a diagram showing a display example of contour lines of the deformed curved surface S2 based on the original curved surface S1. FIG. 11 shows an example of displaying a transition of a radius of curvature line along a specified interpolation line. FIG. 12 shows an example of displaying the transition of the normal line along the interpolation line of the deformed curved surface S2. FIG. 13 shows an example in which the transition of the difference between the designated interpolation line and the original curved surface S1 due to the deformation is displayed. The horizontal axis represents the parameter value, and the vertical axis represents the difference.

The curved surface creating unit 101 displays an option of determining or resetting the deformed curved surface S2 on the display device 104, and waits for an operator's selection (step 21). If the operator is not satisfied with the deformed curved surface S2, a reset is selected. If reset is selected (step 21 NO), the process returns to step 13 and repeats the above processing until the user is satisfied.

When the determination of the deformed surface S2 is selected (step 21 YES), the created shape data of the deformed surface S2 is stored in an external storage device, displayed on the display device 104, and output to the printer 107. (Step 22), the process ends.

As described above, the user can create a desired deformed surface interactively with the computer while checking the state in which the original surface is deformed.

[0038]

As described above, according to the present invention, a smooth interpolation curve including a designated destination point and in contact with an original curved surface at a boundary of a deformation area is generated, and a deformation including a plurality of interpolation curves is generated. Since the curved surface is generated, it is possible to obtain a deformed curved surface in which the connection with the original curved surface outside the deformation region has smooth continuity. Further, the creation of the deformed surface and the evaluation of the deformed surface can be performed continuously, and when the user is not satisfied with the evaluation result, the creation of the deformed surface can be repeated any number of times.

[Brief description of the drawings]

FIG. 1 is a configuration diagram of an information processing apparatus according to an embodiment.

FIG. 2 is a flowchart illustrating a processing flow of a curved surface creation unit 101 according to the embodiment.

FIG. 3 is a diagram illustrating an example of a parametric curved surface.

FIG. 4 is a diagram showing a shape figure of an original curved surface group displayed in the embodiment.

FIG. 5 is a diagram illustrating a method of specifying a deformation area according to the embodiment.

FIG. 6 is a diagram illustrating a relationship between a deformation area and a passing point group SPi according to the embodiment.

FIG. 7 is a diagram illustrating a method of indicating a destination point MPi according to the embodiment.

FIG. 8 is a diagram illustrating an example of an interpolation line CVi.

FIG. 9 is a diagram illustrating an example of a generated interpolation line group CVi.

FIG. 10 is a diagram showing a display example of contour lines of a deformed curved surface.

FIG. 11 is a diagram showing a display example of a curvature distribution of a deformed curved surface.

FIG. 12 is a diagram illustrating a display example of a normal line of a deformed curved surface.

FIG. 13 is a diagram illustrating a display example of a difference value between a deformed curved surface and an original curved surface.

[Explanation of symbols]

 101: surface creation unit, 110: surface data

 ──────────────────────────────────────────────────続 き Continuing on the front page (72) Inventor: Tamotsu Harihara 6-81, Onoecho, Naka-ku, Yokohama-shi, Kanagawa Prefecture In-house Hitachi Software Engineering Co., Ltd. (72) Tomoko Kakura 5030 Totsukacho, Totsuka-ku, Yokohama-shi, Kanagawa Prefecture (72) Inventor Mikihisa Sasaki 2-1-2, Marunouchi, Chiyoda-ku, Tokyo Asahi Glass Co., Ltd.

Claims (5)

[Claims] 1. A method for generating a deformed surface from an original surface by using a computer, wherein a specified three-dimensional space coordinate point outside the original surface is interpolated to generate a deformed surface that is in contact with the original surface. Displaying the shape of the deformed surface on a display device; visually displaying numerical data indicating a change in the shape of the deformed surface on the display device; and instructing to determine the deformed surface. A method for creating a curved surface, comprising repeating the above steps in order until the surface is completed. 2. When displaying numerical data indicating a change in the shape of a deformed curved surface, a plurality of contour lines, a transition of a curvature radius line, a transition of a normal, and a transition of a difference amount between the deformed curved surface and the original curved surface are displayed. 2. The curved surface creating method according to claim 1, wherein the display is performed based on a designated one of a plurality of confirmation means, for example, a display. 3. A computer program embodied on a computer-readable storage medium, the program including the following steps of creating a curved surface deformed from an original surface: (a) Designating a surface outside the original surface (B) displaying the shape of the deformed surface on a display device, and (c) displaying a numerical value indicating a change in the shape of the deformed surface. The data is visually displayed on the display device, and (d) steps (a), (b), and (c) are repeated in order until an instruction to determine the deformed surface is given. 4. A method for creating a deformed surface from an original surface using a computer, wherein at least one passing point is designated on the original surface, and a deformation area on the original surface surrounding the passing point is designated. When a three-dimensional space coordinate point of the destination is designated outside the original surface corresponding to each pass point on the original surface, the designated destination point is interpolated into the original surface at the boundary of the deformation area. A method for creating a curved surface, comprising: generating a smooth interpolating curve that is in contact with a surface, generating a deformed surface for interpolating a plurality of interpolated curves, and displaying the shape of the deformed surface on a display device. 5. The curved surface creating method according to claim 4, wherein at least one of the passing points on the original curved surface exists on a boundary of the deformation area.