JP3153580B2 - Curve and curved shape generator - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a curve and curved surface shape generating device , and more particularly, to a curve and curved surface shape generating device in a three-dimensional shape processing device. For example, CAD / CA
This is applied to shape deformation in the M system.

[0002]

2. Description of the Related Art The following are known documents describing the prior art according to the present invention. First, the following is a conventional technique for controlling a series of smoothly connected curves. Non Uniform Rational B-spline with one series of curves
When represented by curves, the method to manipulate the control points and weights of the curve is "Modifying the shape of rational Bs
pline.Part1: curves '' (Piegl, L., Computer Aided Desig
n, Vol.21, No.8, pp.509-518.1989). As a method of moving one connection point of a series of curves while maintaining curvature continuity in the case of a plane curve, "Design o
f solids with free-form surfaces '' (Chiyokura, H., an
d Kimura, F., Computer Graphics (Proc.SIGGRAPH'83),
Vol.17, No.3, July1983).

The following is a conventional technique for controlling a plurality of smoothly connected curved surfaces. Non Uniform Rational B-spline with multiple curved surfaces
When represented by curves, the method to manipulate the control points and weights of the curve is "Modifying the shape of rational Bs
pline.Part2: curves '' (Piegl, L., Computer Aided Desig
n, Vol.21, No.9, pp.538-546.1989).

In the prior art described above, the shape of the curve is 1
Only when represented by the book's Non Uniform Rational B-spline curves. In this technique, the range in which the shape is deformed depends on the order of the curve and cannot be freely changed.
Further, in the related art, a three-dimensional curve required for three-dimensional CAD cannot be applied because the curve is limited to a plane curve. As described above, according to the conventional technique, the deformation range is arbitrarily set when the shape of the space curve is deformed, and the deformation range changes smoothly, and the curvature vector cannot be held at the boundary of the range. Further, in the above-described conventional technology, similarly to the conventional technology, the shape of the curved surface is one.
Only when represented by NonUniform Rational B-spline curves. In this technique, the range in which the shape is deformed depends on the order of the curved surface and cannot be freely changed.

[0005]

SUMMARY OF THE INVENTION The present invention has been made in view of the above-mentioned circumstances, and a plurality of smoothly connected space curves are deformed in their entirety within a specified range, and a curvature vector at a boundary of the range is not deformed. It is possible to maintain continuity with the surroundings without changing between and after deformation, and it is possible to deform a plurality of spatial curved surfaces defined by the curved mesh in an arbitrary range, at the boundary of the deformation range It is an object of the present invention to provide a curve and curved surface shape generating device capable of maintaining the continuity of a curve for forming a curve mesh.

[0006]

To achieve the above object, the present invention provides (1)
Connecting point information obtaining means for obtaining the positions of connecting points of a series of smoothly connected curves; connecting point information storing means for storing information of connecting points obtained by the connecting point information obtaining means; End point information generating means for obtaining information of the end points at both end points of the curve, end point information storing means for storing the information of the end points obtained by the end point information generating means, and an end point information storing means for obtaining the connecting points obtained by the connecting point information storing means. The connection point movement amount determining means for determining the movement amount of a connection point other than the connection point for which the movement amount is designated, the connection point information obtained by the connection point movement amount determination means, and the end point information generation means. A curve information generating means for generating information on a curve shape after shape deformation from a tangent vector in the obtained information on the end points; and generating the end point information by generating a curvature vector at an end point of the curve shape obtained by the curve information generating means. Original obtained by means A curvature vector setting means for changing to a curvature vector of a line, and a curve shape storage means for storing a changed curve shape obtained by the curvature vector setting means, or (2) an intersection of a curve mesh. Reference point information obtaining means for obtaining reference point information, reference point information storing means for storing reference point information obtained from the reference point information obtaining means, and smooth inward from a connection point at an end of the deformation range. A curve sequence information obtaining means for obtaining information of a curve sequence connected to, a curve sequence information storing means for storing information at both end points of the curve sequence obtained by the curve sequence information obtaining means, and a curve sequence information obtaining means. Reference point moving amount determining means for determining the moving amount of the reference point for each curve line of the obtained curve line information, and storing the moving amount of the reference point determined by the reference point moving amount determining means. Point shift amount storing means, and the position of the reference point in the information on the curve sequence obtained by the curve sequence information obtaining means is derived from the information on the position of the reference point obtained by the reference point information obtaining means, and the reference Curve sequence information generating means for generating information of a new curve sequence by combining the moving amounts obtained by the point moving amount determining means, and a curvature vector at an end point of the shape of the curve sequence obtained by the curve sequence information generating means. Curvature vector setting means for changing to a curvature vector in a curve obtained by the curve sequence information obtaining means,
Curve sequence shape storing means for storing the shape of the changed curve sequence obtained by the curvature vector setting means, and curved surface information for generating a new curve mesh from the curve sequence information stored in the curve sequence shape storing means And generating means. Hereinafter, a description will be given based on examples of the present invention.

FIG. 1 is a block diagram for explaining an embodiment (claim 1) of a curve shape generating apparatus according to the present invention. In the figure, reference numeral 1 denotes a connection point information acquisition unit, and 2 denotes a connection point information storage unit. , 3
Is an end point information generation unit, 4 is an end point information storage unit, 5 is a connection point movement amount determination unit, 6 is a curve information generation unit, 7 is a curvature vector setting unit, and 8 is a curve shape storage unit. In the embodiment of the present invention, a series of smoothly connected curves and a connection point of a curve designating a moving amount and a moving amount thereof are input, and a curve after shape deformation is obtained. Become.

The connection point information acquisition unit 1 obtains the positions of connection points of a series of smoothly connected curves from the curve data,
It is stored in the connection point information storage unit 2. The end point information generation unit 3
A tangent vector and a curvature vector at both end points of a plurality of continuous curves are obtained from the curve data and stored in the end point information storage unit 4. The connection point movement amount determination unit 5 determines how much the connection point should be moved at connection points other than the connection point whose movement amount is specified among the connection points obtained by the connection point information acquisition unit 1. To determine. This result is stored in the connection point information storage 2 together with the original information. The determination method is as follows.

In FIG. 2, it is assumed that the entire row of smoothly connected curves is the deformation range. Here, the connection point P
Specify m for the amount of movement of. An expression for calculating the amount of movement at another connection point within the deformation range is obtained. An equation is established so that the movement amount of each connection point satisfies the following condition. A large movement amount is given to a connection point closer to the designated connection point P, and a smaller movement amount is given to a connection point farther from the connection point. Since the end point of one ridge line is the boundary of the deformation range, this connection point must not move. The movement amount of the designated connection point P is m.

The movement amount of a certain connection point Pi within the range can be obtained, for example, from the following equation. x = m ((rd) / r) ² (1) d is the distance between the specified connection point P and another connection point pi, and r is the distance between the specified connection point P and the end point of the ridge line. Distance. The end point differs depending on the position of another connection point pi as to which end point of the ridge line. An end point closer to another connection point pi is taken from a connection point P specified in the vertices on the ridge line row. In addition, the following equations can be considered. x = m (cos (dπ / r) +1) / 2 (2) If a movement amount as shown in Expressions (1) and (2) is taken, the movement amount is 0 at the end point and m at the specified connection point P. The magnitude of the movement amount during this time gradually increases from the end point to the connection point P. Furthermore, less the amount of movement changes in farther from the connection point P, the change in the movement amount becomes large as close to the connection point P, hit the entire curve to the connection point P
It can produce the effect of being stretched and skirting .

The curve information generation unit 6 calculates a curve after shape deformation from the connection point information obtained by the connection point movement amount determination unit 5 and the tangent vector in the end point information obtained by the end point information generation unit 3. Generate shape information. Each generated curve is cubic
It is a Bezier curve connected to G ² continuous. The curve shape information generated here is stored in the curve shape storage unit 8. The curvature vector setting unit 7 changes the curvature vector at the end point of the curve shape obtained by the curve information generation unit 6 into the curvature vector of the original curve obtained by the end point information generation unit 3. The curve shape after the change is stored in the curve shape storage unit 8. The change method is as follows. Curves are controlled by changing the degree to the fifth order so that the curvature vector at the boundary of the deformation range is set to the original value for the curves at both ends of the curve sequence, and the connection to the inside of the curve sequence is also a continuous curvature vector. I do. By doing so, the curvature vector of the curve sequence generated by designating only the tangent vector at the end point can be controlled independently of the connectivity with the internal curve sequence.

As shown in FIG. 3, the first curve of the generated curve sequence is R ₀ , and the next curve is R ₁ . Both curves are cubic Bezier curves. Curve R ₀ is the fifth-order Bezier
Considered curve, maintaining the G ² continuity between the curve R _1, and the end point to generate a control point to have the tangent and curvature vectors specified. The tangent vector and the curvature vector at the end point of the curve R ₀ are Tt, Kn (3). Here, T and t are the magnitude and unit vector of the tangent vector, respectively, and K and n are the magnitude and unit vector of the curvature vector, respectively.

As shown in FIG. 4, the control point is set to Pi (0<i<
5), Qj (0<j<3). And the distance between the control points
A₀= P_Five−P₀ B₀= P₁−P₀ C₀= P_Five−P_Four D₀= P_Two−P₁ E₀= P_Three−P_Two F₀= P_Four−P_Three (4) A₁= Q_Three−Q₀ B₁= Q₁−Q₀ C₁= Q_Three−Q_Two D₁= Q_Two−Q₁ (5) If the vector between the control points is found, the control point is also found.
You. First, the end point P₀From the tangent vector at₀Ask for
You. The first derivative of the Bezier curve is the vector between the control points.
When you go,

[0014]

(Equation 1)

## EQU1 ## Since this is equal to Tt, B
₀ is

[0016]

(Equation 2)

It can be seen that Curves R ₀ and R ₁ are connected at a point P ₅ = Q ₀ . In order for the curvature vectors of the two curves to coincide at this connection point, the following conditions are assumed.

[0018]

(Equation 3)

## EQU1 ## The derivative of the Bezier curve is obtained and substituted into equations (8) and (9). If a vector between control points is expressed by using the relations of Expressions (4) and (5), the following two expressions are obtained. _{5C 0 = 3k 1 B 1 20} (C 0 -F 0) = 6K 1 2 (D 1 -B 1) (11) C 0 from the two equations, F ₀ is obtained.

[0020]

(Equation 4)

Since A ₀ is fixed and B ₀ , C ₀ , and F ₀ have been obtained, D ₀ or E ₀ may be obtained. D ₀ is obtained from the condition of the curvature vector at P ₀ . 2 in this regard
The second derivative vector is

[0022]

(Equation 5)

## EQU1 ## The curvature vector is

[0024]

(Equation 6)

[0025] By substituting equations (6) and (13) into this equation,

[0026]

(Equation 7)

Is obtained. Since D ₀ is on the plane created by n and t,

[0028]

(Equation 8)

Can be expressed as That is, if d ₀ is determined, D ₀ is also determined. d ₀ is the length of the vector D ₀ projected in the t direction. Thus, (A ₀ − (F ₀ + C ₀ )), that is, in FIG. 5, half of the length obtained by subtracting the length of B ₀ from the length of G projected in the t direction parallel to the vector B ₀ is d ₀ . This is because the shape of the curve R ₀ is not made wavy.
Control point P ₂ is because it is sufficient to approximate middle position of the control points P ₁ and P _3.

[0030]

(Equation 9)

Thus, the control point of the curve R ₀ is obtained.
By obtaining specified by the control point a tangent vector and the curvature vector of the end point against the last curve of the curve columns in the same manner, to specify the connection point with the curvature vector at both ends can generate G ² continuous curve. The data storage unit includes the following. The connection point information storage unit 2 is a device that stores information on connection points of a plurality of curves. The end point information storage unit 4 is a device that stores tangent vector information and curvature vector information at both end points of a plurality of curves. The curve shape storage unit 8 is a device for storing newly generated curve information.

FIG. 6 is a flowchart for explaining the curve shape generating apparatus according to the present invention. Hereinafter, the steps will be sequentially described. Step 1 : First, a plurality of continuous curves, connection points for designating the movement amount, and the movement amount are obtained. Step 2 : Next, the position information of the connection point is obtained from a plurality of curve data. Step 3 : A tangent vector and a curvature vector of the end points of the plurality of curves are obtained. Step 4 : Determine the moving amount of the connection point of the curve other than the specified connection point. Step 5 : A curve sequence is generated from information of a new connection point and a tangent vector. Step 6 : The curvature vector at the end point of the newly generated curve sequence is set to the same curvature vector as the original.

FIGS. 7A and 7B show an example of the curve shape generated in this manner. FIG. 7 (a), (b)
In FIG. 7, the diagram (a) shown on the left side of the center arrow is the original curve row, and the diagram (b) shown on the right side is after the operation is completed. A point indicated by a point P in FIG. 7A is a connection point for specifying a movement amount. As can be seen from FIG. 8B, the connection points other than the connection point for which the movement amount is specified also move little by little, and a new curve passing through the connection point is generated, so that the deformation over the deformation range can be performed. It can be carried out.
At this time, the tangent vector and the curvature vector at the end of the deformation do not change.

FIG. 8 is a block diagram for explaining an embodiment (claim 2) of a curved surface shape generating apparatus according to the present invention. In FIG. 8, reference numeral 11 denotes a reference point information acquisition unit, and 12 denotes a reference point information storage unit. , 13 is a curve line information acquisition unit, 14 is a curve line information storage unit, 15 is a reference point movement amount determination unit, 16 is a reference point movement amount storage unit, 17 is a curve line information generation unit, and 18 is a curve line shape storage unit. , 19 is a curvature vector setting unit, and 20 is a curved surface information generation unit. The embodiment according to claim 2 obtains a curved surface after shape deformation by inputting an intersection of a plurality of curved surfaces formed by a curved mesh and a curved mesh designating a moving amount and the moving amount thereof. Become.

The reference point information acquiring unit 11 attaches Id to all the intersections of the curved mesh. Hereinafter, this intersection is referred to as a reference point. The Id of the reference point and its position are combined and stored in the reference point information storage unit 12. The curve sequence information acquiring unit 13 smoothly connects inwardly from the connection point at the end of the range in order to smoothly connect the sequence of smoothly connected curves among the curves within the range even after deformation. Examine the sequence of curves that
It is stored in the curve row information storage unit 14 as a row of d. At this time, the tangent vector and the curvature vector at both ends of the curve row are also stored in the curve row information storage unit 14. The reference point movement amount determination unit 15 performs the operation of the connection point movement amount determination unit 5 in claim 1 on each curve sequence of the curve sequence information obtained by the curve sequence information acquisition unit 13, and determines the reference point. It is stored in the reference point movement amount storage unit 16 together with Id. Since the reference point belongs to two vertical and horizontal curve rows, the movement amount is an arithmetic average of the movement amounts obtained from both curve rows.

The curve sequence information generation unit 17 extracts the position of Id in the curve sequence information obtained by the curve sequence information acquisition unit 13 from the information on the position of the reference point obtained by the reference point information acquisition unit 11, Point sequence information for generating a new curve shape is generated by adding the movement amount obtained by the reference point movement amount determination unit 15 to this. New curve data is generated based on this point sequence, and stored in the curve line shape storage unit 18. The curvature vector setting unit 19 performs the operation of the curvature vector setting unit 7 in claim 1 on the end point of the curve shape obtained by the curve sequence information generation unit 17. The curved surface information generation unit 20 generates a curve mesh for interpolating a new curved surface from the information of the curve sequence stored in the curve sequence shape storage unit 18.

The data storage section is as follows. The reference point information storage unit 12 is a device that stores information on the position of the intersection of the curved meshes and the Id attached to the reference point. The curve sequence information storage unit 14 is a device that stores Id of an end point of a curve connected smoothly in a deformation range as curve sequence information and stores the curve sequence information. The tangent vector and the curvature vector at the end point of the curve sequence are also stored here. Reference point movement amount storage unit 16
Is a device for storing the Id of the reference point of the curved mesh and the movement amount thereof. The curve sequence shape storage unit 18 is a device that stores newly generated curve sequence information.

FIG. 9 is a flowchart for explaining a curved surface shape generating apparatus according to the present invention. Hereinafter, the steps will be sequentially described. Step 1 : First, a curve mesh, a reference point for designating a movement amount, and a movement amount of the reference point are obtained. step2 : Next, Id is applied to all the reference points of the curve mesh
Attached. step3 : A combination of the Id of the reference point and the position information of the reference point. Step 4 : Obtain a smoothly connected curve sequence as a sequence of Id at the reference point. Step 5 : Obtain the tangent vector and the curvature vector of the end points of the smoothly connected curve train. Step 6 : Determine the amount of movement of the reference point. Step 7 : Generate a plurality of curve trains from the new reference point information and the tangent vector. Step 8 : The curvature vector at the end point of the newly generated curve sequence is set to the same curvature vector as the original.

FIGS. 10 (a) and 10 (b) show actual examples of the curved surface shape generated in this manner. FIG. 10 (a),
In (b), FIG. (A) shows the original curve mesh, and the bold line shows the ridge line sequence specifying the deformation range. The center point P of this curved mesh was taken as a reference point for designating the movement amount. The amount of movement is upward. The diagram after the operation is completed is shown in FIG. In this case as well, it can be seen that points other than the reference point P for which the movement amount is specified also move, and that the entire deformation range is largely changed.

[0040]

As apparent from the above description, the present invention has the following effects. (1) In the curve shape generating device according to the first aspect, in order to recreate a new curve from the information of the connection points within the designated range, a series of smoothly connected curve shapes are collectively deformed by designating an arbitrary range. Now you can. Even after the deformation, the curvature vector does not change at the boundary of the specified range. (2) In the curved surface shape generating device according to the second aspect, in order to recreate the curve of the curved mesh itself based on the intersection of the curved mesh, a range is designated even for a plurality of curved surfaces formed by the curved mesh. It is now possible to perform a deformation operation within the range as if it were a single surface.

[Brief description of the drawings]

FIG. 1 is a configuration diagram for explaining an embodiment of a curve shape generation device according to the present invention.

FIG. 2 is a diagram showing a movement amount of a connection point.

FIG. 3 is a diagram showing two curves at the end of a curve row.

FIG. 4 is a diagram showing control points of two curves and a vector between the control points.

FIG. 5 is a diagram illustrating determination of a length in a vector tangent direction between control points.

FIG. 6 is a flowchart illustrating a curve shape generation device according to the present invention.

FIG. 7 is a diagram illustrating an example of generating a curved shape;

FIG. 8 is a configuration diagram for explaining an embodiment of a curved surface shape generating device according to the present invention.

FIG. 9 is a flowchart for explaining a curved surface shape generating apparatus according to the present invention.

FIG. 10 is a diagram showing an example of generating a curved surface shape.

[Explanation of symbols]

DESCRIPTION OF SYMBOLS 1 ... Connection point information acquisition part, 2 ... Connection point information storage part, 3 ... Endpoint information generation part, 4 ... Endpoint information storage part, 5 ... Connection point movement amount determination part, 6 ... Curve information generation part, 7 ... Curvature vector Setting unit, 8 ... curve shape storage unit.

────────────────────────────────────────────────── ─── Continuation of the front page (56) References JP-A-1-277969 (JP, A) Information Processing Society of Japan 27th Annual Conference Proceedings, pp. 1529-1530 Rei Hamakawa et al. Proceedings of the 28th Annual Conference of the IPSJ pp. 1537-1538 Rei Hamakawa et al. "Surface processing method in 3D shape processing system" (58) Fields investigated (Int. Cl. ⁷ , DB name) G06F 17/50 626 G06F 17/50 622 G06T 17/40

Claims (2)

(57) [Claims] 1. A connecting point information obtaining means for obtaining a position of a connecting point of a series of smoothly connected curves, and a connecting point information storing means for storing information of connecting points obtained by the connecting point information obtaining means. End point information generating means for obtaining information on the end points at both end points of a plurality of continuous curves; end point information storing means for storing the end point information obtained by the end point information generating means; Connection point movement amount determining means for determining the movement amount of the connection points other than the connection point for which the movement amount is designated, among the connection points, information on the connection points obtained by the connection point movement amount determination means, Curve information generating means for generating information on a curve shape after shape deformation from a tangent vector in the information on the end point obtained by the end point information generating means, and a curvature vector at an end point of the curve shape obtained by the curve information generating means By the end point information generating means Curve shape generation characterized by comprising a curvature vector setting means for changing to a curvature vector of the obtained original curve, and a curve shape storage means for storing the changed curve shape obtained by the curvature vector setting means. Equipment . 2. A reference point information obtaining means for obtaining information of a reference point which is an intersection of a curved mesh, a reference point information storage means for storing information of a reference point obtained from the reference point information obtaining means, a deformation range Curve line information obtaining means for obtaining information of a curve line smoothly connected inward from the connection point at the end of the curve line, and curve line information for storing information at both end points of the curve line obtained by the curve line information obtaining means Storage means; reference point movement amount determination means for determining the movement amount of the reference point for each curve row of the curve row information obtained by the curve row information acquisition means;
A reference point moving amount storing means for storing the moving amount of the reference point determined by the reference point moving amount determining means; and a position of the reference point in the information of the curve sequence obtained by the curve sequence information obtaining means, Curve sequence information generating means for extracting from the information on the position of the reference point obtained by the information obtaining means and generating a new curve sequence information by adding the amount of movement obtained by the reference point moving amount determining means to this, A curvature vector setting means for changing a curvature vector at an end point of the shape of the curve sequence obtained by the curve sequence information generation means into a curvature vector of a curve obtained by the curve sequence information obtaining means; Curve line shape storing means for storing the changed shape of the curve sequence, and generating a curve mesh for interpolating a new curved surface from the information of the curve sequence stored in the curve line shape storing means Curved shape generation apparatus characterized by comprising a curved surface information generating unit that.