JP2003186925A - Three-dimensional shape processor and curved surface interpolation program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a curved surface interpolation method capable of generating a curved surface which can be beautifully interpolated into an N-sided polygon area by generating one B-spline curved surface covering the N-sided polygon area. <P>SOLUTION: In this curved surface interpolation program for interpolating a curved surface into an N-sided polygon area, four boundary planes indicating the range of the area of a curved surface to be interpolated are decided (S1), and segments going from a plurality of points on each boundary curve of the N-sided polygon area down to the surrounding boundary planes are generated (S2), and the boundary planes to which the segments are belonging are decided (S3), and the boundary curve of the curved surface to be interpolated into the N-sided polygon area is generated from the intersection points of those segments and the boundary planes (S4), and the curved surface to be interpolated is generated from the boundary curve and each point on each segment (S5). <P>COPYRIGHT: (C)2003,JPO

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a technique for interpolating a curved surface into an N-gonal region, which is implemented in a dedicated three-dimensional shape processing device, an information processing device such as a personal computer, and particularly, to clean the N-gonal region neatly. The present invention relates to a curved surface interpolation technique capable of generating a curved surface that can be interpolated.

[0002]

2. Description of the Related Art In a three-dimensional shape processing device such as a CAD / CAM device using a graphics display device and a computer, a three-dimensional three-dimensional shape is conventionally generated or the generated three-dimensional three-dimensional shape is deformed. , Other various processing is performed. The three-dimensional solid shape refers to, for example, a shape generated as solid model data in the boundary expression format, and the solid model in the boundary expression format is
It defines a closed area in a three-dimensional space by elements such as ridges, vertices, and faces, and expresses a solid body filled with contents. The present invention relates to curved surface generation, which is one of the three-dimensional shape processing conventionally performed in such a three-dimensional shape processing device, and more specifically, a plurality of B-
The present invention relates to an interpolation curved surface generation method for smoothly interpolating an interpolation curved surface generated by a curve mesh configured using spline curves so that there is no overlap or gap between curved surfaces. In addition,
As a conventional technique in such a field, for example, Grego
There is a free-form surface interpolation method using a ry patch or the like. In this conventional technique, a cross-boundary derivative is designated, the shape of a curved surface is deformed using this, and the curved surfaces are connected to each other or the curved surface is interpolated. A method of generating a smooth curved surface shape using a rational boundary Gregory patch is also known. For example, the free-form surface generation method disclosed in Japanese Unexamined Patent Publication No. 7-28217 is one of the conventional techniques described above, and when generating two curved surfaces having a rational B-spline curve as a shared boundary, the boundary is generated. The continuity at the boundary is determined from the curve and the curve connected to the boundary curve, the connection condition at the boundary is determined from the continuity, and the internal control points of the surface are generated from the calculated connection condition, so that two adjacent free sheets are free. Connect curved shapes smoothly. Further, in the method of generating a curved surface using a curved mesh, for example, “Hiroshi Toritani, Hiroaki Chiyokura, Basics and Applications of 3D CAD, 199”.
1. According to the described technique, an N-gonal region is interpolated by N quadrilateral faces.

[0003]

However, in the above-mentioned free-form surface generating method disclosed in Japanese Patent Laid-Open No. 7-28217, a curved surface that cannot be used as an interpolating curved surface is generated in order to realize a smooth connection. However, in the method of generating a curved surface using the curved mesh described above, as shown in FIG. 14, each of a plurality of boundary curves (curves representing boundaries of the curved surface) of the N-gonal area A is formed. If the lengths of the two are extremely different, the curve C (called an internal curve) other than the boundary curve of the N-shaped area of the interpolation surface is likely to swell,
The interpolated curved surfaces may undulate or the curved surfaces may interfere with each other. There is also a problem that an interpolated surface cannot be generated when there are no continuous vertices forming the N-gonal region or when there is only one. For example, a curved surface cannot be interpolated in a circular area. An object of the present invention is to solve such a problem of the related art, and specifically, one sheet of B- that covers an N-gonal region is used.
An object of the present invention is to provide a curved surface interpolation method that can generate a curved surface that can be neatly interpolated in an N-gonal region by generating a spline curved surface.

[0004]

In order to solve the above-mentioned problems, according to the invention of claim 1, in a three-dimensional shape processing apparatus capable of interpolating a curved surface in an N-gonal region, Plane determining means for determining four boundary planes representing the range of the area; line segment generating means for generating a line segment drawn from a plurality of points on each boundary curve of the N-gonal area to the surrounding boundary planes; Boundary curve generating means for determining the boundary plane to which the line segment belongs, and generating a boundary curve of a curved surface to be interpolated in the N-gonal region from the intersection of the line segment and the boundary plane, and the boundary curve and each of the line segments. And an interpolated curved surface generating means for generating a curved surface to be interpolated from the respective points. In the invention according to claim 2, in a curved surface interpolation program for interpolating a curved surface into an N polygonal area, four boundary planes representing the range of the curved surface area to be interpolated are determined, and the N
A line segment is drawn from a plurality of points on each boundary curve of the polygonal region to the surrounding boundary plane, the boundary plane to which the line segment belongs is determined, and an N-sided polygon is formed from the intersection of the line segment and the boundary plane. It is characterized in that a boundary curve of a curved surface to be interpolated in a region is generated, and a curved surface to be interpolated is generated from the boundary curve and each point on each line segment. Further, in the invention according to claim 3, in the invention according to claim 2, the side forming the N-gonal region is arranged on a curved surface generated within a permissible error range specified by the user. Characterize. The invention according to claim 4 is characterized in that, in the invention according to claim 2, the range of the region determined by the four boundary planes is made wider than the N-gonal region. The invention according to claim 5 is characterized in that, in the invention according to claim 2, the number of sides forming the N-gonal region is not limited. Further, the invention according to claim 6 is characterized in that, in the invention according to claim 2, the number of vertices constituting the N-gonal region is not limited. Further, the invention according to claim 7 is characterized in that the program according to any one of claims 2 to 6 is stored in a storage medium storing the program.

[0005]

BEST MODE FOR CARRYING OUT THE INVENTION Embodiments of the present invention will be described in detail below with reference to the drawings. FIG. 1 is a configuration block diagram of a computer system showing an example of a system in which the present invention is implemented. As illustrated, the computer system of this embodiment includes an input unit 1, an output unit 2, a CPU 3, a memory (for example, RAM) 4, a storage unit (for example, a hard disk device) 5, a medium driving unit 6, and the like. In the above description, the input unit 1 has an input device such as a mouse or a keyboard that receives the N-shaped region displayed on the display device that constitutes the output unit 2. The N-gonal region is composed of geometrical shape data such as points and curves forming these shapes and phase data showing a correlation between the geometrical shape data. The output unit 2 is an output unit that reads out and outputs the shape data stored in the storage unit 5, and has a display device such as a display and an output device such as a printer. The storage unit 5 stores a plurality of shape data indicating the shape of the design object, a program, and the like, and the medium driving unit 6 drives a removable storage medium such as a CD-ROM or a floppy (registered trademark) disk. , The program according to the present invention is read from the recording medium. In this embodiment, the plane determining means, the line segment generating means, the boundary curve generating means, and the interpolated curved surface generating means according to claim 1 are realized by the memory 4 storing the program, the CPU 3 operating according to the program, and the like. To be done. With such a configuration, in this embodiment, according to the program, the CPU 3 first displays the target three-dimensional shape model on the display device, prompts the user to specify the N-gonal region, and sets the specified N-gonal region. The related data is acquired and the data is stored in the storage unit 5. For example, in FIG.
, The triangular region A generated by rounding the target ridgeline with different rounding radii.
Is an N-gonal region (the curved surface generated by the rounding process is not always in smooth contact with the original surface subjected to the process). The user designates such an N-shaped region to be operated and one side with a mouse or the like. Figure 2
When the N-shaped polygonal area and the one side are selected by clicking with a mouse or the like, one boundary curve of the finally generated B-spline curved surface becomes substantially parallel to the designated side.

FIG. 3 shows an operation flow of this embodiment.
The operation of this embodiment will be described below with reference to FIG. 3 using the example shown in FIG. In this embodiment, first, 4 representing the range of the interpolated curved surface area corresponding to the designated N polygonal area.
Two boundary planes are determined (S1). It determines the rough size of the curved surface to be generated. Therefore, first, the center of the boundary curve string of the N-gonal region and the average normal vector are obtained. The center of the boundary curve sequence is the coordinate value of the control point of the curve (the sequence of points between the two end points of the free curve, and the shape of the curve can be represented by these control points and two end points). Is the average value of. Also, the average normal vector is a smooth curved surface with a boundary curve as the boundary,
It is an integral of the unit vector of the surface, and the vector obtained as a result of this area depends only on the boundary curve. Such an average normal vector is calculated by a known method using a boundary curve. Then, one plane is generated using the center of the boundary curve sequence and the average normal vector. The origin of the plane and the normal vector are the center of the boundary curve sequence and the average normal vector, respectively. Further, the boundary curve sequence is projected onto the plane to generate a projected boundary curve sequence, and a coordinate system is constructed on the plane. The direction of the Z axis of the coordinate system matches the direction of the plane normal vector. The direction of the X-axis is the direction of the vector from the center (the origin) to the center position of the projective curve of one side of the N-gonal region initially designated by the user. The direction of the Y axis is the direction of the outer product vector of the Z axis and the X axis. In this way, a bounding box (a bounding box circumscribing the projection curve string) of the projection curve string in such a coordinate system is obtained. The bounding box is a quadrangle parallel to the X and Y axes. In addition, the bounding box should be made slightly larger (for example, the length of one side should be increased by about 5%). This is because the size of the bounding box affects the size of the curved surface that is finally generated, and by making it slightly larger, it becomes easier to cleanly insert the curved surface into the N-gonal region with desired accuracy. Then, four boundary planes parallel to the Z axis are generated from the bounding box. This is to use these four boundary planes later when defining the boundary of the B-spline curved surface to be interpolated. In Figure 4,
The bounding box B as viewed from the Z axis is shown.

Next, a line segment based on the boundary curve of the N-gonal area is generated (S2). Therefore, first, a plurality of sampling points are generated on each boundary curve. The number of sampling points is, for example, twice the order of the boundary curve. Then, the vector in the direction crossing the boundary curve at the sampling point is determined. For example, one of the following two methods can be used for the determination. One is a method of utilizing the boundary derivative of the adjacent surface in the boundary curve of the N-gonal region, which makes the connection between the interpolation surface and the adjacent surface smoother. The other one is a method of using the tangent vector of the boundary curve of the N-gonal region, and uses a vector obtained by the outer product of the normal vector of the sampling points of the N-gonal region and the tangent vector of the boundary curve. At the common point of the two boundary curves, the sum vector of the unit tangent vectors for each boundary curve at the common point is used. Therefore, the vector can be specified even if the two boundary curves are smoothly connected. Then, the intersection point of the determined vector and the four boundary planes is obtained, and the determined line segment is obtained at the closest intersection point and the point on the boundary curve. The boundary plane having the closest intersection is the boundary plane to which the line segment belongs. These line segments will be used later when generating the point cloud. FIG. 5 shows a group of generated line segments.

In the above, when the line segments of all sampling points on the boundary curve do not belong to the same boundary plane,
It is necessary to divide the line segment group and the intersection point group into respective boundary planes to which they belong, and further to determine a common line segment that is a line segment of either of the two boundary planes. For example, in the example shown in FIG. 11, it is necessary to divide the ridge line (boundary curve). Therefore, next, the boundary curve is divided and the boundary plane to which the line segment belongs is determined as follows, and the common line segment is obtained (S3). First, a ruled curved surface is generated using the boundary curve and the line segment direction, and an intersecting line where the ruled curved surface and two boundary planes intersect is obtained. Then, the boundary curve is divided using the unidirectional parameter (u or v) at the position where the intersecting boundary plane of the ruled curved surface changes as the boundary curve dividing parameter. Further, an interference point between a straight line on which the line segment at the division point rides and an intersection line of the two boundary planes is obtained, and the line segment determined by the division point and the interference point is set as a common line segment of the two boundary planes. Note that the interference point is not limited to the intersection point, and even when two straight lines are in a twisted position, the point where the straight lines are closest to each other is calculated as the interference point. Thus, finally, the line segments of all the sampling points on one boundary curve belong to the same boundary plane. As is clear from the above description, one end point of each line segment generated in step S2 is a sampling point, and the other end point is a point on the boundary plane. Generate a curve from the end points of using the method of least squares,
The curve is used as the boundary curve of the curved surface to be interpolated (see FIG. 6).
(S4). When generating this boundary curve, the sequence of points from which the boundary curve is generated must be aligned from the starting point to the ending point of the curve to be approximated. Further, when there is no boundary curve belonging to a certain boundary plane, a straight line (approximate curve) is generated by using the end points of the boundary curves generated on the boundary planes on both sides of that plane. At that time, when the boundary curve for making the end point of the approximate curve does not exist in the adjacent planes, the approximate curve is linearly extended in the tangential direction to the adjacent boundary plane. In the above, the end points of the four boundary curves of the curved surface to be interpolated do not always coincide with each other. Therefore, next, adjustment is made so that the positions of the end points coincide with each other. Finally, a curved surface to be interpolated is generated (S
5). The curved surface is generated under the constraint conditions of the four boundary curves which become the four boundary curves of the generated curved surface.
Therefore, first, for each line segment described above, a point group composed of the other end point of the line segment and an intermediate sampling point is obtained. FIG. 7 shows a point cloud on the generated line segment. As the number of intermediate sampling points increases, the shape outside the N side (N side) region of the generated curved surface approaches the shape of the surrounding surface, but the number of control points increases and the processing speed increases. descend. Therefore, in this embodiment, the number of intermediate sampling points is set to 3. However, if each side forming the N-gonal region does not fit on the interpolation surface generated depending on the number of sampling points within the allowable error range specified by the user, the number of sampling points is set to Increase the number of control points.

Next, a Coons surface of a bilinear blend is defined from the four boundary curves. Further, the parameters of the points projected from the points on the curved surface to the boundary curve are set as the initial parameters of the points. Then, the approximated curved surface is generated as a B-spline curved surface by the least squares method with the boundary curve as the boundary. FIG. 8 shows the control points of the generated curved surface (a plurality of points expressing the curved surface, which exist substantially along the curved surface). Further, FIG. 9 shows contour lines of the curved surface finally generated. Furthermore, as an example of generating a curved surface to be interpolated,
FIG. 10 shows an example where the N-gonal region is a triangular region, FIG. 11 shows an example of a quadrilateral region, FIG. 12 shows an example of a pentagonal region, and FIG. 13 shows an example of a hexagonal region. Thus, N according to the present invention
The curved surface interpolation into the polygonal region does not limit the number of sides forming the N-gonal region and the number of vertices forming the N-gonal region. Finally, the shape data of the curved surface thus generated is written in the storage unit 5. As described above, one embodiment of the present invention has been described. However, a program programmed according to the curved surface interpolation method for the N-gonal region as described above is stored in, for example, a removable storage medium, and the storage medium has been used in the present invention. By mounting it on an information processing device such as a personal computer that could not perform curved surface interpolation into the N-gonal region, or by transferring such a program to such an information processing device via a network, Also in the information processing device, curved surface interpolation to the N-gonal region according to the present invention can be performed.

[0010]

As described above, according to the present invention,
According to the first and second aspects of the present invention, when a curved surface is interpolated in an N-gonal area, the range of the curved surface area to be interpolated is expressed.
One boundary plane is determined, a line segment drawn from a plurality of points on each boundary curve of the N-gonal region to the peripheral boundary plane is generated, a boundary plane to which the line segment belongs is determined, and the line segment and its A boundary curve of a curved surface to be interpolated in the N polygonal area is generated from the intersection with the boundary plane, and a curved surface to be interpolated from the boundary curve and each point on each of the line segments is generated. One B-spline curved surface can be generated, which allows the curved surface to be neatly interpolated into the N-gonal region. Further, in the invention according to claim 3, in the invention according to claim 2, since the sides forming the N-gonal region ride on the curved surface generated within the allowable error range specified by the user, the curved surface is the N-gonal region. It is possible to interpolate neatly with desired accuracy. Further, in the invention according to claim 4, in the invention according to claim 2, the range of the region determined by the four boundary planes is wider than the N-gonal region, so that the curved surface is neatly and accurately contained within the N-gonal region. Easy to insert. Further, in the invention according to claim 5, in the invention according to claim 2, since the number of sides forming the N polygonal region is not limited, the applicable range of the curved surface interpolation to the N polygonal region is widened. Further, in the invention according to claim 6, in the invention according to claim 2, since the number of vertices forming the N 2 polygonal region is not limited, similarly, the applicable range of the curved surface interpolation to the N 2 polygonal region is widened. . In the invention according to claim 7, the program according to any one of claims 2 to 6 is stored in, for example, a removable storage medium. The information processing apparatus according to any one of items 6 to 6, wherein the information processing apparatus is mounted on an information processing apparatus such as a personal computer that cannot perform curved surface interpolation into an N-gonal region, and the information processing apparatus also includes the information processing apparatus. The effect of the invention described in any one of 6 can be obtained.

[Brief description of drawings]

FIG. 1 is a configuration block diagram of a computer system showing an example of a system in which the present invention is implemented.

FIG. 2 is an explanatory diagram showing an N-shaped region according to an embodiment of the present invention.

FIG. 3 is a flowchart of a curved surface interpolation program showing an embodiment of the present invention.

FIG. 4 is an explanatory diagram of a curved surface interpolation method showing an embodiment of the present invention.

FIG. 5 is another explanatory diagram of the curved surface interpolation method showing the embodiment of the present invention.

FIG. 6 is another explanatory diagram of the curved surface interpolation method showing the embodiment of the present invention.

FIG. 7 is another explanatory diagram of the curved surface interpolation method showing the embodiment of the present invention.

FIG. 8 is another explanatory diagram of the curved surface interpolation method showing the embodiment of the present invention.

FIG. 9 is another explanatory diagram of the curved surface interpolation method showing the embodiment of the present invention.

FIG. 10 is another explanatory diagram of the curved surface interpolation method showing the embodiment of the present invention.

FIG. 11 is another explanatory diagram of the curved surface interpolation method showing the embodiment of the present invention.

FIG. 12 is another explanatory diagram of the curved surface interpolation method showing the embodiment of the present invention.

FIG. 13 is another explanatory diagram of the curved surface interpolation method according to the embodiment of the present invention.

FIG. 14 is an explanatory diagram of a curved surface interpolation method according to the related art and the present invention.

[Explanation of symbols]

1 Input section 2 Output section 3 CPU 4 memory 5 memory 6 Medium drive

Claims (7)

[Claims] 1. A three-dimensional shape processing apparatus capable of interpolating a curved surface into an N-gonal area, wherein: plane determining means for determining four boundary planes representing a range of the area of the curved surface to be interpolated; and the N-gonal area. Line segment generating means for generating a line segment drawn from a plurality of points on each boundary curve to the surrounding boundary plane, and determining the boundary plane to which the line segment belongs, and the intersection of the line segment and the boundary plane Boundary curve generating means for generating a boundary curve of a curved surface to be interpolated from N to N polygonal area, and interpolation curved surface generating means for generating a curved surface to be interpolated from the boundary curve and each point on each line segment. A three-dimensional shape processing device characterized by: 2. In a curved surface interpolation program for interpolating a curved surface in an N-gonal area, the range of the curved surface area to be interpolated is expressed as 4
Determine one boundary plane, generate a line segment drawn from a plurality of points on each boundary curve of the N-gonal region to the peripheral boundary plane, and determine the boundary plane to which the line segment belongs,
A curved surface characterized by generating a boundary curve of a curved surface to be interpolated in an N-gonal region from an intersection of a line segment and its boundary plane, and generating a curved surface to be interpolated from the boundary curve and each point on each line segment. Interpolation program. 3. The curved surface interpolation program according to claim 2, wherein edges forming the N-gonal region are on a curved surface generated within a permissible error range designated by the user. Insertion program. 4. The curved surface interpolation program according to claim 2, wherein a range of an area determined by four boundary planes is N.
A curved surface interpolation program that is wider than a rectangular area. 5. The curved surface interpolation program according to claim 2, wherein the number of sides forming the N-gonal region is not limited. 6. The curved surface interpolation program according to claim 2, wherein there is no limitation on the number of vertices forming the N polygonal area. 7. A storage medium storing a program, wherein the program according to any one of claims 2 to 6 is stored.