JP4163446B2 - Curved surface interpolation method, curved surface interpolation program and storage medium - Google Patents

Description

[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a technique for interpolating a curved surface in an N-gonal area implemented in an information processing apparatus such as a dedicated three-dimensional shape processing apparatus or a personal computer, and in particular, interpolating so that there is no overlap or gap in the N-gonal area. The present invention relates to a curved surface interpolation technique capable of generating a possible curved surface.
[0002]
[Prior art]
Conventionally, in a 3D shape processing apparatus such as a CAD / CAM device using a graphics display device and a computer, a 3D solid shape is generated, the generated 3D solid shape is deformed, and various other Processing is in progress. The three-dimensional solid shape refers to, for example, a shape generated as solid model data in a boundary representation format. The solid model in the boundary representation format is defined in a three-dimensional space by elements such as edges, vertices, and faces. It defines a closed area and expresses a solid solid.
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 apparatus, and more specifically, is configured using a plurality of B-spline curves. The present invention relates to an interpolation curved surface generation method for smoothly interpolating an interpolation curved surface generated by a curved mesh so that there is no overlap or gap between curved surfaces.
[0003]
As a conventional technique in such a field, there is a free-form surface interpolation method using, for example, a Gregory patch. In this prior art, a cross-boundary derivative is specified, and the shape of the curved surface is deformed by using this, and the curved surfaces are connected to each other or the curved surface is interpolated. In addition, a method of generating a smooth curved surface shape using a rational boundary Gregory patch is also known.
For example, the free curved surface generation method disclosed in Japanese Patent Laid-Open No. 7-282117 is one of the prior arts as described above, and when generating two curved surfaces having a rational B-spline curve as a common boundary, By determining the continuity at the boundary from the boundary curve and the curve connected to the boundary curve, obtaining the connection condition at the boundary from the continuity, and generating the internal control points of the surface from the obtained connection condition, two adjacent sheets This is a method of smoothly connecting the free-form surface shapes.
In the method of generating a curved surface using a curved mesh, for example, according to the technique described in “Hiroshi Toritani, Hiroaki Chiyokura, Basics and Applications of 3D CAD, 1991.”, N square regions are divided into N quadrilaterals. This is a method of interpolating with a surface.
[0004]
[Problems to be solved by the invention]
However, the free curved surface generation method disclosed in Japanese Patent Laid-Open No. 7-282117 has a problem that a curved surface that cannot be used as an interpolated curved surface is generated in order to realize a smooth connection. In the method of generating a curved surface using the curved mesh described above, as shown in FIG. 15, when the lengths of a plurality of boundary curves (curves representing the boundary of the curved surface) of the N-gonal region A are extremely different, Since the curve C (referred to as an internal curve) other than the boundary curve of the N-shaped area of the interpolated surface tends to swell, the interpolated curved surfaces may swell or the curved surfaces may interfere with each other.
Further, when there are no continuous vertices constituting the N-gonal area or when there is only one vertex, for example, there is a problem that a curved surface cannot be interpolated in a circular area.
An object of the present invention is to solve such a problem of the prior art. Specifically, by generating a single B-spline curved surface that covers the N-gonal region, it is possible to clean the N-gonal region. Another object of the present invention is to provide a curved surface interpolation method capable of generating a curved surface that can be interpolated into a curved surface.
[0005]
[Means for Solving the Problems]
In order to solve the above problems, in the first aspect of the present invention, represented in the curved surface in the interpolation method interpolating a curved surface N rectangular region, the plane determining means, the range of the area on the inner挿曲surface interpolating 4 A step of determining two boundary planes and a direction determined by the line generation means using a boundary derivative of an adjacent surface in the boundary curve of the N-gonal region from a plurality of points on each boundary curve of the N-gonal region A step of generating a line segment down to the surrounding boundary plane, and a boundary curve generating means determines the boundary plane to which each line segment belongs , and the boundary of the interpolation curved surface from the intersection of each line segment and each boundary plane generating a curve, the inner挿曲surface generating means, characterized in that consists of the steps of generating a curved surface interpolating the color and each point on the line segment and the boundary curve.
Further, in the invention described in claim 2, in curved surface in interpolation method interpolating curved surfaces in N rectangular region, the plane determining means determines the four boundary plane representing the range of the area on the inner挿曲surface interpolating step And a line segment generating unit calculates a cross product of a normal vector at an arbitrary point in the N-gonal region and a tangent vector of the boundary curve in the N-gonal region from a plurality of points on each boundary curve of the N-gonal region. Generating a line segment drawn down to the surrounding boundary plane in the direction of the vector obtained by the step, and a boundary curve generating means determines the boundary plane belonging to each line segment, and an intersection of each line segment and each boundary plane generating a boundary curve of the inner挿曲plane from the inner挿曲plane generation unit, and generating a curved surface interpolating the color and each point on the line segment and the boundary curve, that consists of Features.
The invention according to claim 3 is a program feature for causing a computer to execute the curved surface interpolation method according to claim 1 or claim 2 .
The invention according to claim 4 is characterized by a computer-readable storage medium storing the program according to claim 3.
[0006]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, embodiments of the present invention will be described in detail 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 accepts an N-gon area displayed on the display device constituting the output unit 2. Note that the N-gon area includes geometric data such as points and curves constituting these shapes, and phase data indicating the correlation between the geometric data.
The output unit 2 is an output unit that reads out and outputs the shape data stored in the storage unit 5 and includes 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 and programs indicating the shape of the design object, and the medium drive unit 6 drives a removable storage medium such as a CD-ROM or a flexible disk, for example. The related program is read from the recording medium. In this embodiment, the plane determining means, line segment generating means, boundary curve generating means, and interpolated curved surface generating means described in claim 1 are realized by the memory 4 storing the program and the CPU 3 operating according to the program. Is done.
[0007]
With such a configuration, in this embodiment, according to the program, first, the CPU 3 displays the target three-dimensional shape model on the display device, causes the user to designate the N-gonal area, and sets the designated N-gonal area to the designated N-gonal area. The related data is acquired, and the data is stored in the storage unit 5. For example, in FIG. 2, the triangular area A generated by rounding the target ridgeline with different rounding radii is an N-gonal area (the curved surface generated by the rounding process has been subjected to the processing). It may not be in smooth contact with the original surface). The user designates such an N-shaped area and one side to be operated with a mouse or the like. When the N-gonal area and one side in FIG. 2 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.
[0008]
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, four boundary planes representing the range of the interpolated curved surface area corresponding to the designated N-gonal area are determined (S1). Determine the approximate size of the surface to be generated. Therefore, first, the center of the boundary curve row of the N-gonal region and the average normal vector are obtained. Note that the center of the boundary curve row is the coordinate value of the curve control point (a sequence of points between the two end points of the free curve, and the shape of the curve can be expressed by the plurality of control points and the two end points). Is the average value. The average normal vector is obtained by integrating the unit vector of a surface on a smooth arbitrary curved surface bounded by the boundary curve, 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.
[0009]
Subsequently, one plane is generated using the center of the boundary curve row and the average normal vector. The origin and normal vector of the plane are the center of the boundary curve sequence and the average normal vector, respectively. Further, a 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 coincides with the direction of the normal vector of the plane. The direction of the X axis is the direction of a vector from the center (the origin) toward the center position of the projection curve on one side of the N-gonal area specified by the user first. 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 of the projection curve sequence (boundary box circumscribing the projection curve sequence) in such a coordinate system is obtained. The bounding box is a quadrilateral parallel to the X and Y axes. Note that the bounding box is slightly larger (for example, the length of one side is increased by about 5%). This is because the size of the bounding box affects the size of the finally generated curved surface, and by slightly increasing the size, it becomes easy to insert the curved surface neatly with a desired accuracy in the N-gonal region.
Subsequently, four boundary planes parallel to the Z axis are generated from the bounding box. This is because the four boundary planes are used later when defining the boundary of the B-spline curved surface to be interpolated. FIG. 4 shows the bounding box B when viewed from the Z-axis.
[0010]
Next, a line segment based on the boundary curve of the N-gon area is generated (S2). Therefore, first, a plurality of sampling points are generated on each boundary curve. Note that the number of sampling points is, for example, twice the order of the boundary curve. Then, a vector in a direction crossing the boundary curve at the sampling point is determined. There are a plurality of methods for determination, but two examples are shown below.
One is a method that uses the boundary derivative of the adjacent surface in the boundary curve of the N-gonal region. According to this method, the connection between the generated interpolation surface and the adjacent surface becomes smoother. FIG. 5 shows the generated line segment group. However, in this method, when the N-gonal region is the upper surface of the cylinder shown in FIG. 6, all the partial differential vectors in the direction crossing the boundary curve with the adjacent surface of the N-gonal region are directed to the central axis direction of the cylinder. Therefore, the intersection with the plane cannot be obtained.
The other is a method 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 at the sampling point of the N-gonal region and the tangent vector of the boundary curve. Note that, at the common point of two boundary curves, the sum vector of unit tangent vectors for each boundary curve at the common point is used. Therefore, as shown in FIG. 6, even if two boundary curves are smoothly connected, the vector can be specified. The line segment shown in FIG. 6 is a line segment obtained by such a method. In addition, the variation of the curved surface shape to produce | generate can be increased by changing how to determine the vector of the direction which crosses the boundary curve in a sampling point. Subsequently, an intersection between the determined vector and the four boundary planes is obtained, and a line segment determined by the closest intersection and a point on the boundary curve is obtained. The boundary plane having the closest intersection is the boundary plane to which the line segment belongs. These line segments are used later when generating point clouds.
[0011]
In the above, when the line segments of all sampling points on the boundary curve do not belong to the same boundary plane, the line segment group and the intersection group are divided into the boundary planes to which they belong, and further, which line segment of the two boundary planes It is necessary to determine the common line segment that also becomes. For example, in the example as shown in FIG. 11, it is necessary to divide the ridgeline (boundary curve).
Therefore, next, as described below, the boundary curve is divided to determine the boundary plane to which the line segment belongs, and the common line segment is obtained (S3).
First, a ruled surface is generated using the boundary curve and the line segment direction, and an intersection line where the ruled 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 intersecting line on the ruled curved surface changes as a 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 between the two boundary planes is obtained, and a 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. In this way, finally, the line segments of all sampling points on one boundary curve belong to the same boundary plane.
[0012]
As apparent 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. A curve is generated from the end points using the least square method, and the curve is set as a boundary curve of the curved surface to be interpolated (see FIG. 7) (S4). When generating this boundary curve, the point sequence from which the boundary curve is generated must be aligned from the start point to the end point of the curve to be approximated. When there is no boundary curve belonging to a certain boundary plane, a straight line (approximate curve) is generated using the end points of the boundary curves generated on the boundary planes on both sides of the plane. At this time, if the boundary curve for making the end point of the approximate curve does not exist in the adjacent plane, the approximate curve is further extended to the adjacent boundary plane in a tangential direction in a straight line shape.
In the above, the end points of the four boundary curves of the curved surface to be interpolated do not always match. Then, it adjusts so that the position of end points may correspond next.
[0013]
Finally, a curved surface to be interpolated is generated (S5). A curved surface is generated using the four boundary curves, which are the four boundary curves of the generated curved surface, as constraint conditions. 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. 8 shows a point group on the generated line segment. As the number of intermediate sampling points increases, the number of control points increases as the shape outside the N-side (N side) area of the curved surface approaches the shape of the surrounding surface, and the processing speed increases. descend. Therefore, in this embodiment, the number of intermediate sampling points is set to 3. However, if each side constituting the N-gonal area does not ride within the tolerance range specified by the user on the interpolation surface generated depending on the number of sampling points, the number of sampling points is Increase the number of control points.
[0014]
Next, a Coons surface of 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, an approximate curved surface is generated as a B-spline curved surface by the least square method with the boundary curve as a boundary. FIG. 9 shows the generated curved surface control points (a plurality of points representing the curved surface, which exist substantially along the curved surface). FIG. 10 shows contour lines of a curved surface that is finally generated. Further, as an example of generating a curved surface to be interpolated, the N-gonal region is a triangular region as shown in FIG. 11, a quadrangular region as an example in FIG. 12, a pentagonal region as an example in FIG. An example is shown in FIG. As described above, the curved surface interpolation to the N-gonal area according to the present invention has no limitation on the number of sides constituting the N-gonal area, and no limitation on the number of vertices constituting the N-gonal area.
Finally, the curved surface shape data generated in this way is written into the storage unit 5.
[0015]
Although one embodiment of the present invention has been described above, a program programmed in accordance with the curved surface interpolation method into the N-gonal area as described above is stored in, for example, a removable storage medium, and the storage medium is used in the present invention so far. By mounting it on an information processing device such as a personal computer that could not perform curved surface interpolation to the N-gonal region, or by transferring such a program to such an information processing device via a network, Also in the information processing apparatus, curved surface interpolation into an N-gonal area according to the present invention can be performed.
[0016]
【The invention's effect】
As described above, according to the present invention, according to the first aspect of the present invention, it is possible to generate a single B-spline curved surface that covers an N-gonal region, thereby converting the curved surface into an N-gonal region. Can be interpolated neatly.
In the invention according to claim 2, variations of the curved surface shape to be generated can be increased, and therefore a more appropriate interpolated curved surface can be obtained.
In the invention according to claim 3, since the program programmed according to the curved surface interpolation method according to claim 1 or claim 2 can be executed on the information processing apparatus, The effect of the invention of claim 2 can be obtained.
In the invention according to claim 4, since the program according to claim 3 can be stored in a removable storage medium, the storage medium according to the invention according to claim 1 or claim 2 can be used. By mounting the information processing apparatus such as a personal computer that cannot perform curved surface interpolation on the square region, the effect of the invention according to claim 1 or 2 can be obtained in the information processing apparatus.
[Brief description of 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.
FIG. 2 is an explanatory diagram showing an N-gonal 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 according to an embodiment of the present invention.
FIG. 5 is another explanatory diagram of a curved surface interpolation method showing an embodiment of the present invention.
FIG. 6 is another explanatory diagram of a curved surface interpolation method showing an embodiment of the present invention.
FIG. 7 is another explanatory diagram of a curved surface interpolation method showing an embodiment of the present invention.
FIG. 8 is another explanatory diagram of a curved surface interpolation method showing an embodiment of the present invention.
FIG. 9 is another explanatory diagram of a curved surface interpolation method showing an embodiment of the present invention.
FIG. 10 is another explanatory diagram of a curved surface interpolation method showing an embodiment of the present invention.
FIG. 11 is another explanatory diagram of a curved surface interpolation method showing an embodiment of the present invention.
FIG. 12 is another explanatory diagram of a curved surface interpolation method showing an embodiment of the present invention.
FIG. 13 is another explanatory diagram of a curved surface interpolation method showing an embodiment of the present invention.
FIG. 14 is another explanatory diagram of a curved surface interpolation method showing an embodiment of the present invention.
FIG. 15 is an explanatory diagram of a curved surface interpolation method according to the prior art and the present invention.
[Explanation of symbols]
1 input unit, 2 output unit, 3 CPU, 4 memory, 5 storage unit, 6 medium drive unit

Claims (4)

In a curved surface interpolation method for interpolating a curved surface in an N-gonal region,
Plane determining means, determining the four boundary plane representing the range of the area on the inner挿曲surface interpolating,
The line segment generation means descends from a plurality of points on each boundary curve of the N-gonal region to the surrounding boundary plane in a direction determined using boundary derivatives of adjacent surfaces in the boundary curve of the N-gonal region. generating a line segment,
A boundary curve generating means determining the boundary plane belonging to each line segment, and generating a boundary curve of the interpolated curved surface from the intersection of each line segment and each boundary plane;
An interpolation curved surface generating means generating a curved surface to be interpolated from the boundary curve and each point on each line segment ;
A curved surface interpolation method characterized by comprising: In a curved surface interpolation method for interpolating a curved surface in an N-gonal region,
Plane determining means, determining the four boundary plane representing the range of the area on the inner挿曲surface interpolating,
The line segment generating means is obtained from a plurality of points on each boundary curve of the N-gonal region by an outer product of a normal vector at an arbitrary point in the N-gonal region and a tangent vector of the boundary curve of the N-gonal region. generating a line segment drawn to the boundary plane around in the direction of the resulting vector,
A boundary curve generating means determining the boundary plane belonging to each line segment, and generating a boundary curve of the interpolated curved surface from the intersection of each line segment and each boundary plane;
An interpolation curved surface generating means generating a curved surface to be interpolated from the boundary curve and each point on each line segment ;
A curved surface interpolation method characterized by comprising: A program for causing a computer to execute the curved surface interpolation method according to claim 1 or 2. A computer-readable storage medium storing the program according to claim 3.

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