JP3679436B2 - Method and apparatus for extracting points inside and outside region in three-dimensional upper region, and method and device for determining arrangement order of points on same curve - Google Patents

Description

[0001]
[Industrial application fields]
The present invention is adapted to the graphics processing apparatus such as CAD, extraction method and apparatus of the points in the region and outside in a three-dimensional region, and are those related to ordering determination method and apparatus of the points on the same curve.
[0002]
[Prior art]
As a method for calculating a point outside the region in the two-dimensional region, when considering the point where the x value or the y value is sufficiently large with respect to the size of the region when considered on the xy plane as shown in FIG. A point outside the range can be obtained practically.
[0003]
In the two-dimensional case, the x value and the y value are calculated using random numbers, it is determined whether the point is inside or outside the region, and if it is outside the region, the point is set as a point outside the region. In the case of being within the area, a method is known in which an arbitrary point is obtained again using a random number and is repeated until it is determined that the area is out of the area.
[0004]
Even in the three-dimensional case, the surface on which the region rides is a plane, a cylindrical surface, a conical surface, etc., such as FIG. In such a case, a method is known in which a point outside the region is obtained by calculating a point on such a curve that is sufficiently away from a point representing the region.
[0005]
[Problems to be solved by the invention]
When a point outside a three-dimensional area is obtained by using a computer such as a conventional CAD, for example, when the surface on which the area is placed is a curved surface closed like a sphere, a point sufficiently away from the area is added to the area. However, there is a problem that a method of using a point that is sufficiently away from the region as a point outside the region cannot be used.
[0006]
Even if there is a curve on the surface where the start and end points are at infinity in a certain direction, such as a cylindrical surface or a conical surface, the area is When it is necessary to find a point outside the region that is on a closed curve such as a circle or ellipse on the surface, it is not possible to use a method that uses a point far from the region as a point outside the region.
[0007]
In general, when the arrangement order of points on a curve is determined, the determination is based on the geometric characteristics of the curve, and it has been difficult to adapt to any curve.
[0008]
[Means for Solving the Problems]
And [Action]
The first aspect of the present invention has been made in view of such a problem, and intends to provide a method and an apparatus that make it possible to obtain a point outside the region without depending on the type of the surface on which the region is mounted. To do.
[0009]
In order to solve this problem, for example, a method for extracting internal and external points in a three-dimensional upper region of the present invention includes the following steps. That is,
A calculation step of calculating, by a calculation unit, a reference point that is sufficiently far from a geometrical tolerance regarding the length from the end point on a predetermined ridge line that forms a boundary of the three-dimensional upper region stored in the storage unit; ,
A setting step of setting a plane that does not have an intersection with the ridge line at a distance within the geometric tolerance from the reference point through the reference point;
And curves obtaining a curve that intersects a plane of the set plane as in the setting unit area,
A tangent vector step for obtaining two tangent vectors that are sufficiently smaller than the geometric tolerance at the reference point of the cross curve obtained in the curve step;
An outer vector step of determining which one of the tangent vectors obtained in the tangent vector step is directed to the outside of the region by using a determination unit, and setting the direction toward the outside as an out-of-region direction vector;
A storage step of dropping a perpendicular from the end point of the vector specified by the reference point and the out-of-region vector to a surface on which the region is located, and storing an intersection with the perpendicular as a point outside the region in the storage unit; Is provided.
[0012]
【Example】
Hereinafter, embodiments according to the present invention will be described in detail with reference to the accompanying drawings.
[0013]
FIG. 1 is a flowchart for explaining the operation flow of the embodiment of the present invention.
[0014]
FIG. 2 is a block diagram of a graphics processing apparatus used by the present invention. A bus 1 (including control lines, data, addresses, and control buses) includes a central processing unit (hereinafter referred to as CPU) 2, a read-only A memory (hereinafter referred to as ROM) 3, a random access memory (hereinafter referred to as RAM) 4, an input device 6 via an input interface 5, a CRT 8 via a CRT interface 7, and an external storage device interface 9 An external storage device 10 such as a magnetic disk or a magnetic tape is connected.
[0015]
The CPU 2 performs various processes and controls, for example, graphic input control, graphic display, pick processing, hidden surface processing, inside / outside determination, and the like, using the RAM 4 as a temporary storage device in accordance with a program stored in the ROM 3.
[0016]
The input device 6 is a keyboard, tablet, mouse or the like and inputs graphic data. The graphic data may be received from a host computer. The CRT 8 includes a plurality of bit maps, planes, and the like as necessary, and displays graphics, various menus, and the like.
[0017]
Next, a preferred embodiment of the present invention will be described with reference to FIGS. 1, 3, 4, and 5. Processing and determination described below are performed by the CPU 2 in accordance with a program stored in the ROM 3.
[0018]
<Definition of area>
In the present embodiment, there are geometric shapes such as flat surfaces and cylindrical surfaces, conical surfaces, spheres, and other free-form surfaces such as torus, Bezier surfaces, and NURBS (Non Uniform Rational B-spline) surfaces as shown in FIG. A region that is on a surface and surrounded by a boundary line consisting of ridge lines having geometric shapes such as line segments, circular arcs, elliptical arcs, parabolas, hyperbolic curves, Bezier curves, NURBS (Non Uniformed Rational B-spline) curves, etc. It is determined whether or not a point on a certain space is within the region. The ridge line referred to here means an edge part that specifies the boundary of the region.
[0019]
Here, as shown in FIG. 4, the boundary is composed of a set of ridge lines, and each ridge line is composed of an outer peripheral loop and an inner peripheral loop. The outer periphery loop is a loop that represents the outermost periphery of the region, and the inner periphery loop is a loop that represents a “hole” in the region. It is assumed that the outer circumferential loop has a counterclockwise direction as a positive direction, and the inner circumferential loop has a clockwise direction as a positive direction, and ridge lines are arranged in that order. In other words, it is assumed that when the loop is advanced in the positive direction on the ridge line, there is a region entity on the left side.
[0020]
In the following, the calculation processing of points outside the region in the three-dimensional region will be described according to the order of steps S1 to S13 in the flowchart showing the flow of the present embodiment in FIG.
[0021]
<S1: Extract an arbitrary ridge line E0 of the boundary B of the three-dimensional region>
Data of a target three-dimensional area (assumed to be input from the input device 6 in advance) is extracted from the external storage device 10 or the RAM 4 and arbitrarily selected from the ridgelines constituting the boundary B, for example, paying attention The first ridge line E0 constituting the loop is selected. When the geometrical tolerance of the length of the ridge line E0 is ε, the central processing unit determines whether it is larger than 2ε, and the one larger than 2ε is taken out and stored in the RAM 4 (see FIG. 5). For ridge lines smaller than 2ε, the length of the ridge line is sufficiently small and can be ignored, and the following processing is omitted. Also, the reason why the value twice as large as ε is taken into account is that the center point of the edge E0 is used as a reference, as will be described below. This is also because the allowable error can be set to ε.
[0022]
<S2: Calculate midpoint P0 on ridgeline E0>
The data of the ridge line E0 is taken out from the external storage device 10 or the RAM 4, the midpoint P0 on the ridge line E0 is calculated by the CPU 2, and stored in the RAM 4 (see FIG. 5).
[0023]
<S3: Calculation of cutting plane passing through the point P0>
Here, a plane is considered as the cut surface. The CPU 2 determines whether the data of the point P0 taken out from the RAM 4, one arbitrary point fixed in advance, and one point obtained using the random number generated by the CPU 2 are aligned on the same straight line. Since a plane can be specified by three points, a plane passing through the three points is stored in the RAM 4 as a cut surface. If the plane cannot be specified, that is, if it is determined that the planes are aligned, points are obtained using random numbers generated by the CPU 2 until they are not aligned. Here, by using a random number to obtain the cut surface, the probability of obtaining a cut surface having an intersection with E0 within the points P0 and ε is reduced. If there is an intersection with E0 within the points P0 and ε, a point outside the region may not be obtained correctly.
[0024]
<S4: Calculation of intersection line C between cut surface and surface S where region is on>
The obtained cutting plane and the surface S on which the region is placed are taken out from the RAM 4 and the intersection line C is calculated by the CPU 2.
[0025]
<S5: Calculate normal vector n0 of surface S at point P0>
The data of the point P0 and the surface S are extracted from the RAM 4, the surface S normal vector n0 on which the region at the point P0 is located is calculated by the CPU 2, and stored in the RAM 4 (see FIG. 5).
[0026]
<S6: Calculation of tangent vectors TE1 and TE2 of edge E0 at point P0>
The data of the point P0 and the ridgeline E0 are taken out from the external storage device 10 or the RAM4, the unit direction vectors TE1 and TE2 of the tangent line of the ridgeline E0 at the point P0 are calculated by the CPU2, and stored in the RAM4. At this time, it is not possible to specify which of TE1 and TE2 is facing out of the region.
[0027]
<S7: TE1 and TE2 having the same direction as the direction of the boundary are set as TE> The data of the obtained tangent vectors TE1 and TE2 are extracted from the RAM 4, and the CPU 2 determines which is the same direction as the direction of the boundary. Then, the same is set as TE and stored in the RAM 4 (see FIG. 5).
[0028]
<S8: Calculate tangent vectors TC1 and TC2 of curve C at point P0>
The data of the curve C obtained in the above step S4 is extracted from the RAM 4, and the tangent direction vector at the point P0 and the vector having a magnitude sufficiently smaller than the geometric tolerance ε is calculated by the CPU 2, and stored in the RAM 4 as TC1 and TC2. (See FIG. 5).
[0029]
<S9: Calculation of outer product n1 of TC1 and TE and outer product n2 of TC2 and TE>
The data of TC1, TC2, TE is taken out from RAM4,
n1 = TC1 × TE (1)
n2 = TC2 × TE (2)
The CPU 2 calculates the outer product n1 of TC1 and TE and the outer product n2 of TC2 and TE2, and stores them in the RAM 4.
[0030]
<S10: Calculation of θ1 formed by n0 and n1 and angle θ2 formed by n0 and n2>
The data of n0, n1, n2 is taken out from the RAM 4,
θ1 = (angle formed by n0 and n1) (0 ≦ θ1 ≦ π) (3)
θ2 = (angle formed by n0 and n2) (0 ≦ θ2 ≦ π) (4)
Θ1 and θ2 are calculated by the CPU 2 and stored in the RAM 4.
[0031]
<S11: θi (i = 1, 2) <When π / 2, TC = TCi>
When the data of θ1 and θ2 are extracted from the RAM 4, either one of θ1 or θ2 should be smaller than π / 2 and the other should be larger than π / 2. When θi (i = 1, 2) <π / 2, TC = TCi is stored in the RAM 4. That is, this allows the vector TC to be identified as going out of the region.
[0032]
<S12: Pout0 = P0 + TC>
The data of P0 and TC are extracted from the RAM 4, and Pout0 = P0 + TC is calculated by the CPU 2 and stored in the RAM 4 (see FIG. 5).
[0033]
<S13: A perpendicular foot from Pout0 to the intersection line C is a point outside the region>
The data of Pout0 obtained in S12 and the intersection line C obtained in S4 is taken out from the random access memory, and the vertical line extending from Pout0 to the curve (intersection line) C is obtained by the CPU, and this is used as a point outside the region. The data is stored in the RAM 4 or the external storage device 10 (see FIG. 5).
[0034]
By doing so, for example, even if the surface on which the region is placed is a sphere-like surface, it is possible to uniquely obtain points outside the region. In other words, 3D graphics processing, such as inside / outside determination in 3D areas, is allowed by finding points outside the area in 3D or higher areas that are on any type of surface and surrounded by any type of boundary. There is an effect that it can be performed stably within a range of errors.
[0035]
Moreover, although the example which calculates | requires the point outside an area | region was shown in the said Example, it cannot be overemphasized that it is applicable also when calculating | requiring the point in an area | region.
[0036]
In the above embodiment, as a method for obtaining the curve C on the same plane of the region of interest that does not intersect with E0 at a distance within ε from the point P0, it is generated using P0, the given point, and a random number. Rather than obtaining as a line of intersection between the plane passing through the specified point and the plane on which the region is located, a plane is created from one of a plurality of points prepared in advance with P0 and a fixed point and appropriate variations, If the obtained intersection line has an intersection point with E0 at a distance within ε from the point P0, a plane may be generated using another point to obtain the intersection line. In this case, one point outside the region can be calculated by a method of obtaining an intersection line having no intersection with E0 at a distance within ε from the point P0 with high reliability, although the processing efficiency is slightly reduced.
[0037]
Further, in the above-described embodiment, the step point P0 for calculating an arbitrary point P0 on the arbitrary ridge line E0 on the boundary of the three-dimensional upper area and sufficiently separated from the geometrical tolerance ε regarding the length from the end point is obtained. In addition, when it is necessary to set a point on a specific intersection line to P0 instead of taking the middle point on the ridge line E0, as in the inside / outside determination outside the region, the intersection point between the specific intersection line and E0 is set. One point outside the region can be calculated by checking whether the distance from the end point is larger than ε as P0.
[0038]
<Description of the second embodiment>
Next, a second embodiment will be described.
[0039]
In general, there are several methods for recognizing the arrangement order of points on the same curve. For example, on a straight line, the arrangement of points can be identified by the distance from a certain reference point. In the case of a circle, the arrangement of points can be identified based on the angle between a line segment connecting the center of the circle and a reference line (line segment connecting the reference point and the center of the circle).
[0040]
However, the method for identifying or recognizing the arrangement order of the points depends on individual geometric features for each curve (including straight lines), and thus has a problem that it is not versatile.
[0041]
In the second embodiment, an attempt is made to eliminate such a problem.
[0042]
Hereinafter, a description will be given with reference to FIGS. The apparatus configuration is the same as that shown in FIG. 2 in the first embodiment, and details thereof are omitted. However, the ROM 3 stores a program based on the flowchart of FIG.
[0043]
<S21: A given curve is parametric>
Curve data in a two-dimensional or three-dimensional space is extracted from the external storage device 10 or the RAM 4 and converted into a parametric expression by the CPU 2. The converted result is stored in the RAM 4. However, it is necessary to convert the parametric expression so that the parameter monotonously increases / decreases in accordance with the traveling direction of the curve C (see the directions → in FIGS. 9 to 11). An example of a parametric would be:
[0044]
(1) In the case of a straight line P = P0 + tV (−∝ ≦ t ≦ ∝)
Here, P0: any one point on the straight line V: straight line direction vector t: parameter.
[0045]
(2) In the case of a circle P = C + r (u · cos (t) + v · sin (t)) (0 ≦ t ≦ 2π)
Here, C: circle center r: circle radius u: reference vector 1 (unit vector on the same plane as the circle)
v: reference vector 2 (unit vector on the same plane as the circle)
However, u · v = 0, | u | = | v | = 1
t: parameter.
[0046]
(3) In the case of an ellipse P = C + a · cos (t) + b · sin (t) (0 ≦ t ≦ 2π)
Here, C: center of ellipse a: major axis vector b: minor axis vector where a · b = 0
t: parameter.
[0047]
Although three types of curves are shown here, the types are not limited thereto. The point is that it makes sense to parametrically represent a curve.
[0048]
<S22: Calculate the parametric value of each point on the curve>
Based on the parametric expression, the coordinate value of each point on the curve is taken out from the external storage device 10 or the RAM 4, the parametric value in the parametric expression is obtained by the CPU 2, and stored in the RAM 4 in association with the original point.
[0049]
For example, in the case of a straight line,
t = (P−P0) · V / (V · V)
It becomes.
[0050]
For a circle,
cos (t) = ((P−C) · u) / r
sin (t) = ((P−C) · u) / r
Here, since the range is 0 ≦ t ≦ 2π, the parameter is uniquely determined.
[0051]
For an ellipse,
cos (t) = ((P−C) · a) / | a | ^ 2
sin (t) = ((P−C) · b) / | b | ^ 2
Here, since the range is 0 ≦ t ≦ 2π, the parameter is uniquely determined. | X | indicates the absolute value of x, and x ^ y indicates x to the power of y.
[0052]
<S23: Sort parametric values>
The parameter obtained in step S22 is extracted from the RAM 4, the parameter and the corresponding point are calculated, the calculated point is sorted by the CPU 2 using quick sort, bubble sort, etc., and the sorted result is stored in the RAM 4. . Of course, there are various sort methods, and other methods may be adopted.
[0053]
<S24: Sort points by order sorted by parametric value>
The correspondence between the order of the parameters sorted in step S23 and the points of the parameters is retrieved from the RAM 4 and is referred to, and the order of the points is recognized by the CPU 2.
[0054]
As described above, according to the second embodiment, by recognizing the arrangement of points on the same curve, geometric processing such as area inside / outside determination in CAD etc. can be performed generically and easily. Is possible.
[0055]
In the above-described first and second embodiments, the example applied to one apparatus has been described, but the present invention may be applied to a system constituted by a plurality of devices. Needless to say, the present invention can also be applied to a case where the present invention is achieved by supplying a program to a system or apparatus.
[0056]
【The invention's effect】
As described above, according to the present invention, a point outside the region can be obtained without depending on the type of the surface on which the region is placed.
[0057]
According to another second invention, a sequence of points on a given curve is converted from a function expressing the curve into a common expression called a parametric expression, and depends on a geometric expression of the curve. It is possible to uniquely determine the order of the points on the curve.
[0058]
[Brief description of the drawings]
FIG. 1 is a flowchart illustrating a preferred embodiment of the present invention.
FIG. 2 is a block diagram of a graphics processing apparatus using the present invention.
FIG. 3 is a diagram illustrating a configuration of an area handled in the present embodiment.
FIG. 4 is a diagram illustrating an outer peripheral loop and an inner peripheral loop.
FIG. 5 is a diagram illustrating a method for obtaining a point outside an area;
FIG. 6 is a diagram for explaining a conventional method for obtaining a point outside a region on an xy plane.
FIG. 7 is a diagram illustrating a case where a point outside a region can be calculated by selecting a point sufficiently away from the region in a three-dimensional region.
FIG. 8 is a flowchart showing a processing procedure in the second embodiment.
FIG. 9 is a diagram illustrating a relationship between an increasing / decreasing direction of a straight line parameter and an arrangement order of points in the second embodiment.
FIG. 10 is a diagram illustrating a relationship between an increase / decrease direction of a circle parameter and an arrangement order of points in the second embodiment.
FIG. 11 is a diagram illustrating a relationship between an increase / decrease direction of an ellipse parameter and an arrangement order of points in the second embodiment.
[Explanation of symbols]
1 Bus 2 Central processing unit (CPU)
3 Read-only memory (ROM)
4 Random access memory (RAM)
5 Input Interface 6 Input Device 7 CRT Interface 8 CRT Device 9 External Storage Device Interface 10 External Storage Device

Claims (2)

A calculation step of calculating, by a calculation unit, a reference point sufficiently separated from an end point of the predetermined ridge line forming the boundary of the three-dimensional upper region stored in the storage unit as compared to a geometric tolerance regarding the length; ,
A setting step of setting a plane that passes through the reference point and does not have an intersection with the ridge line at a distance within the geometric tolerance from the reference point;
And curves obtaining a curve that intersects a plane of the set plane as in the setting unit area,
A tangent vector step for obtaining two tangent vectors that are sufficiently smaller than the geometric tolerance at the reference point of the cross curve obtained in the curve step;
An outer vector step of determining which one of the tangent vectors obtained in the tangent vector step is directed to the outside of the region by the determining means, and setting the direction toward the outside as an out-of-region direction vector;
A storage step of dropping a perpendicular from the end point of the vector specified by the reference point and the out-of-region vector to a surface on which the region is located, and storing an intersection with the perpendicular as a point outside the region in the storage unit; A method for extracting points inside and outside the three-dimensional upper region. Calculating means for calculating a reference point sufficiently separated from the geometric tolerance of the length from the end point on a predetermined ridge line forming the boundary of the three-dimensional upper region stored in the storage means;
Setting means for setting a surface that passes through the reference point and does not have an intersection with the ridgeline at a distance within the geometric tolerance from the reference point;
And the curve means for obtaining a curve that intersects a plane of the set plane as in the setting unit area,
Tangent vector means for obtaining two tangent vectors that are sufficiently smaller than the geometric tolerance at the reference point of the cross curve obtained by the curve means;
Determining which one of the tangent vectors determined by the tangent vector means is directed to the outside of the region;
Storage control means for dropping a perpendicular line from the end point of the vector specified by the reference point and the out-of-area vector to the surface on which the area is located, and storing the intersection with the perpendicular line as a point outside the area in the storage means An apparatus for extracting points inside and outside a three-dimensional upper region, characterized by comprising:

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