JPH02309461A - Modeling processing method for generalized cylinder - Google Patents

Abstract

PURPOSE:To obtain the model of a generalized cylinder free from twists even when modeling having complexly curved skeletons unifirmly processed by successively correcting the rotational angles of rings on respective nodes so that no twist is generated. CONSTITUTION:In respective segments of an applied broken line in a prescribed space shown by model definition data, an applied polygon is formed on one end of each segment so as to form a prescribed angle from the segment and a generalized cylinder model approximate to a required generalized cylinder is formed by a polyhedron having respective sides of the polygon and segments connecting respective vertexes corresponding to the adjacent polygon on the broken line as edges. The polygons are rotated so that the prescribed corresponding vertexes of both the adjacent polygons and the segments in the broken line held between both the polygons are positioned on the same plane and the processing is successively executed in respective contacts to form the polyhedron. Consequently, even when the bends of respective skeletons are complexly changed, the model free from twists is formed by the uniform procedure.

Description

[Detailed Description of the Invention] [Summary] Regarding generalized cylinder modeling processing in computer graphics processing, it is possible to easily create a model without twisting even when the degree of bending of a skeleton changes in a complicated manner using a uniform procedure. We aim at a modeling process for a generalized cylinder that can create, for each line segment of a given polygonal line in a given space, each given polygon with one end of the line segment A model of the required generalized cylinder is made of a polyhedron set to form an angle and whose edges are the sides of the polygon and the line segments connecting the corresponding vertices of the polygons adjacent on the polygon. When generating, for each adjacent polygon, rotate the polygon so that both predetermined corresponding vertices and a line segment in the polygon line sandwiched between both polygons are located on the same plane. Then, trlj is created to generate the polyhedron.

[Industrial application field]

The present invention relates to a generalized cylinder modeling processing method in computer graphics processing.

[Prior art and problems to be solved by the invention] As is well known, the generalized cylinder moves a closed curve on a two-dimensional plane along a curve in a three-dimensional space, and also moves the size of the closed curve, for example. A figure obtained as the locus of a closed curve when it changes as a function of position.1 An ordinary cylinder is a special case of a generalized cylinder, which is obtained by moving a constant circle along a straight line. .

In addition, when handling the generalized cylinder with a computer, the curve that moves the closed curve described above is approximated by a polygonal line (hereinafter, this polygonal line is referred to as a skeleton, and both ends of each polyline segment are referred to as nodes), and the closed curve is approximated for each node. This polygon is approximated by the defined polygon (hereinafter, this polygon is called a ring),
The polyhedron determined by them is used as a model of the -a cylinder.

That is, for example, if the origin of the coordinates representing each ring is placed at the node,
For example, the orientation and arrangement of the rings are determined so that a predetermined main axis of the ring (e.g., a vector pointing to a predetermined vertex) takes a predetermined direction with respect to the line segment of the polygonal line, and each corresponding vertex is sequentially connected between the rings. For example, a polyhedron as shown in FIG. 5(a) is formed.

For this purpose, a coordinate transformation calculation called Frenet closure (Do
Carmo+M,P,+″Differential
Geometry of Curves and 5u
rfaces”, Prentice-11all, 19
76, etc.), in order to calculate the rotation angle that determines the direction of the main axis of the ring using the curvature vector of the skeleton, if the direction of bending of the skeleton changes in the opposite direction, the rotation angle of the ring at that node is calculated using the curvature vector of the skeleton. The rotation angle changes by 180 degrees, creating a twist between the rings as illustrated in FIG. 5(b).

For this purpose, it is necessary, for example, to appropriately divide the skeleton, obtain a figure for each section individually by Frenay closure, and then combine them in an appropriate manner to form the whole figure.

An object of the present invention is to provide a generalized cylinder modeling processing method that can easily create an untwisted model using a uniform procedure even when the degree of curvature of a skeleton changes in a complicated manner.

[Means to solve the problem]

FIG. 1 is a process flowchart showing the configuration of the present invention.

The figure shows the configuration of the generalized cylinder modeling processing method, in which for each line segment of a given polygonal line in a predetermined space indicated by model definition data 5, in processing steps 1 and 3, each given polygon is A polyhedron whose edges are the sides of the polygon and the line segments connecting the corresponding vertices of the polygons adjacent on the polygonal line. , in a process 7 for generating a generalized cylinder model 6 that approximates a required generalized cylinder, in process step 2, for each adjacent polygon, the predetermined two corresponding vertices and the vertices sandwiched between the two polygons are calculated. The polygon is rotated so that the line segments in the polygonal line are located on the same plane, identified in processing step 4, and the above process is sequentially performed for each contact point of the polygonal line to generate the polyhedron.

[For production]

With the above processing method, the rotation angle of the ring at each node is corrected sequentially to avoid twisting, so even if modeling of the entire skeleton with complex bends is uniformly processed at once, there will be no twisting. It becomes possible to obtain a model of a generalized cylinder.

〔Example〕

FIG. 2 is a block diagram showing an example of the configuration of a graphics processing system that generates and displays a generalized cylinder model according to the present invention. Skeleton and ring data that define the model are stored in a data storage unit 20 consisting of a magnetic disk storage device or the like. The processing device 21 reads out the model definition data from the data storage section 20 and processes it as described below, thereby generating a model of a required generalized cylinder and displaying it on the display section 22.

The model definition data stored in the data storage unit 20 is
For example, data that defines a skeleton as a sequence of m nodes, 5keleton = (So, S++Sz+ '--
−-'-"+5l11-1) different = (sxH, sy4
．． szl ) (i = o, L, 2.-, m-1) and the point sequence of each n vertex that defines each ring of the n-gon is defined for m rings corresponding to m nodes data, ringS-(rjngo+rlngt+rlngzl
°−1rlng+1l−1−]ringi ”' (r
l+o +rl-1rj+Z+"'-' +rt+n-
1) r it j ”” (rXi+ j+ r'y
i+ it rZL j )(j-0,1,2,~,n
4) Consists of. Note that each ring is defined, for example, as a figure on the x-y plane, and therefore all rings have rZ
i, j'''0. Also, the vector of the vertex r++O of each ring is processed as the main axis.

FIG. 3 is a diagram showing an example of a detailed processing flow of the generalized cylinder modeling processing performed by the processing device 21. When the processing is started by initializing i=0 in processing step 30, the node A unit vector in the direction of a line segment (let's call it a line segment SL) from SL-□ to S, and from nodes S to S5. A line segment S toward 1. The traveling direction vector a1 is obtained as the average value of the unit vector in the direction of 1. However, when i=o, and when the line segment s+si=m-1, the unit vector parallel to the line segment S+++-1 is ai.

Next, in processing step 32, a unit vector C4 on the x-y plane and perpendicular to a is obtained, and in processing step 33, Z
Only the angle formed by the unit vector e2 in the axial direction and a, C4
A rotation transformation matrix M1 of 4×4 elements for rotating a figure around − as an axis. , and in processing step 34 M, L and ri
, o is calculated.

That is, tri. is the vector of the principal axis when ring i is rotated so that the normal to ring i is parallel to a.

Next, the main axis of this ring i and the ring j-
1 main axis '1. -+,. A rotation transformation matrix for rotating ring i is determined so that the vector S of the skeleton line segment sandwiched between both rings is on the same plane.

That is, first, in processing step 35, a value is selected and a vector ' a =qi −+ + is obtained. Find ri so that +t, Xsi is perpendicular to a, processing step 3
In step 6, the angle W between r and the previously determined qi r o is determined, and in step 37, a rotation transformation matrix M2 of 4×4 elements for rotating by the angle W around a is determined.

The relationships among the above vectors are as illustrated in FIG. 4, where r is qi −+ +. This is the intersection line between the plane containing ring i and the plane containing ring i when rotated by the rotation transformation matrix M11 to make it perpendicular to ai and moving the origin to the node S. Therefore, by rotating ring i by W around 1, the main axis (li,. and qi −+ +.

will lie on the same plane. Note that when i=0, for example, processing steps 35 to 37 are skipped, and M t i=1.

Next, in processing step 38, a 4×4 element movement transformation matrix Mh for parallel translation of the origin to node S is obtained, and in processing step 39, a transformation matrix Mi = which integrates the above transformations is obtained.
Find M+tXMziXM3i.

After setting j to 0 in processing step 40, Qi, i =MHXr□1. is calculated, and this coordinate transformation calculation is repeated until j=n-1 under the control of process steps 42 and 43, thereby completing the process for all vertices of ring i. Controlled by process steps 44.45,
The above processing steps 31 to 43 are executed for all m rings.

In the above, processing such as finding the angle between vectors and determining a rotation transformation matrix and a translation transformation matrix can be performed using known techniques such as ordinary coordinate transformation.

[Effects of the Invention] As is clear from the above description, according to the present invention, in graphic processing by a computer, - in modeling processing of a membrane cylinder, when the degree of curvature of a skeleton changes in a complicated manner by a uniform procedure; However, it has the remarkable effect of making it possible to easily create a model without twisting.

[Brief explanation of the drawing]

FIG. 1 is a process flowchart showing the configuration of the present invention, FIG. 2 is a block diagram of a configuration example of a graphic processing system, FIG. 3 is a process flowchart of the present invention, and FIG. 4 is a detailed explanatory diagram of the present invention. FIG. 5 is an explanatory diagram of a model of a mm cylinder. In the figure, 1 to 4, 30 to 45 are processing steps, 5 is model definition data, 6 is a generalized cylinder model, 7 is processing, 20 is a data storage section, 21 is a processing device, and 22 is a display section.

Claims (1)

[Claims] For each line segment of a given polygonal line (5) in a predetermined space, each given polygon is set to form a predetermined angle with the line segment at one end of the line segment. (1) Generate the required generalized cylinder model (6) consisting of a polyhedron whose edges are the sides of the polygon and the line segments connecting the corresponding vertices of the polygons adjacent on the polygonal line. do (3, 4
), for each adjacent polygon, the predetermined corresponding vertices and
The polygon is rotated (2) so that the line segment in the polygonal line sandwiched between the two polygons is located on the same plane, thereby generating the polyhedron. A generalized cylinder modeling process.