JPH0421079A - Three-dimensional graphic display system - Google Patents

Abstract

PURPOSE:To easily and quickly perform three-dimensional display with high accuracy by software by projecting supplied three-dimensional coordinates on a plane sharing an origin and perpendicular to a view-point vector. CONSTITUTION:This system is equipped with a viewpoint coordinate input means 2 which inputs viewpoint coordinates on three-dimensional space, a coordinate transform matrix generating means 3 which generates a coordinate transform matrix, a scaling means 4 which transforms displayed three-dimensional graphic data to two-dimensional coordinates by using the coordinate transform matrix and adjusts the size of a graphic so as to be housed in a set display frame, and display means 5-8. The coordinate transform matrix generating means 3 generates a 3D 2D coordinate transform matrix from the viewpoint vector on a two-dimensional plane perpendicular to the viewpoint vector connecting the viewpoint of the three-dimensional space to the origin and sharing the origin by setting the two-dimensional coordinates in which an intersection with the X-Y plane of the three-dimensional space becomes an X-axis. Thereby, it is possible to easily display three-dimensional shape with high accuracy observing from an arbitrary viewpoint on the two-dimensional plane by the software.

Description

[Detailed Description of the Invention] [Industrial Field of Application] This invention is a method for displaying three-dimensional shapes on a computer CRT or XY
This relates to the method of displaying on a plotter.

[Prior Art] Fig. 5 and Fig. 6 are diagrams showing a conventional example disclosed in Japanese Unexamined Patent Publication No. 62-16172. In Fig. 5, 121 is a central processing unit (CPU), and 122 is a two-dimensional A figure display processing unit, 123 a three-dimensional figure display processing unit, 124 a two-dimensional frame buffer, 125 a three-dimensional frame buffer,
126 is a synthesis section, 127 is a parallel/serial (P/S
) conversion section, 128 is a digital/analog (D/A) conversion section, and 129 is a display (CRT). In addition, in FIG. 6, 130 is a screen, 131 is a two-dimensional figure, and 132
is a three-dimensional figure.

That is, in this conventional example, the 2
A two-dimensional figure display processing unit that performs processing to display a two-dimensional figure on a display device using dimensional figure data and generates an output; a three-dimensional graphic display processing section that performs processing for displaying and generates output; a combining section that combines the outputs of both of the graphic display processing sections and generates an output for display on a single screen; and the combining section It is equipped with a display section that displays on the display based on the output signal of The figure was being displayed.

[Problems to be Solved by the Invention] The conventional three-dimensional figure display system is configured as described above, but 3D for displaying three-dimensional figures on a two-dimensional screen
(3D) → 2D (2D) conversion is complex and requires a considerable amount of processing, so it is practically dependent on hardware, and it has been difficult to determine it using software in terms of speed and accuracy. . Furthermore, there is a problem in that since there are many planes perpendicular to the viewpoint vector connecting the viewpoint and the origin, it is necessary to determine these planes.

The present invention was made to solve the above-mentioned problems, and an object of the present invention is to provide a three-dimensional graphic display method that can easily and quickly realize highly accurate three-dimensional display.

[Means for Solving the Problems] A three-dimensional graphic display method according to the present invention includes a viewpoint coordinate input means for inputting viewpoint coordinates in a three-dimensional space, and a viewpoint coordinate input means for inputting viewpoint coordinates in a three-dimensional space, and a viewpoint coordinate input means for inputting viewpoint coordinates in a three-dimensional space, and a viewpoint coordinate input means for inputting viewpoint coordinates in a three-dimensional space. a coordinate transformation matrix generating means for generating a coordinate transformation matrix for transforming into two-dimensional coordinates on a plane; The apparatus includes a scaling means for adjusting the size of a figure, and a display means for displaying the adjusted figure data.

[Operation] In order to easily and accurately project three-dimensional coordinate data onto a two-dimensional plane according to the viewpoint, the coordinate transformation matrix generation means in this invention projects the origin at a point perpendicular to the viewpoint vector connecting the viewpoint and the origin in the three-dimensional space. On a two-dimensional plane that shares
A 3D → 2D coordinate conversion matrix is created from the viewpoint vector by setting the 2D coordinates whose intersection with the xy plane of the 3D space is the X axis, so it is a simple 2D conversion matrix to any 3D coordinate. By multiplying by , a three-dimensional shape viewed from an arbitrary viewpoint can be easily and precisely displayed on a two-dimensional plane, and three-dimensional figure display using software becomes practically possible.

[Example] An embodiment of the present invention will be described below with reference to the drawings.

FIG. 1 is a functional block diagram showing an embodiment of the three-dimensional graphic display method according to the present invention. In FIG. 1, numeral 1 indicates a display frame input means for inputting the lengths of the two-dimensional plane to be displayed in the X and Y directions. , 2 is a viewpoint coordinate input means for inputting viewpoint coordinates on a three-dimensional space, and 3 is for converting three-dimensional (3D) coordinates into two-dimensional (2D) coordinates on a plane having a common origin and perpendicular to the viewpoint vector. A coordinate transformation matrix generation means 4 converts the three-dimensional figure data to be displayed into two-dimensional coordinates using the coordinate transformation matrix, and adjusts the size of the figure so that it fits within the set display frame. 5 to 8 are display means respectively; 5 is a node display means for displaying the nodes of the graphic data whose size has been adjusted; 6 is a nodal line display means for drawing a straight line from the node connection file. , 7 is a plane display means for drawing a plane from a surface display file, and 8 is a coordinate axis display means for drawing a three-dimensional coordinate axis. Note that each of the above means is realized by computer software that can be created based on the flowchart shown in detail in FIG.

Next, the effect will be explained.

Figure 3 shows the three-dimensional coordinate 1 when projecting three-dimensional coordinates onto an arbitrary two-dimensional plane α that is perpendicular to the viewpoint vector and shares the origin.
1 (X, Y, Z) and two-dimensional coordinates (U, V).

First, the space o-xyz and the plane 0-UV share the origin O. Next, the OU axis is set to be the intersection of the plane α and the XY plane. OU thin axis unit vector u = (ux, u,
, u, ) is on the xy plane, so uR=o f11 Also, since sai is on the α plane, the viewpoint vector haze=(1, m, n
) is perpendicular, so it is vertical - 〇 (orthogonality condition by inner product) (2) From the above formula (1), +21, 1 ux + muy = O + 31 Also, from the unit vector, u , 12 + u y” + u ,I”=1
(41 formula (1), (from 4+, u," + u," = 1
(5) From equation (31, (5)), (m2/1" + 1)u,"=1,, uy=l/m + (el
u, = -m/f ding ding 7' + 71 On the other hand, the unit vector on the 0 ■ axis v = (vX.

Since Vu, ■yo) is perpendicular to De and Maro, the unit vector on the viewpoint vector
/s, m/s, n/s)
(8) (However, s= +m +n), then Ma is expressed as the cross product of Ryo and Ma.

v = a X u i
According to 91.

7=(1/s, m/s, n/s) x (ux, uy,
u, )・(ntLz2"h0muni"h-]muni")
(10) SS,
S Therefore, the unit vectors u and v of the U axis and ■ axis of the 0-UV plane are respectively '=(-1r, 7T, 0) ''(uxpuy 1ull) = (v, ,v, ,v, )
(11).

Next, the xyz space teno point P (X, Y, Z) is
A method of converting to a point Q (U, V) on a plane is shown.

Here, the U-axis component of σa is the inner product of σ1' and 1, and σ
What is the V-axis component of T? Since it is the inner product of 57 and V, U= u , l X+ u , Y + u z ZV=
v, l
= (0, O, n) is not handled.

In this case, when n > O, 曾= (1,0,0), 7=
(0,1,0) When n < O, “ili' = (
-1,0,0), v = (0,-1,0), and by applying equation (12), a three-dimensional figure can be expressed.

Next, the operation shown in FIG. 1 will be explained with reference to the flowchart shown in FIG.

The display frame input means 1 in Fig. 1 is step 1 in Fig. 2 fa).
Corresponds to step 2, and inputs the display range on the CRT. Steps 10 and 11 before that are input processing of data to be displayed. The viewpoint coordinate input means 2 corresponds to step 13, and from the viewpoint coordinate inputted in step 13, that is, the viewpoint vector, the coordinate transformation matrix generation means 3 corresponds to step 14.
~22 (3D+ by processing in Figure 2 fat, (b+)
Generate a 2D coordinate transformation matrix. Also, step 2
By processing steps 4 to 29 (Figure 2 0:, ), (C)), 3
The dimensional coordinates are converted into two-dimensional coordinates, and the size of the graphic is adjusted by the scaling means 4 so that the entire graphic shape fits appropriately within the display frame of the screen. Then, in step 3o by the node display means 5, nodes are displayed on two-dimensional coordinates that have been subjected to 3D→2D conversion and scaling. In step 31, it is selected whether the shape to be displayed is defined as a beam or a plane shell (plate).

In the case of a beam, step 32 to
37 will be implemented. In the case of a flat shell, steps 38 to 48 (FIG. 2(d)) are executed by the flat display means 7.

Finally, the steps 49 to 51 are performed by the coordinate axis display means 8.
By performing (FIG. 2(e)) and displaying the three-dimensional coordinate axes, a three-dimensional shape as shown in FIG. 4 can be displayed. In the example of FIG. 4, 53-56 are displayed as beams, 57-60 are square planar shells, 61.57.
62, 62, 58, 63, 63, 59, 64, and 64°60.61 are displayed as triangular plane shells, 65 is a three-dimensional coordinate axis, and 66 is an explanation of the shape.

In the above embodiment, beams and plane shells are displayed as representative examples, but curved surfaces can also be displayed by connecting points with spline curves.

Further, in the above embodiment, the display frame input means 1 is provided so that the size of the display frame can be arbitrarily set, but this is not necessary if the size of the display frame is fixed.

[Effects of the Invention] As described above, according to the present invention, given three-dimensional coordinates are configured so that they can be projected onto a plane that shares the origin and is perpendicular to the viewpoint vector. This has the effect of allowing highly accurate three-dimensional display.

[Brief explanation of the drawing]

FIG. 1 is a functional block diagram showing an embodiment of the present invention, FIG. 2 (a) to tel are flowcharts showing the operation of the embodiment, and FIG. FIG. 4 is a diagram showing a display example according to the embodiment, and FIGS. 5 and 6 are diagrams showing a conventional example. 1 is a display frame input means, 2 is a viewpoint coordinate input means, 3 is a coordinate transformation matrix generation means, 4 is a scaling means, 5 is a node display means, 6 is a nodal line display means, 7 is a plane display means, and 8 is a coordinate axis Display means. Agent: Patent Attorney Miyazono Pure procedural amendment (voluntary) 1. Display of the case Patent Application No. 123722/1992/2. Name of the invention 3-dimensional graphic display method/3. Amended person Representative Ki Moriya of the amendment Target drawing. Contents of amendment (1) Drawings, Figure 2 (a) to f8+ will be corrected as shown in the attached sheet. that's all

Claims (1)

[Claims] A viewpoint coordinate input means for inputting viewpoint coordinates in a three-dimensional space, and a coordinate transformation matrix for generating a coordinate transformation matrix for transforming the three-dimensional coordinates into two-dimensional coordinates on a plane having a common origin and perpendicular to the viewpoint vector. a generating means, a scaling means for converting the three-dimensional figure data into two-dimensional coordinates using the coordinate conversion matrix and adjusting the size of the figure so that it fits within the display frame, and a display for displaying the adjusted figure data. A three-dimensional graphic display method characterized by comprising means.