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10 REM CUBOID DRAWING<br />
20 LET OX-=30: LET OY=40<br />
30 LET A-30: LET B=40: LET C=1<br />
5: LET D-20<br />
40 PLOT OX,OY<br />
50 DRAW 0,A: DRAW B,0: DRAW 0,<br />
-A: DRAW -B,0<br />
60 DRAW C,D: DRAW B,0: DRAW -C<br />
70 PLOT OX+0,OY+A! DRAW C,D: D<br />
RAW B,9I DRAW -C,-D<br />
80 PLOT OX+C,OY+D! DRAW 0,A! D<br />
RAW B,0: DRAW 0,-A<br />
90 LET A-A+L! LET B*B+L: LET C<br />
«=c + l: LET D=D+1<br />
Figure 3<br />
100 STOP<br />
make a flat two-dimensional<br />
representation appear threedimensional<br />
and provide the<br />
basis for animating such an object.<br />
The diagram in figure 5<br />
shows how a single point viewed<br />
from the origin of the coordinateslx.y<br />
and z) can be<br />
represented on the picture plane<br />
at a set distance from the view<br />
point. The picture plane of<br />
course is our television screen<br />
and the x and y coordinates of<br />
the point on it with respect to<br />
the bottom left hand coner are<br />
calculated as x times (distance<br />
of picture plane to viewpoint<br />
axis divided by z). This is called<br />
transforming and is good for any<br />
object where the viewpoint and<br />
the origin of the coordinate<br />
system are the same place.<br />
Some degree of animation is<br />
now possible once the threedimensions<br />
are transformed into<br />
two on the picture plane. The<br />
x ,y coordinates can be<br />
transformed around the screen<br />
enlarged, reduced, moved or<br />
rotated and the perspective<br />
altered by shifting the picture<br />
plane. Rotation presents an interesting<br />
problem because one<br />
has to resort to sines and<br />
cosines to solve the shifting of x<br />
and y coordinates about the centre<br />
of rotation. Taking an anticlockwise<br />
rotation through a<br />
specifiedangle, A, then the new<br />
coordinates of the point x,y will<br />
be calculated as x cosine A-y<br />
sine A for the x coordinate, and x<br />
sine A + y sine A for the y coordinate.<br />
This idea is incorporated<br />
Figure 5<br />
ZX CRAPHICS<br />
Figure 4<br />
VIEWED POINT AT x,y,z<br />
x = 0<br />
y = 0<br />
(ON SCREEN)<br />
x{d/z|<br />
y(d/z)<br />
10 REM DOUBLE SIZE CHARACTERS<br />
20 LET XC-L: LET YC-1<br />
30 PRINT AT 10,10("A"<br />
40 DIM A (8 , 8)<br />
30 REM SCAN CHARACTER<br />
60 FOR X»0 TO 7<br />
70 FOR Y=0 TO 7<br />
80 IF POINT (X+80,Y+88)=1 THEN<br />
LET A(X+L,Y+L)=1<br />
90 NEXT Y<br />
100 NEXT X<br />
110 REM REPRODUCE ENLARGED<br />
120 FOR<br />
130 FOR<br />
140 LET<br />
HEN LET<br />
X=1 TO 16<br />
Y=1 TO 16<br />
YC=INT (Y/2): IF YC=0 T<br />
YC = 1<br />
130 IF A < XC,YC)<br />
96,Y+84<br />
160 LET XC-INT (X/2)<br />
HEN LET XC-1<br />
170 NEXT Y<br />
180 NEXT X<br />
PICTURE PLANE (SCREEN)<br />
PARALLEL TO x,y PLANE<br />
TRANSFORMED<br />
POINT AT x,y<br />
ORIGIN AND VIEWPOINT<br />
(0.0,0)<br />
1 THEN PLOT X+<br />
IF XC=0 T<br />
DISTANCE OF PICTURE<br />
PLANE FROM ORIGIN<br />
34 ZX COMPUTING DECEMBER/JANUARY 1985
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