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The C Users' Group Library 1994 August
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wc-cdrom-cusersgrouplibrary-1994-08.iso
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vol_300
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302_01
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vm.c
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/* Vector multiplication
Copyright (c) 1988 by Gus O'Donnell
Revision history:
Version 1.00 February 29, 1988 As released.
Version 1.01 March 20, 1988 Created libraries for all
memory models
*/
#include <3d.h>
#include <float.h>
#include <math.h>
#include <stdio.h>
typedef double HOMO [CMAX];
void vec_mul (VERTEX *this_vec, MATRIX this_mat, VERTEX *prod)
/* Multiply a vertex in homogeneous coordinates by a 4x4 matrix.
Points in 3-space are converted to homogeneous coordinates prior to
transformation. This consists simply of adding a fourth coordinate
w = 1.0, called the scale factor:
[x y z] -> [wx wy wz w]
Mathematically, the value of w is not important; 1.0 is chosen for
convenience. To convert back to world coordinates, divide each coordinate
by w and drop the last coordinate.
The value of w does not change as a result of scaling, translation, or
rotation, but it does change as a result of perspective transformation.
Given a vector v in homogeneous coordinates and a matrix m, each coordinate
of the product p[j] is given by the dot product of v and column j of m,
that is:
p [j] = v [0] * m [0] [j]
+ v [1] * m [1] [j]
+ v [2] * m [2] [j]
+ v [3] * m [3] [j]
*/
{
HOMO tvec,pvec; /* tvec is temporary storage for the
vertex to be multiplied, pvec is the
product. */
int cc,cl;
for (cc = 0; cc < DIM; cc++) /* Copy this_vec to
temp storage */
tvec [cc] = this_vec -> coord [cc];
tvec [CMAX - 1] = 1.0; /* Convert to homo-
geneous coordinates */
for (cl = 0; cl < CMAX; cl++) /* Outside loop to
calculate each coor-
dinate */
{
pvec [cl] = 0.0;
for (cc = 0; cc < CMAX; cc++) /* Inside loop to cal-
culate dot product */
pvec [cl] = pvec [cl]
+ tvec [cc] * this_mat [cc] [cl];
}
for (cc = 0; cc < DIM; cc++) /* Convert back to world
coordinates */
prod -> coord [cc] = pvec [cc]/pvec [CMAX - 1];
}