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#include <math.h>
#include <stdio.h>
#include "transform.h"
#include "hpoint3.h"
#include "vec4.h"
make_tform(p1, p2, p3, m)
HPoint3 *p1, *p2, *p3;
Transform m;
/* Generate a Euclidean isometry which moves (0,0,0) -> p1.
Furthermore,
the vector (1,0,0) will go a vector tx based at p1 and ending at p2.
the vector (0,1,0) will go a vector ty based at p1, perpendicular to tx,
and lying in the plane of p1-p2-p3, in the "direction" of p3.
the vector (0,0,1) will go a vector tz based at p1, perpendicular to tx and ty.
The rotational part is computed by make_rotation. See comments there */
{
register int i;
HPoint3 nv1, nv2;
Transform trans;
VSUB3(p2, p1, &nv1);
VSUB3(p3, p2, &nv2);
nv1.w = 1.0; nv2.w = 1.0;
NORMALIZE3(&nv1);
NORMALIZE3(&nv2);
if ( !make_rotation(&nv1, &nv2, m)) /* if collinear, use most recent rotation */
{
#ifdef DEBUG
fprintf(stderr,"Non-independent vectors: make_rotation\n");
#endif
return(-1);
}
/* compute translation to take p1->(0,0,0) */
TmTranslate(trans, p1->x, p1->y, p1->z);
/* first do the rotation, then the translation */
TmConcat(m, trans, m);
return(0);
}
/* make rotation that takes (1,0,0) to v1; and (0,1,0) to the orthog. proj of v2 onto
the perpendicular subspace of v1. Return (0) if v1 and v2 are collinear.
*/
make_rotation(v1, v2, m)
HPoint3 *v1, *v2;
Transform m;
{
int i;
double a;
HPoint3 t1, t2;
a = VDOT3(v1, v2);
if (a > .9999 || a < -.9999) return(0);
t1.x = v1->x * a;
t1.y = v1->y * a;
t1.z = v1->z * a;
VSUB3(v2, &t1, &t2) /* now t2 is orthogonal to v1 */
NORMALIZE3(&t2);
TmIdentity(m);
m[0][0] = v1->x; m[0][1] = v1->y; m[0][2] = v1->z;
m[1][0] = t2.x; m[1][1] = t2.y; m[1][2] = t2.z;
/* last row is cross product of the first two rows */
m[2][0] = v1->y*t2.z - v1->z*t2.y;
m[2][1] = v1->z*t2.x - v1->x*t2.z;
m[2][2] = v1->x*t2.y - v1->y*t2.x;
return(1);
}
These are the contents of the former NiCE NeXT User Group NeXTSTEP/OpenStep software archive, currently hosted by Netfuture.ch.