289 lines
6.3 KiB
C++
289 lines
6.3 KiB
C++
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/*
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* Trackball code:
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*
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* Implementation of a virtual trackball.
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* Implemented by Gavin Bell, lots of ideas from Thant Tessman and
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* the August '88 issue of Siggraph's "Computer Graphics," pp. 121-129.
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*
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* Vector manip code:
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*
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* Original code from:
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* David M. Ciemiewicz, Mark Grossman, Henry Moreton, and Paul Haeberli
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*
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* Much mucking with by:
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* Gavin Bell
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*/
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#include <math.h>
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#include "trackbal.h"
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/*
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* This size should really be based on the distance from the center of
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* rotation to the point on the object underneath the mouse. That
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* point would then track the mouse as closely as possible. This is a
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* simple example, though, so that is left as an Exercise for the
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* Programmer.
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*/
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#define TRACKBALLSIZE (0.8)
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/*
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* Local function prototypes (not defined in trackball.h)
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*/
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static float tb_project_to_sphere(float, float, float);
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static void normalize_quat(float [4]);
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void
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vzero(float *v)
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{
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v[0] = 0.0;
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v[1] = 0.0;
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v[2] = 0.0;
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}
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void
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vset(float *v, float x, float y, float z)
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{
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v[0] = x;
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v[1] = y;
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v[2] = z;
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}
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void
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vsub(const float *src1, const float *src2, float *dst)
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{
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dst[0] = src1[0] - src2[0];
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dst[1] = src1[1] - src2[1];
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dst[2] = src1[2] - src2[2];
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}
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void
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vcopy(const float *v1, float *v2)
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{
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register int i;
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for (i = 0 ; i < 3 ; i++)
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v2[i] = v1[i];
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}
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void
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vcross(const float *v1, const float *v2, float *cross)
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{
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float temp[3];
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temp[0] = (v1[1] * v2[2]) - (v1[2] * v2[1]);
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temp[1] = (v1[2] * v2[0]) - (v1[0] * v2[2]);
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temp[2] = (v1[0] * v2[1]) - (v1[1] * v2[0]);
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vcopy(temp, cross);
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}
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float
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vlength(const float *v)
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{
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return sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);
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}
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void
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vscale(float *v, float div)
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{
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v[0] *= div;
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v[1] *= div;
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v[2] *= div;
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}
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void
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vnormal(float *v)
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{
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vscale(v,1.0/vlength(v));
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}
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float
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vdot(const float *v1, const float *v2)
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{
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return v1[0]*v2[0] + v1[1]*v2[1] + v1[2]*v2[2];
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}
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void
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vadd(const float *src1, const float *src2, float *dst)
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{
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dst[0] = src1[0] + src2[0];
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dst[1] = src1[1] + src2[1];
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dst[2] = src1[2] + src2[2];
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}
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/*
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* Ok, simulate a track-ball. Project the points onto the virtual
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* trackball, then figure out the axis of rotation, which is the cross
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* product of P1 P2 and O P1 (O is the center of the ball, 0,0,0)
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* Note: This is a deformed trackball-- is a trackball in the center,
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* but is deformed into a hyperbolic sheet of rotation away from the
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* center. This particular function was chosen after trying out
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* several variations.
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*
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* It is assumed that the arguments to this routine are in the range
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* (-1.0 ... 1.0)
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*/
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void
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trackball(float q[4], float p1x, float p1y, float p2x, float p2y)
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{
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float a[3]; /* Axis of rotation */
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float phi; /* how much to rotate about axis */
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float p1[3], p2[3], d[3];
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float t;
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if (p1x == p2x && p1y == p2y) {
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/* Zero rotation */
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vzero(q);
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q[3] = 1.0;
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return;
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}
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/*
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* First, figure out z-coordinates for projection of P1 and P2 to
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* deformed sphere
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*/
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vset(p1,p1x,p1y,tb_project_to_sphere(TRACKBALLSIZE,p1x,p1y));
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vset(p2,p2x,p2y,tb_project_to_sphere(TRACKBALLSIZE,p2x,p2y));
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/*
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* Now, we want the cross product of P1 and P2
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*/
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vcross(p2,p1,a);
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/*
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* Figure out how much to rotate around that axis.
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*/
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vsub(p1,p2,d);
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t = vlength(d) / (2.0*TRACKBALLSIZE);
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/*
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* Avoid problems with out-of-control values...
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*/
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if (t > 1.0) t = 1.0;
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if (t < -1.0) t = -1.0;
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phi = 2.0 * asin(t);
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axis_to_quat(a,phi,q);
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}
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/*
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* Given an axis and angle, compute quaternion.
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*/
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void
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axis_to_quat(float a[3], float phi, float q[4])
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{
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vnormal(a);
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vcopy(a,q);
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vscale(q,sin(phi/2.0));
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q[3] = cos(phi/2.0);
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}
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/*
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* Project an x,y pair onto a sphere of radius r OR a hyperbolic sheet
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* if we are away from the center of the sphere.
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*/
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static float
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tb_project_to_sphere(float r, float x, float y)
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{
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float d, t, z;
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d = sqrt(x*x + y*y);
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if (d < r * 0.70710678118654752440) { /* Inside sphere */
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z = sqrt(r*r - d*d);
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} else { /* On hyperbola */
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t = r / 1.41421356237309504880;
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z = t*t / d;
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}
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return z;
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}
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/*
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* Given two rotations, e1 and e2, expressed as quaternion rotations,
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* figure out the equivalent single rotation and stuff it into dest.
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*
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* This routine also normalizes the result every RENORMCOUNT times it is
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* called, to keep error from creeping in.
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*
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* NOTE: This routine is written so that q1 or q2 may be the same
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* as dest (or each other).
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*/
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#define RENORMCOUNT 97
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void
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add_quats(float q1[4], float q2[4], float dest[4])
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{
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static int count=0;
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int i;
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float t1[4], t2[4], t3[4];
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float tf[4];
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vcopy(q1,t1);
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vscale(t1,q2[3]);
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vcopy(q2,t2);
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vscale(t2,q1[3]);
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vcross(q2,q1,t3);
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vadd(t1,t2,tf);
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vadd(t3,tf,tf);
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tf[3] = q1[3] * q2[3] - vdot(q1,q2);
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dest[0] = tf[0];
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dest[1] = tf[1];
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dest[2] = tf[2];
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dest[3] = tf[3];
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if (++count > RENORMCOUNT) {
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count = 0;
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normalize_quat(dest);
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}
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}
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/*
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* Quaternions always obey: a^2 + b^2 + c^2 + d^2 = 1.0
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* If they don't add up to 1.0, dividing by their magnitued will
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* renormalize them.
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*
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* Note: See the following for more information on quaternions:
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*
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* - Shoemake, K., Animating rotation with quaternion curves, Computer
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* Graphics 19, No 3 (Proc. SIGGRAPH'85), 245-254, 1985.
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* - Pletinckx, D., Quaternion calculus as a basic tool in computer
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* graphics, The Visual Computer 5, 2-13, 1989.
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*/
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static void
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normalize_quat(float q[4])
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{
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int i;
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float mag;
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mag = (q[0]*q[0] + q[1]*q[1] + q[2]*q[2] + q[3]*q[3]);
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for (i = 0; i < 4; i++) q[i] /= mag;
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}
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/*
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* Build a rotation matrix, given a quaternion rotation.
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*
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*/
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void
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build_rotmatrix(float m[4][4], float q[4])
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{
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m[0][0] = 1.0 - 2.0 * (q[1] * q[1] + q[2] * q[2]);
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m[0][1] = 2.0 * (q[0] * q[1] - q[2] * q[3]);
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m[0][2] = 2.0 * (q[2] * q[0] + q[1] * q[3]);
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m[0][3] = 0.0;
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m[1][0] = 2.0 * (q[0] * q[1] + q[2] * q[3]);
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m[1][1]= 1.0 - 2.0 * (q[2] * q[2] + q[0] * q[0]);
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m[1][2] = 2.0 * (q[1] * q[2] - q[0] * q[3]);
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m[1][3] = 0.0;
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m[2][0] = 2.0 * (q[2] * q[0] - q[1] * q[3]);
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m[2][1] = 2.0 * (q[1] * q[2] + q[0] * q[3]);
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m[2][2] = 1.0 - 2.0 * (q[1] * q[1] + q[0] * q[0]);
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m[2][3] = 0.0;
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m[3][0] = 0.0;
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m[3][1] = 0.0;
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m[3][2] = 0.0;
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m[3][3] = 1.0;
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}
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