flightgear/src/GUI/trackball.c

/*
 * Trackball code:
 *
 * Implementation of a virtual trackball.
 * Implemented by Gavin Bell, lots of ideas from Thant Tessman and
 *   the August '88 issue of Siggraph's "Computer Graphics," pp. 121-129.
 *
 * Vector manip code:
 *
 * Original code from:
 * David M. Ciemiewicz, Mark Grossman, Henry Moreton, and Paul Haeberli
 *
 * Much mucking with by:
 * Gavin Bell
 */

#if defined(_WIN32) && !defined( __CYGWIN32__ )
#pragma warning (disable:4244)          /* disable bogus conversion warnings */
#endif
#include <math.h>
#include <stdio.h>
#include "trackball.h"

/*
 * This size should really be based on the distance from the center of
 * rotation to the point on the object underneath the mouse.  That
 * point would then track the mouse as closely as possible.  This is a
 * simple example, though, so that is left as an Exercise for the
 * Programmer.
 */
#define TRACKBALLSIZE  (0.8f)
#define SQRT(x) sqrt(x)

/*
 * Local function prototypes (not defined in trackball.h)
 */
static float tb_project_to_sphere(float, float, float);
static void normalize_quat(float [4]);

static void
   vzero(float *v)
{
	v[0] = 0.0;
	v[1] = 0.0;
	v[2] = 0.0;
}

static void
   vset(float *v, float x, float y, float z)
{
	v[0] = x;
	v[1] = y;
	v[2] = z;
}

static void
   vsub(const float *src1, const float *src2, float *dst)
{
	dst[0] = src1[0] - src2[0];
	dst[1] = src1[1] - src2[1];
	dst[2] = src1[2] - src2[2];
}

static void
   vcopy(const float *v1, float *v2)
{
	register int i;
	for (i = 0 ; i < 3 ; i++)
		v2[i] = v1[i];
}

static void
   vcross(const float *v1, const float *v2, float *cross)
{
	float temp[3];

	temp[0] = (v1[1] * v2[2]) - (v1[2] * v2[1]);
	temp[1] = (v1[2] * v2[0]) - (v1[0] * v2[2]);
	temp[2] = (v1[0] * v2[1]) - (v1[1] * v2[0]);
	vcopy(temp, cross);
}

static float
   vlength(const float *v)
{
	float tmp = v[0] * v[0] + v[1] * v[1] + v[2] * v[2];
	return SQRT(tmp);
}

static void
   vscale(float *v, float div)
{
	v[0] *= div;
	v[1] *= div;
	v[2] *= div;
}

static void
   vnormal(float *v)
{
	vscale(v,1.0/vlength(v));
}

static float
   vdot(const float *v1, const float *v2)
{
	return v1[0]*v2[0] + v1[1]*v2[1] + v1[2]*v2[2];
}

static void
   vadd(const float *src1, const float *src2, float *dst)
{
	dst[0] = src1[0] + src2[0];
	dst[1] = src1[1] + src2[1];
	dst[2] = src1[2] + src2[2];
}

/*
 *  Given an axis and angle, compute quaternion.
 */
void
   axis_to_quat(float a[3], float phi, float q[4])
{
	double sinphi2, cosphi2;
	double phi2 = phi/2.0;
	sinphi2 = sin(phi2);
	cosphi2 = cos(phi2);
	vnormal(a);
	vcopy(a,q);
	vscale(q,sinphi2);
	q[3] = cosphi2;
}

/*
 * Project an x,y pair onto a sphere of radius r OR a hyperbolic sheet
 * if we are away from the center of the sphere.
 */
static float
   tb_project_to_sphere(float r, float x, float y)
{
	float d, t, z, tmp;

	tmp = x*x + y*y;
	d = SQRT(tmp);
	if (d < r * 0.70710678118654752440) {    /* Inside sphere */
		tmp = r*r - d*d;
		z = SQRT(tmp);
	} else {           /* On hyperbola */
		t = r / 1.41421356237309504880;
		z = t*t / d;
	}
	return z;
}

/*
 * Quaternions always obey:  a^2 + b^2 + c^2 + d^2 = 1.0
 * If they don't add up to 1.0, dividing by their magnitued will
 * renormalize them.
 *
 * Note: See the following for more information on quaternions:
 *
 * - Shoemake, K., Animating rotation with quaternion curves, Computer
 *   Graphics 19, No 3 (Proc. SIGGRAPH'85), 245-254, 1985.
 * - Pletinckx, D., Quaternion calculus as a basic tool in computer
 *   graphics, The Visual Computer 5, 2-13, 1989.
 */
static void
   normalize_quat(float q[4])
{
	int i;
	float mag, tmp;

	tmp = q[0]*q[0] + q[1]*q[1] + q[2]*q[2] + q[3]*q[3];
	mag = 1.0 / SQRT(tmp);
	for (i = 0; i < 4; i++)
		q[i] *= mag;
}

/*
 * Ok, simulate a track-ball.  Project the points onto the virtual
 * trackball, then figure out the axis of rotation, which is the cross
 * product of P1 P2 and O P1 (O is the center of the ball, 0,0,0)
 * Note:  This is a deformed trackball-- is a trackball in the center,
 * but is deformed into a hyperbolic sheet of rotation away from the
 * center.  This particular function was chosen after trying out
 * several variations.
 *
 * It is assumed that the arguments to this routine are in the range
 * (-1.0 ... 1.0)
 */
void
   trackball(float q[4], float p1x, float p1y, float p2x, float p2y)
{
	float a[3]; /* Axis of rotation */
	float phi;  /* how much to rotate about axis */
	float p1[3], p2[3], d[3];
	float t;

	if (p1x == p2x && p1y == p2y) {
		/* Zero rotation */
		vzero(q);
		q[3] = 1.0;
		return;
	}

	/*
	 * First, figure out z-coordinates for projection of P1 and P2 to
	 * deformed sphere
	 */
	vset(p1,p1x,p1y,tb_project_to_sphere(TRACKBALLSIZE,p1x,p1y));
	vset(p2,p2x,p2y,tb_project_to_sphere(TRACKBALLSIZE,p2x,p2y));

	/*
	 *  Now, we want the cross product of P1 and P2
	 */
	vcross(p2,p1,a);

	/*
	 *  Figure out how much to rotate around that axis.
	 */
	vsub(p1,p2,d);
	t = vlength(d) / (2.0*TRACKBALLSIZE);

	/*
	 * Avoid problems with out-of-control values...
	 */
	if (t > 1.0) t = 1.0;
	if (t < -1.0) t = -1.0;
	phi = 2.0 * asin(t);

	axis_to_quat(a,phi,q);
}

/*
 * Given two rotations, e1 and e2, expressed as quaternion rotations,
 * figure out the equivalent single rotation and stuff it into dest.
 *
 * This routine also normalizes the result every RENORMCOUNT times it is
 * called, to keep error from creeping in.
 *
 * NOTE: This routine is written so that q1 or q2 may be the same
 * as dest (or each other).
 */

#define RENORMCOUNT 97

void
   add_quats(float q1[4], float q2[4], float dest[4])
{
	static int count=0;
	float t1[4], t2[4], t3[4];
	float tf[4];

#if 0
	printf("q1 = %f %f %f %f\n", q1[0], q1[1], q1[2], q1[3]);
	printf("q2 = %f %f %f %f\n", q2[0], q2[1], q2[2], q2[3]);
#endif

	vcopy(q1,t1);
	vscale(t1,q2[3]);

	vcopy(q2,t2);
	vscale(t2,q1[3]);

	vcross(q2,q1,t3);
	vadd(t1,t2,tf);
	vadd(t3,tf,tf);
	tf[3] = q1[3] * q2[3] - vdot(q1,q2);

#if 0
	printf("tf = %f %f %f %f\n", tf[0], tf[1], tf[2], tf[3]);
#endif

	dest[0] = tf[0];
	dest[1] = tf[1];
	dest[2] = tf[2];
	dest[3] = tf[3];

	if (++count > RENORMCOUNT) {
		count = 0;
		normalize_quat(dest);
	}
}

/*
 * Build a rotation matrix, given a quaternion rotation.
 *
 */
void  build_rotmatrix(float m[4][4], float q[4])
{
	m[0][0] = 1.0 - 2.0 * (q[1] * q[1] + q[2] * q[2]);
	m[0][1] = 2.0 * (q[0] * q[1] - q[2] * q[3]);
	m[0][2] = 2.0 * (q[2] * q[0] + q[1] * q[3]);
	m[0][3] = 0.0;

	m[1][0] = 2.0 * (q[0] * q[1] + q[2] * q[3]);
	m[1][1]= 1.0 - 2.0 * (q[2] * q[2] + q[0] * q[0]);
	m[1][2] = 2.0 * (q[1] * q[2] - q[0] * q[3]);
	m[1][3] = 0.0;

	m[2][0] = 2.0 * (q[2] * q[0] - q[1] * q[3]);
	m[2][1] = 2.0 * (q[1] * q[2] + q[0] * q[3]);
	m[2][2] = 1.0 - 2.0 * (q[1] * q[1] + q[0] * q[0]);

	m[2][3] = 0.0;
	m[3][0] = 0.0;
	m[3][1] = 0.0;
	m[3][2] = 0.0;
	m[3][3] = 1.0;
}

void  build_transposed_rotmatrix(float m[4][4], float q[4])
{
	m[0][0] = 1.0 - 2.0 * (q[1] * q[1] + q[2] * q[2]);
	m[0][1] = 2.0 * (q[0] * q[1] + q[2] * q[3]);
	m[0][2] = 2.0 * (q[2] * q[0] - q[1] * q[3]);
	m[0][3] = 0.0;

	m[1][0] = 2.0 * (q[0] * q[1] - q[2] * q[3]);
	m[1][1] = 1.0 - 2.0 * (q[2] * q[2] + q[0] * q[0]);
	m[1][2] = 2.0 * (q[1] * q[2] + q[0] * q[3]);
	m[1][3] = 0.0;

	m[2][0] = 2.0 * (q[2] * q[0] + q[1] * q[3]);
	m[2][1] = 2.0 * (q[1] * q[2] - q[0] * q[3]);
	m[2][2] = 1.0 - 2.0 * (q[1] * q[1] + q[0] * q[0]);
	m[2][3] = 0.0;

	m[3][0] = 0.0;
	m[3][1] = 0.0;
	m[3][2] = 0.0;
	m[3][3] = 1.0;
}