examples/glview/trackball.cc - third_party/tinygltf - Git at Google

 /*
  * (c) Copyright 1993, 1994, Silicon Graphics, Inc.
  * ALL RIGHTS RESERVED
  * Permission to use, copy, modify, and distribute this software for
  * any purpose and without fee is hereby granted, provided that the above
  * copyright notice appear in all copies and that both the copyright notice
  * and this permission notice appear in supporting documentation, and that
  * the name of Silicon Graphics, Inc. not be used in advertising
  * or publicity pertaining to distribution of the software without specific,
  * written prior permission.
  *
  * THE MATERIAL EMBODIED ON THIS SOFTWARE IS PROVIDED TO YOU "AS-IS"
  * AND WITHOUT WARRANTY OF ANY KIND, EXPRESS, IMPLIED OR OTHERWISE,
  * INCLUDING WITHOUT LIMITATION, ANY WARRANTY OF MERCHANTABILITY OR
  * FITNESS FOR A PARTICULAR PURPOSE.  IN NO EVENT SHALL SILICON
  * GRAPHICS, INC.  BE LIABLE TO YOU OR ANYONE ELSE FOR ANY DIRECT,
  * SPECIAL, INCIDENTAL, INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY
  * KIND, OR ANY DAMAGES WHATSOEVER, INCLUDING WITHOUT LIMITATION,
  * LOSS OF PROFIT, LOSS OF USE, SAVINGS OR REVENUE, OR THE CLAIMS OF
  * THIRD PARTIES, WHETHER OR NOT SILICON GRAPHICS, INC.  HAS BEEN
  * ADVISED OF THE POSSIBILITY OF SUCH LOSS, HOWEVER CAUSED AND ON
  * ANY THEORY OF LIABILITY, ARISING OUT OF OR IN CONNECTION WITH THE
  * POSSESSION, USE OR PERFORMANCE OF THIS SOFTWARE.
  *
  * US Government Users Restricted Rights
  * Use, duplication, or disclosure by the Government is subject to
  * restrictions set forth in FAR 52.227.19(c)(2) or subparagraph
  * (c)(1)(ii) of the Rights in Technical Data and Computer Software
  * clause at DFARS 252.227-7013 and/or in similar or successor
  * clauses in the FAR or the DOD or NASA FAR Supplement.
  * Unpublished-- rights reserved under the copyright laws of the
  * United States.  Contractor/manufacturer is Silicon Graphics,
  * Inc., 2011 N.  Shoreline Blvd., Mountain View, CA 94039-7311.
  *
  * OpenGL(TM) is a trademark of Silicon Graphics, Inc.
  */
 /*
  * 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
  */
 #include <math.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 (0.8)

 /*
  * 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) {
   return sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);
 }

 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];
 }

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

 /*
  * 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;

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

 /*
  * 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];

   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);

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

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

 /*
  * 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;

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

 /*
  * Build a rotation matrix, given a quaternion rotation.
  *
  */
 void build_rotmatrix(float m[4][4], const 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;
 }
	/*
	* (c) Copyright 1993, 1994, Silicon Graphics, Inc.
	* ALL RIGHTS RESERVED
	* Permission to use, copy, modify, and distribute this software for
	* any purpose and without fee is hereby granted, provided that the above
	* copyright notice appear in all copies and that both the copyright notice
	* and this permission notice appear in supporting documentation, and that
	* the name of Silicon Graphics, Inc. not be used in advertising
	* or publicity pertaining to distribution of the software without specific,
	* written prior permission.
	*
	* THE MATERIAL EMBODIED ON THIS SOFTWARE IS PROVIDED TO YOU "AS-IS"
	* AND WITHOUT WARRANTY OF ANY KIND, EXPRESS, IMPLIED OR OTHERWISE,
	* INCLUDING WITHOUT LIMITATION, ANY WARRANTY OF MERCHANTABILITY OR
	* FITNESS FOR A PARTICULAR PURPOSE. IN NO EVENT SHALL SILICON
	* GRAPHICS, INC. BE LIABLE TO YOU OR ANYONE ELSE FOR ANY DIRECT,
	* SPECIAL, INCIDENTAL, INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY
	* KIND, OR ANY DAMAGES WHATSOEVER, INCLUDING WITHOUT LIMITATION,
	* LOSS OF PROFIT, LOSS OF USE, SAVINGS OR REVENUE, OR THE CLAIMS OF
	* THIRD PARTIES, WHETHER OR NOT SILICON GRAPHICS, INC. HAS BEEN
	* ADVISED OF THE POSSIBILITY OF SUCH LOSS, HOWEVER CAUSED AND ON
	* ANY THEORY OF LIABILITY, ARISING OUT OF OR IN CONNECTION WITH THE
	* POSSESSION, USE OR PERFORMANCE OF THIS SOFTWARE.
	*
	* US Government Users Restricted Rights
	* Use, duplication, or disclosure by the Government is subject to
	* restrictions set forth in FAR 52.227.19(c)(2) or subparagraph
	* (c)(1)(ii) of the Rights in Technical Data and Computer Software
	* clause at DFARS 252.227-7013 and/or in similar or successor
	* clauses in the FAR or the DOD or NASA FAR Supplement.
	* Unpublished-- rights reserved under the copyright laws of the
	* United States. Contractor/manufacturer is Silicon Graphics,
	* Inc., 2011 N. Shoreline Blvd., Mountain View, CA 94039-7311.
	*
	* OpenGL(TM) is a trademark of Silicon Graphics, Inc.
	*/
	/*
	* 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
	*/
	#include <math.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 (0.8)

	/*
	* 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) {
	return sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);
	}

	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];
	}

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

	/*
	* 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;

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

	/*
	* 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];

	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);

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

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

	/*
	* 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;

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

	/*
	* Build a rotation matrix, given a quaternion rotation.
	*
	*/
	void build_rotmatrix(float m[4][4], const 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;
	}