/*

 * (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 * Unpublished-- rights reserved under the copyright laws of the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]);

void

vzero(float *v)

{

    v[0] = 0.0;

    v[1] = 0.0;

    v[2] = 0.0;

}

void

vset(float *v, float x, float y, float z)

{

    v[0] = x;

    v[1] = y;

    v[2] = z;

}

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];

}

void

vcopy(const float *v1, float *v2)

{

    int i;

    for (i = 0 ; i < 3 ; i++)

        v2[i] = v1[i];

}

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);

}

float

vlength(const float *v)

{

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

}

void

vscale(float *v, float div)

{

    v[0] *= div;

    v[1] *= div;

    v[2] *= div;

}

void

vnormal(float *v)

{

    vscale(v,1.0/vlength(v));

}

float

vdot(const float *v1, const float *v2)

{

    return v1[0]*v2[0] + v1[1]*v2[1] + v1[2]*v2[2];

}

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], 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;

}