/*
 * (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 * Unpublished-- rights reserved under the copyright laws of the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 <cmath>
#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)

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

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

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

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

void vcopy( const double *v1, double *v2 )
{
    register int i;

    for( i = 0 ; i < 3 ; i++ )
        v2[i] = v1[i];
}

void vcross( const double *v1, const double *v2, double *cross )
{
    double 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);
}

double vlength( const double *v )
{
    return (double) sqrt( v[0] * v[0] + v[1] * v[1] + v[2] * v[2] );
}

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

void vnormal( double *v )
{
    vscale( v, 1.0f / vlength( v ) );
}

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

void vadd( const double *src1, const double *src2, double *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( double q[4], double p1x, double p1y, double p2x, double p2y )
{
    double a[3]; /* Axis of rotation */
    double phi;  /* how much to rotate about axis */
    double p1[3], p2[3], d[3];
    double 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 ) / (2.0f * TRACKBALLSIZE);

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

    if( t < -1.0 )
        t = -1.0;

    phi = 2.0f * (double) asin( t );

    axis_to_quat( a, phi, q );
}

/*
 *  Given an axis and angle, compute quaternion.
 */
void axis_to_quat( double a[3], double phi, double q[4] )
{
    vnormal( a );
    vcopy( a, q );
    vscale( q, (double) sin( phi / 2.0) );
    q[3] = (double) 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 double tb_project_to_sphere( double r, double x, double y )
{
    double d, z;

    d = (double) sqrt( x*x + y*y );

    if( d < r * 0.70710678118654752440 )
    {    /* Inside sphere */
        z = (double) sqrt( r*r - d*d );
    }
    else
    {           /* On hyperbola */
        const double t = r / 1.41421356237309504880f;
        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( double q1[4], double q2[4], double dest[4] )
{
    static int count=0;
    double t1[4], t2[4], t3[4];
    double 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( double q[4] )
{
    int i;
    double 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], double q[4] )
{
    m[0][0] = (float)(1.0 - 2.0 * (q[1] * q[1] + q[2] * q[2]));
    m[0][1] = (float)(2.0 * (q[0] * q[1] - q[2] * q[3]));
    m[0][2] = (float)(2.0 * (q[2] * q[0] + q[1] * q[3]));
    m[0][3] = 0.0f;

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

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

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