Max 5 API Reference

trackball.c

/*
 * (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
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 * ADVISED OF THE POSSIBILITY OF SUCH LOSS, HOWEVER CAUSED AND ON
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 * 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 * Unpublished-- rights reserved under the copyright laws of the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"
#include "jit.gl.h"
#include "jit.math.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  (0.4)

/*
 * 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 normalize_quatd(double [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)
{
    register 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 jit_math_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];
}


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

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

void
vdsub(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
vdcopy(const double *v1, double *v2)
{
    register int i;
    for (i = 0 ; i < 3 ; i++)
        v2[i] = v1[i];
}

void
vdcross(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]);
    vdcopy(temp, cross);
}

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

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

void
vdnormal(double *v)
{
    vdscale(v,1.0/vdlength(v));
}

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

void vdadd(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(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 * jit_math_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,jit_math_sin(phi/2.0));
    q[3] = jit_math_cos(phi/2.0);
}


// compute axis/angle rotation from quaternion. added by rej. 
void
quat_to_axis(float q[4], float axis[3], float * phi)
{
    float cos_a, sin_a;
    
    cos_a = q[3];
    *phi = jit_math_acos(cos_a) * 2.;
    sin_a = jit_math_sqrt(1.0 - cos_a * cos_a);
    
    if (fabs(sin_a) < 0.0005)
        sin_a = 1;
        
    axis[0] = q[0] / sin_a;
    axis[1] = q[1] / sin_a;
    axis[2] = q[2] / sin_a;
}

void
xyz_to_axis(float xyz[3], float axis[3], float * phi)
{
    float vec[3];
    float q1[4],q2[4],q3[4];
    
    // convert xyz to angle/axis
    jit_gl_set_floats(vec, 3, 1., 0., 0.);      
    axis_to_quat(vec, xyz[0], q1);  

    jit_gl_set_floats(vec, 3, 0., 1., 0.);      
    axis_to_quat(vec, xyz[1], q2);  
    add_quats(q1,q2,q3);
    
    jit_gl_set_floats(vec, 3, 0., 0., 1.);      
    axis_to_quat(vec, xyz[2], q2);  
    add_quats(q3,q2,q1);
    
    normalize_quat(q1); // to solve people's complaints with rotatexyz differing by ~0.00001%
    
    quat_to_axis(q1, axis, phi);    
}

void
axis_to_xyz(float axis[3], float phi, float xyz[3])
{
    double fCos = cos(phi);
    double fSin = sin(phi);
    double fOneMinusCos = 1.0-fCos;
    double fX2 = axis[0]*axis[0];
    double fY2 = axis[1]*axis[1];
    double fZ2 = axis[2]*axis[2];
    double fXYM = axis[0]*axis[1]*fOneMinusCos;
    double fXZM = axis[0]*axis[2]*fOneMinusCos;
    double fYZM = axis[1]*axis[2]*fOneMinusCos;
    double fXSin = axis[0]*fSin;
    double fYSin = axis[1]*fSin;
    double fZSin = axis[2]*fSin;
    double m[9];

    // convert axis angle to rotation matrix
    m[0] = fX2*fOneMinusCos+fCos;
    m[1] = fXYM-fZSin;
    m[2] = fXZM+fYSin;
    m[3] = fXYM+fZSin;
    m[4] = fY2*fOneMinusCos+fCos;
    m[5] = fYZM-fXSin;
    m[6] = fXZM-fYSin;
    m[7] = fYZM+fXSin;
    m[8] = fZ2*fOneMinusCos+fCos;


    // convert matrix to euler angles

    // fromEulerAnglesZYX (ZYX the mathematical order of matrix concatenation)
    // rot =  cy*cz           cz*sx*sy-cx*sz  cx*cz*sy+sx*sz
    //        cy*sz           cx*cz+sx*sy*sz -cz*sx+cx*sy*sz
    //       -sy              cy*sx           cx*cy

    if ( m[6] < 1.0 )
    {
        if ( m[6] > -1.0 )
        {
            xyz[2] = atan2(m[3],m[0]);
            xyz[1] = asin(-(double)m[6]);
            xyz[0] = atan2(m[7],m[8]);
        }
        else
        {
            // WARNING.  Not unique.  ZA - XA = -atan2(r01,r02)
            xyz[2] = -atan2(m[1],m[2]);
            xyz[1] = PI/2.0;
            xyz[0] = 0.0;
        }
    }
    else
    {
        // WARNING.  Not unique.  ZA + XA = atan2(-r01,-r02)
        xyz[2] = atan2(-m[1],-m[2]);
        xyz[1] = -PI/2.0;
        xyz[0] = 0.0;
    }
}

/*
 * 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 = jit_math_sqrt(x*x + y*y);
    if (d < r * 0.70710678118654752440) {    /* Inside sphere */
        z = jit_math_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 0 //97


void
add_quats(float q1[4], float q2[4], float dest[4])
{
    static int count=0;
    double qd1[4],qd2[4];
    double t1[4], t2[4], t3[4];
    double tf[4];
    
    //vdcopy(qd1,t1);
    t1[0] = qd1[0] = q1[0];
    t1[1] = qd1[1] = q1[1];
    t1[2] = qd1[2] = q1[2];
    t1[3] = qd1[3] = q1[3];

    //vdcopy(qd2,t2);
    t2[0] = qd2[0] = q2[0];
    t2[1] = qd2[1] = q2[1];
    t2[2] = qd2[2] = q2[2];
    t2[3] = qd2[3] = q2[3];

    vdscale(t1,qd2[3]);
    vdscale(t2,qd1[3]);

    vdcross(qd2,qd1,t3);
    vdadd(t1,t2,tf);
    vdadd(t3,tf,tf);
    tf[3] = qd1[3] * qd2[3] - vddot(qd1,qd2);

    normalize_quatd(tf);

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

}

/*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 magnitude 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 = 1./(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;
}

static void
normalize_quatd(double q[4])
{
    int i;
    double mag;

    mag = 1./(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.
 * where the matrix is m1       m4      m8      m12
 *                     m2       m5      m9      m13
 *                     m3       m6      m10     m14
 *                     m4       m7      m11     m15
 *
 */
 
void
build_rotmatrix(float m[16], float q[4])
{
    m[0] = 1.0 - 2.0 * (q[1] * q[1] + q[2] * q[2]);
    m[4] = 2.0 * (q[0] * q[1] - q[2] * q[3]);
    m[8] = 2.0 * (q[2] * q[0] + q[1] * q[3]);
    m[12] = 0.0;

    m[1] = 2.0 * (q[0] * q[1] + q[2] * q[3]);
    m[5] = 1.0 - 2.0 * (q[2] * q[2] + q[0] * q[0]);
    m[9] = 2.0 * (q[1] * q[2] - q[0] * q[3]);
    m[13] = 0.0;

    m[2] = 2.0 * (q[2] * q[0] - q[1] * q[3]);
    m[6] = 2.0 * (q[1] * q[2] + q[0] * q[3]);
    m[10] = 1.0 - 2.0 * (q[1] * q[1] + q[0] * q[0]);
    m[14] = 0.0;

    m[3] = 0.0;
    m[7] = 0.0;
    m[11] = 0.0;
    m[15] = 1.0;
}


/*
 * Transform a point (column vector) by a 4x4 matrix.  I.e.  out = m * in
 * Input:  m - the 4x4 matrix
 *         in - the 4x1 vector
 * Output:  out - the resulting 4x1 vector.
 */
void transform_point(const float in[4], const float m[16], float out[4])
{
#define M(row,col)  m[col*4+row]
   out[0] =
      M(0, 0) * in[0] + M(0, 1) * in[1] + M(0, 2) * in[2] + M(0, 3) * in[3];
   out[1] =
      M(1, 0) * in[0] + M(1, 1) * in[1] + M(1, 2) * in[2] + M(1, 3) * in[3];
   out[2] =
      M(2, 0) * in[0] + M(2, 1) * in[1] + M(2, 2) * in[2] + M(2, 3) * in[3];
   out[3] =
      M(3, 0) * in[0] + M(3, 1) * in[1] + M(3, 2) * in[2] + M(3, 3) * in[3];
#undef M
}

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