trackball.cpp

/*
 * (c) Copyright 1993, 1994, Silicon Graphics, Inc.
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 * restrictions set forth in FAR 52.227.19(c)(2) or subparagraph
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 * Unpublished-- rights reserved under the copyright laws of the
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 * Inc., 2011 N.  Shoreline Blvd., Mountain View, CA 94039-7311.
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/*
 * 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], 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;
}