quaternion.cpp

/***********************************************************************

  quaternion.cpp - A quaternion class

  -------------------------------------------------------------------

  GLUI User Interface Toolkit (LGPL)
  Copyright (c) 1998 Paul Rademacher

  WWW:    http://sourceforge.net/projects/glui/
  Forums: http://sourceforge.net/forum/?group_id=92496

  This library is free software; you can redistribute it and/or
  modify it under the terms of the GNU Lesser General Public
  License as published by the Free Software Foundation; either
  version 2.1 of the License, or (at your option) any later version.

  This library is distributed in the hope that it will be useful,
  but WITHOUT ANY WARRANTY; without even the implied warranty of
  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  Lesser General Public License for more details.

  You should have received a copy of the GNU Lesser General Public
  License along with this library; if not, write to the Free Software
  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA

************************************************************************

  Feb 1998, Paul Rademacher (rademach@cs.unc.edu)
  Oct 2003, Nigel Stewart - GLUI Code Cleaning
  
************************************************************************/

#include "quaternion.h"
#include <cmath>
#include "glui_internal.h"

/******************************************* constructors **************/

quat::quat()
{
    *this = quat_identity();
}

quat::quat(const float x, const float y, const float z, const float w)
{
    v.set( x, y, z );
    s = w;
}

quat::quat(const vec3 &_v, const float _s)
{
    set( _v, _s );
}

quat::quat(const float _s, const vec3 &_v)
{
    set( _v, _s );
}

quat::quat(const float *d)
{
    v[0] = d[0];
    v[1] = d[1];
    v[2] = d[2];
    s    = d[3];
}

quat::quat(const double *d)
{
    v[0] = (float) d[0];
    v[1] = (float) d[1];
    v[2] = (float) d[2];
    s    = (float) d[3];
}

quat::quat(const quat &q)
{
    v = q.v;
    s = q.s;
}

void quat::set(const vec3 &_v, const float _s)
{
    v = _v;
    s = _s;
}

quat &quat::operator=(const quat &q)
{ 
    v = q.v;  
    s = q.s; 
    return *this; 
}

/******** quat friends ************/

quat operator + (const quat &a, const quat &b)
{
    return quat( a.s+b.s, a.v+b.v );
}

quat operator - (const quat &a, const quat &b)
{
    return quat( a.s-b.s, a.v-b.v );
}

quat operator - (const quat &a )
{
    return quat( -a.s, -a.v );
}

quat operator * ( const quat &a, const quat &b)
{
    //return quat( a.s*b.s - a.v*b.v, a.s*b.v + b.s*a.v + a.v^b.v );
    return quat( a.s*b.s - a.v*b.v, a.s*b.v + b.s*a.v + (a.v^b.v) );
}

quat operator * ( const quat &a, const float t)
{
    return quat( a.v * t, a.s * t );
}

quat operator * ( const float t, const quat &a )
{
    return quat( a.v * t, a.s * t );
}

mat4 quat::to_mat4() const
{
    float xs, ys, zs, wx, wy, wz, xx, xy, xz, yy, yz, zz;

    float t  = 2.0f / (v*v + s*s);

    xs = v[VX]*t;   ys = v[VY]*t;   zs = v[VZ]*t;
    wx = s*xs;      wy = s*ys;      wz = s*zs;
    xx = v[VX]*xs;  xy = v[VX]*ys;  xz = v[VX]*zs;
    yy = v[VY]*ys;  yz = v[VY]*zs;  zz = v[VZ]*zs;

    mat4 matrix( 
           1.0f-(yy+zz), xy+wz,        xz-wy,        0.0f,
           xy-wz,        1.0f-(xx+zz), yz+wx,        0.0f,
           xz+wy,        yz-wx,        1.0f-(xx+yy), 0.0f,
           0.0f,         0.0f,         0.0f,         1.0f );

    return matrix;
}

/************************************************* quat_identity() *****/
/* Returns quaternion identity element                                 */

quat quat_identity() 
{
    return quat( vec3( 0.0, 0.0, 0.0 ), 1.0 );
}

/************************************************ quat_slerp() ********/
/* Quaternion spherical interpolation                                 */

quat quat_slerp(const quat &from, const quat &to, float t)
{
    quat to1;
    float omega, cosom, sinom, scale0, scale1;

    /* calculate cosine */
    cosom = from.v * to.v + from.s + to.s;

    /* Adjust signs (if necessary) */
    if ( cosom < 0.0 ) 
    {
        cosom = -cosom;
        to1 = -to;
    }
    else
    {
        to1 = to;
    }

    /* Calculate coefficients */
    if ((1.0 - cosom) > FUDGE ) 
    {
        /* standard case (slerp) */
        omega =  (float) acos( cosom );
        sinom =  (float) sin( omega );
        scale0 = (float) sin((1.0 - t) * omega) / sinom;
        scale1 = (float) sin(t * omega) / sinom;
    }
    else 
    {
        /* 'from' and 'to' are very close - just do linear interpolation */
        scale0 = 1.0f - t;
        scale1 = t;      
    }

    return scale0 * from + scale1 * to1;
}

/********************************************** set_angle() ************/
/* set rot angle (degrees)                                             */

void quat::set_angle(float f)
{
    vec3 axis = get_axis();

    s = (float) cos( DEG2RAD( f ) / 2.0 );

    v = axis * (float) sin(DEG2RAD(f) / 2.0);
}

/********************************************** scale_angle() ************/
/* scale rot angle (degrees)                                             */

void quat::scale_angle(float f)
{
    set_angle( f * get_angle() );
}

/********************************************** get_angle() ************/
/* get rot angle (degrees).  Assumes s is between -1 and 1             */

float quat::get_angle() const
{
    return (float) RAD2DEG( 2.0 * acos( s ) );
}

/********************************************* get_axis() **************/

vec3 quat::get_axis() const
{
    float scale = (float) sin( acos( s ) );

    if ( scale < FUDGE AND scale > -FUDGE )
        return vec3( 0.0, 0.0, 0.0 );
    else
        return  v / scale;
}

/******************************************* quat::print() ************/

void quat::print(FILE *dest, const char *name) const
{
    fprintf( dest, "%s:   v:<%3.2f %3.2f %3.2f>  s:%3.2f\n", 
        name, v[0], v[1], v[2], s );
}