trackball.cpp

#include <math.h>
#include "trackball.hpp"

/*******************************************************
 * 
 * void vCalcRotVec(float fNewX, float fNewY, 
 *                  float fOldX, float fOldY,
 *                  float fDiameter,
 *                  float *fVecX, float *fVecY, float *fVecZ);
 *
 *    Calculates a rotation vector based on mouse motion over
 *    a virtual trackball.
 *
 *    The fNew and fOld mouse positions
 *    should be in 'trackball' space. That is, they have been
 *    transformed into a coordinate system centered at the middle
 *    of the trackball. fNew, fOld, and fDiameter must all be specified
 *    in the same units (pixels for example).
 *
 * Parameters: fNewX, fNewY - New mouse position in trackball space.
 *                            This is the second point along direction
 *                            of rotation.
 *             fOldX, fOldY - Old mouse position in trackball space.
 *                            This is the first point along direction
 *                            of rotation.
 *             fDiameter - Diameter of the trackball. This should
 *                         be specified in the same units as fNew and fOld.
 *                         (ie, usually pixels if fNew and fOld are transformed
 *                         mouse positions)
 *             fVec - The output rotation vector. The length of the vector
 *                    is proportional to the angle of rotation.
 *
 *******************************************************/
void vCalcRotVec(float fNewX, float fNewY,
                 float fOldX, float fOldY,
                 float fDiameter,
                 float *fVecX, float *fVecY, float *fVecZ) {
   long  nXOrigin, nYOrigin;
   float fNewVecX, fNewVecY, fNewVecZ,        /* Vector corresponding to new mouse location */
         fOldVecX, fOldVecY, fOldVecZ,        /* Vector corresponding to old mouse location */
         fLength;

   /* Vector pointing from center of virtual trackball to
    * new mouse position
    */
   fNewVecX    = fNewX * 2.0 / fDiameter;
   fNewVecY    = fNewY * 2.0 / fDiameter;
   fNewVecZ    = (1.0 - fNewVecX * fNewVecX - fNewVecY * fNewVecY);

   /* If the Z component is less than 0, the mouse point
    * falls outside of the trackball which is interpreted
    * as rotation about the Z axis.
    */
   if (fNewVecZ < 0.0) {
      fLength = sqrt(1.0 - fNewVecZ);
      fNewVecZ  = 0.0;
      fNewVecX /= fLength;
      fNewVecY /= fLength;
   } else {
      fNewVecZ = sqrt(fNewVecZ);
   }

   /* Vector pointing from center of virtual trackball to
    * old mouse position
    */
   fOldVecX    = fOldX * 2.0 / fDiameter;
   fOldVecY    = fOldY * 2.0 / fDiameter;
   fOldVecZ    = (1.0 - fOldVecX * fOldVecX - fOldVecY * fOldVecY);
 
   /* If the Z component is less than 0, the mouse point
    * falls outside of the trackball which is interpreted
    * as rotation about the Z axis.
    */
   if (fOldVecZ < 0.0) {
      fLength = sqrt(1.0 - fOldVecZ);
      fOldVecZ  = 0.0;
      fOldVecX /= fLength;
      fOldVecY /= fLength;
   } else {
      fOldVecZ = sqrt(fOldVecZ);
   }

   /* Generate rotation vector by calculating cross product:
    * 
    * fOldVec x fNewVec.
    * 
    * The rotation vector is the axis of rotation
    * and is non-unit length since the length of a crossproduct
    * is related to the angle between fOldVec and fNewVec which we need
    * in order to perform the rotation.
    */
   *fVecX = fOldVecY * fNewVecZ - fNewVecY * fOldVecZ;
   *fVecY = fOldVecZ * fNewVecX - fNewVecZ * fOldVecX;
   *fVecZ = fOldVecX * fNewVecY - fNewVecX * fOldVecY;
}

/*******************************************************
 * void vAxisRotMatrix(float fVecX, float fVecY, float fVecZ, Matrix mNewMat)
 *    
 *    Calculate the rotation matrix for rotation about an arbitrary axis.
 *    
 *    The axis of rotation is specified by (fVecX,fVecY,fVecZ). The length
 *    of the vector is the amount to rotate by.
 *
 * Parameters: fVecX,fVecY,fVecZ - Axis of rotation
 *             mNewMat - Output matrix of rotation in column-major format
 *                       (ie, translation components are in column 3 on rows
 *                       0,1, and 2).
 *
 *******************************************************/
glm::mat4 vAxisRotMatrix(float fVecX, float fVecY, float fVecZ) {
	glm::mat4 mNewMat;
    float fRadians, fInvLength, fNewVecX, fNewVecY, fNewVecZ;

    /* Find the length of the vector which is the angle of rotation
     * (in radians)
     */
    fRadians = sqrt(fVecX * fVecX + fVecY * fVecY + fVecZ * fVecZ);

    /* If the vector has zero length - return the identity matrix */
    if (fRadians > -0.000001 && fRadians < 0.000001) {
        mNewMat = glm::mat4();
        return mNewMat;
    }

    /* Normalize the rotation vector now in preparation for making
     * rotation matrix. 
     */
    fInvLength = 1 / fRadians;
    fNewVecX   = fVecX * fInvLength;
    fNewVecY   = fVecY * fInvLength;
    fNewVecZ   = fVecZ * fInvLength;

    /* Create the arbitrary axis rotation matrix */
    double dSinAlpha = sin(fRadians);
    double dCosAlpha = cos(fRadians);
    double dT = 1 - dCosAlpha;

    mNewMat[0][0] = dCosAlpha + fNewVecX*fNewVecX*dT;
    mNewMat[0][1] = fNewVecX*fNewVecY*dT + fNewVecZ*dSinAlpha;
    mNewMat[0][2] = fNewVecX*fNewVecZ*dT - fNewVecY*dSinAlpha;
    mNewMat[0][3] = 0;

    mNewMat[1][0] = fNewVecX*fNewVecY*dT - dSinAlpha*fNewVecZ;
    mNewMat[1][1] = dCosAlpha + fNewVecY*fNewVecY*dT;
    mNewMat[1][2] = fNewVecY*fNewVecZ*dT + dSinAlpha*fNewVecX;
    mNewMat[1][3] = 0;

    mNewMat[2][0] = fNewVecZ*fNewVecX*dT + dSinAlpha*fNewVecY;
    mNewMat[2][1] = fNewVecZ*fNewVecY*dT - dSinAlpha*fNewVecX;
    mNewMat[2][2] = dCosAlpha + fNewVecZ*fNewVecZ*dT;
    mNewMat[2][3] = 0;

    mNewMat[3][0] = 0;
    mNewMat[3][1] = 0;
    mNewMat[3][2] = 0;
    mNewMat[3][3] = 1;
    
    return mNewMat;
}