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2 bj 1 
#include "Vec3f.h"
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#include "Quaternion.h"
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12 jab 4 
namespace CGLA
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{
171 bj 6 
 
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	void Quaternion::make_rot(const Mat4x4f& m)
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	{
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		float trace = m[0][0] + m[1][1] + m[2][2]  + 1.0f;
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		//If the trace of the matrix is greater than zero, then
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		//perform an "instant" calculation.
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		if ( trace > TINY )
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		{
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			float S = sqrt(trace) * 2.0f;
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			qv = Vec3f(m[2][1] - m[1][2], m[0][2] - m[2][0], m[1][0] - m[0][1] );
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			qv /= S;
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			qw = 0.25f * S;
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		}
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		else
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		{
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			//If the trace of the matrix is equal to zero (or negative...) then identify
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			//which major diagonal element has the greatest value.
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			//Depending on this, calculate the following:
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			if ( m[0][0] > m[1][1] && m[0][0] > m[2][2] )  {	// Column 0:
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				float S  = sqrt( 1.0 + m[0][0] - m[1][1] - m[2][2] ) * 2.0f;
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				qv[0] = 0.25f * S;
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				qv[1] = (m[1][0] + m[0][1] ) / S;
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				qv[2] = (m[0][2] + m[2][0] ) / S;
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				qw = (m[2][1] - m[1][3] ) / S;
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			} else if ( m[1][1] > m[2][2] ) {			// Column 1:
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				float S  = sqrt( 1.0 + m[1][1] - m[0][0] - m[2][2] ) * 2.0f;
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				qv[0] = (m[1][0] + m[0][1] ) / S;
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				qv[1] = 0.25f * S;
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				qv[2] = (m[2][1] + m[1][2] ) / S;
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				qw = (m[0][2] - m[2][0] ) / S;
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			} else {						// Column 2:
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				float S  = sqrt( 1.0 + m[2][2] - m[0][0] - m[1][1] ) * 2.0f;
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				qv[0] = (m[0][2] + m[2][0] ) / S;
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				qv[1] = (m[2][1] + m[1][2] ) / S;
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				qv[2] = 0.25f * S;
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				qw = (m[1][0] - m[0][1] ) / S;
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			}
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		}
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		//The quaternion is then defined as:
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		//  Q = | X Y Z W |
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	}
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	void Quaternion::make_rot(float angle, const Vec3f& v)
12 jab 51 
  {
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    angle = angle/2;
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    qv = CGLA::normalize(v);
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    qv *= sin(angle);
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    qw  = cos(angle);
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  };
2 bj 57 
 
12 jab 58 
  void Quaternion::make_rot(const Vec3f& _v0, const Vec3f& _v1)
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  {
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    Vec3f v0 = CGLA::normalize(_v0);
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    Vec3f v1 = CGLA::normalize(_v1);
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    qv = cross(v0, v1);
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    float l = qv.length();
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    if(l<TINY)
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      qv = Vec3f(1,0,0);
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    else
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      qv.normalize();
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    float a = acos(dot(v0,v1))/2;
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    qw  = cos(a);
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    qv *= sin(a);
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  };
2 bj 72 
 
12 jab 73 
  void Quaternion::get_rot(float& angle, Vec3f& v)
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  {
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    angle=2*acos(qw);
2 bj 76 
 
12 jab 77 
    if (angle<TINY)
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      v = Vec3f(1,0,0);
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    else
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      v = qv / sin(angle);
2 bj 81 
 
12 jab 82 
    if (angle>M_PI)
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      v = -v;
2 bj 84 
 
12 jab 85 
    v.normalize();
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  }
2 bj 87 
 
12 jab 88 
  Mat3x3f Quaternion::get_mat3x3f() const
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  {
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    float s=2/norm();
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    float m[9] = {1 - s*(qv[1]*qv[1]+qv[2]*qv[2]),
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		  s*(qv[0]*qv[1]-qw*qv[2]),
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		  s*(qv[0]*qv[2]+qw*qv[1]),
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		  s*(qv[0]*qv[1]+qw*qv[2]),
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		  1 - s*(qv[0]*qv[0]+qv[2]*qv[2]),
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		  s*(qv[1]*qv[2]-qw*qv[0]),
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		  s*(qv[0]*qv[2]-qw*qv[1]),
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		  s*(qv[1]*qv[2]+qw*qv[0]),
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		  1 - s*(qv[0]*qv[0]+qv[1]*qv[1])};
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    Mat3x3f mat;
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    raw_assign(mat, m);
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    return mat;
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  }
2 bj 104 
 
105 
 
12 jab 106 
  //This function just need to call the right initialiser
2 bj 107 
 
12 jab 108 
  Mat4x4f Quaternion::get_mat4x4f() const
109 
  {
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    float s=2/norm();
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    float m[16] = {1 - s*(qv[1]*qv[1]+qv[2]*qv[2]),
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		   s*(qv[0]*qv[1]-qw*qv[2]),
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		   s*(qv[0]*qv[2]+qw*qv[1]),
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		   float(0),
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		   s*(qv[0]*qv[1]+qw*qv[2]),
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		   1 - s*(qv[0]*qv[0]+qv[2]*qv[2]),
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		   s*(qv[1]*qv[2]-qw*qv[0]),
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		   float(0),
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		   s*(qv[0]*qv[2]-qw*qv[1]),
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		   s*(qv[1]*qv[2]+qw*qv[0]),
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		   1 - s*(qv[0]*qv[0]+qv[1]*qv[1]),
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		   float(0),
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		   float(0),
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		   float(0),
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		   float(0),
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		   float(1)};
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    Mat4x4f mat;
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    raw_assign(mat, m);
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    return mat;
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  }
2 bj 131 
 
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12 jab 133 
  Vec3f Quaternion::apply(const Vec3f& vec) const
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  {
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    return Vec3f((*this)*Quaternion(vec)*inverse());
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  }
2 bj 137 
 
138 
 
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}