mesh_conv::MC_quaternion Class Reference

Class of quaternion. More...

#include <MC_quaternion.hpp>

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List of all members.

Public Member Functions
	MC_quaternion ()
	zero contructor (set unitary axis (0,0,1) and zero angle )
	MC_quaternion (const MC_v3d &axis, const double &angle)
	constructor from axis and angle
	MC_quaternion (const MC_v4d &v)
	constructor from base class: v4d
	MC_quaternion (const MC_quaternion &q)
	copy constructor
	MC_quaternion (const double &x, const double &y, const double &z, const double &w)
	direct constructor from coefficients
MC_matrix	matrix () const
	compute the rotation matrix associated to the current quaternion
MC_quaternion	conjugated () const
	get the conjugate of the current quaterion
MC_quaternion &	operator*= (const MC_quaternion &q1)
	internal multiplication between quaternion
MC_quaternion	pow (const double &t) const
	power of a quaternion with a double
MC_quaternion	inverted () const
	invert the quaternion
MC_v3d	log () const
	log map
MC_v3d	axis () const
	get the unit axis corresponding to the quaternion
double	angle () const
	get the angle corresponding to the quaternion
Static Public Member Functions
static MC_quaternion	exp (const MC_v3d &v)
	exp map
static MC_quaternion	slerp (const MC_quaternion &q0, const MC_quaternion &q1, const double &t)
	Spherical Linear Interpolation SLERP.
static MC_quaternion	quat_interp (const std::vector< MC_quaternion > &quaternion_vec, const MC_double_vector &weights)
static MC_matrix	quat_interp (const std::vector< MC_matrix > &matrix_vec, const MC_double_vector &weights)
	Generalized approximate spherical interpolation for rotation and linear one for translation.
static MC_matrix	quat_interp (const std::vector< MC_quaternion > &quaternion_vec, const MC_double_vector &weights, const MC_v3d_vector &translation_vec)
	Generalized approximate spherical interpolation for rotation and linear one for translation.
Friends
MC_quaternion	operator* (const MC_quaternion &q0, const MC_quaternion &q1)
	multiplication between quaternion

Detailed Description

Class of quaternion.

internally based on v4d (axis_x,axis_y,axis_z,angle)

Definition at line 43 of file MC_quaternion.hpp.

Constructor & Destructor Documentation

mesh_conv::MC_quaternion::MC_quaternion ( )

zero contructor (set unitary axis (0,0,1) and zero angle )

Definition at line 13 of file MC_quaternion.cpp.

Referenced by exp(), and quat_interp().

00014             :MC_v4d(1,0,0,0)
00015     {}

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mesh_conv::MC_quaternion::MC_quaternion	(	const MC_v3d &	axis,
		const double &	angle
	)

constructor from axis and angle

Definition at line 16 of file MC_quaternion.cpp.

References mesh_conv::MC_v4d::MC_v4d(), and mesh_conv::MC_v3d::normalized().

00017             :MC_v4d(0,0,0,0)
00018     {
00019         double sin_phi=sin(angle/2.0);
00020         MC_v3d n_axis=axis.normalized();
00021         *this=MC_v4d(n_axis[0]*sin_phi,n_axis[1]*sin_phi,n_axis[2]*sin_phi,cos(angle/2.0));
00022     }

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mesh_conv::MC_quaternion::MC_quaternion ( const MC_v4d & v )

constructor from base class: v4d

Definition at line 23 of file MC_quaternion.cpp.

00024             :MC_v4d(v)
00025     {}

mesh_conv::MC_quaternion::MC_quaternion ( const MC_quaternion & q )

copy constructor

Definition at line 26 of file MC_quaternion.cpp.

00027             :MC_v4d(q[0],q[1],q[2],q[3])
00028     {}

mesh_conv::MC_quaternion::MC_quaternion	(	const double &	x,
		const double &	y,
		const double &	z,
		const double &	w
	)

direct constructor from coefficients

Definition at line 29 of file MC_quaternion.cpp.

00030             :MC_v4d(x,y,z,w)
00031     {}

Member Function Documentation

double mesh_conv::MC_quaternion::angle ( ) const

get the angle corresponding to the quaternion

Definition at line 96 of file MC_quaternion.cpp.

00097     {return 2*acos((*this)[3]);}

MC_v3d mesh_conv::MC_quaternion::axis ( ) const

get the unit axis corresponding to the quaternion

Definition at line 94 of file MC_quaternion.cpp.

References mesh_conv::MC_v3d::normalized().

00095     {return MC_v3d((*this)(0),(*this)(1),(*this)(2)).normalized();}

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MC_quaternion mesh_conv::MC_quaternion::conjugated ( ) const

get the conjugate of the current quaterion

Definition at line 61 of file MC_quaternion.cpp.

Referenced by mesh_conv::MC_trackball::apply_rotation(), mesh_conv::MC_navigator_tool::current_cam1(), mesh_conv::MC_navigator_tool::current_light1(), display_callback(), draw_orientation(), draw_pointer(), mesh_conv::MC_navigator_tool::go_forward_trackball_cam1(), mesh_conv::MC_navigator_tool::go_right_trackball_cam1(), mesh_conv::MC_navigator_tool::go_up_trackball_cam1(), inverted(), motion_callback(), mesh_conv::operator*(), and mesh_conv::MC_v3d::operator*=().

00062     {
00063         MC_quaternion q2;
00064         for(int k_dim=0;k_dim<3;k_dim++)
00065             q2[k_dim]=-(*this)[k_dim];
00066         q2[3]=(*this)[3];
00067         return q2;
00068     }

MC_quaternion mesh_conv::MC_quaternion::exp ( const MC_v3d & v ) [static]

exp map

the exp is going from R3 -> S3

Definition at line 136 of file MC_quaternion.cpp.

References MC_quaternion(), and mesh_conv::MC_v3d::norm().

Referenced by pow().

00137     {
00138         double epsilon=0.000001;
00139         double n=v.norm();
00140         if(n<epsilon)
00141             return MC_quaternion(0,0,0,1);
00142 
00143         double a = sin(n)/n;
00144 
00145         return MC_quaternion(a*v[0],a*v[1],a*v[2],cos(n));
00146     }

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MC_quaternion mesh_conv::MC_quaternion::inverted ( ) const

invert the quaternion

Returns:: Q^-1 = (Q*)/||Q||

Definition at line 114 of file MC_quaternion.cpp.

References conjugated(), and mesh_conv::MC_v4d::norm().

00115     {
00116         double n=norm();
00117         double epsilon=0.000001;
00118         if(n<epsilon)
00119         {std::cout<<"Error in Quaternion::invert(), norm is zero"<<std::endl;exit(-1);}
00120 
00121         MC_quaternion Q = conjugated()/(n*n);
00122         return Q;
00123     }

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MC_v3d mesh_conv::MC_quaternion::log ( ) const

log map

the log is going from S3 -> R3

Definition at line 124 of file MC_quaternion.cpp.

Referenced by pow().

00125     {
00126 
00127         double n=sqrt(1-(*this)[3]*(*this)[3]);
00128         double acos_w = acos((*this)[3]);
00129 
00130         double epsilon=0.0001;
00131         if(n<epsilon)
00132             return MC_v3d(0,0,0);
00133 
00134         return acos_w/n*MC_v3d((*this)[0],(*this)[1],(*this)[2]);
00135     }

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MC_matrix mesh_conv::MC_quaternion::matrix ( ) const

compute the rotation matrix associated to the current quaternion

Returns:: a 3x3 rotation matrix

Definition at line 33 of file MC_quaternion.cpp.

Referenced by mesh_conv::MC_navigator_tool::current_cam1(), mesh_conv::MC_navigator_tool::current_light1(), display_callback(), draw_orientation(), draw_pointer(), and quat_interp().

00034     {
00035         double x2 = (*this)[0]*(*this)[0];
00036         double y2 = (*this)[1]*(*this)[1];
00037         double z2 = (*this)[2]*(*this)[2];
00038         double xy = (*this)[0]*(*this)[1];
00039         double xz = (*this)[0]*(*this)[2];
00040         double yz = (*this)[1]*(*this)[2];
00041         double wx = (*this)[3]*(*this)[0];
00042         double wy = (*this)[3]*(*this)[1];
00043         double wz = (*this)[3]*(*this)[2];
00044 
00045         MC_matrix M(3,3);
00046         M(0,0) = 1-2*(y2+z2);
00047         M(1,0) =   2*(xy+wz);
00048         M(2,0) =   2*(xz-wy);
00049 
00050         M(0,1) =   2*(xy-wz);
00051         M(1,1) = 1-2*(x2+z2);
00052         M(2,1) =   2*(yz+wx);
00053 
00054         M(0,2) =   2*(xz+wy);
00055         M(1,2) =   2*(yz-wx);
00056         M(2,2) = 1-2*(x2+y2);
00057 
00058         return M;
00059     }

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MC_quaternion & mesh_conv::MC_quaternion::operator*= ( const MC_quaternion & q1 )

internal multiplication between quaternion

Definition at line 81 of file MC_quaternion.cpp.

References mesh_conv::MC_v3d::cross(), mesh_conv::MC_v3d::dot(), and mesh_conv::MC_v4d::set_v3d().

00082     {
00083 
00084         double w0=(*this)[3],w1=q1[3];
00085         MC_v3d v0=MC_v3d((*this)[0],(*this)[1],(*this)[2]);
00086         MC_v3d v1=MC_v3d(q1[0],q1[1],q1[2]);
00087 
00088         (*this)[3]=w0*w1-v0.dot(v1);
00089         set_v3d(w0*v1+w1*v0-v0.cross(v1));
00090 
00091         return *this;
00092     }

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MC_quaternion mesh_conv::MC_quaternion::pow ( const double & t ) const

power of a quaternion with a double

Returns:: exp(t*log_q(q))

Definition at line 112 of file MC_quaternion.cpp.

References exp(), and log().

00113     {return MC_quaternion::exp( t * log());}

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MC_matrix mesh_conv::MC_quaternion::quat_interp	(	const std::vector< MC_quaternion > &	quaternion_vec,
		const MC_double_vector &	weights,
		const MC_v3d_vector &	translation_vec
	)			`[static]`

Generalized approximate spherical interpolation for rotation and linear one for translation.

Definition at line 163 of file MC_quaternion.cpp.

References matrix(), quat_interp(), mesh_conv::MC_matrix::set_block(), mesh_conv::MC_v3d_vector::size(), mesh_conv::MC_double_vector::size(), and mesh_conv::MC_v3d_vector::sum().

00164     {
00165         MC_matrix res(4,4);
00166 
00167         if(weights.size()!=translation_vec.size())
00168         {std::cout<<"Error in MC_quaternion::quat_interp(vector<MC_quaternion>("<<quaternion_vec.size()<<"),MC_double_vector("<<weights.size()<<"),MC_v3d_vector("<<translation_vec.size()<<")), size are not compatible"<<std::endl;exit(-1);}
00169 
00170         //first do the rotation
00171         MC_quaternion rot = MC_quaternion::quat_interp(quaternion_vec,weights);
00172         res.set_block(0,2,0,2,rot.matrix());
00173 
00174         //then the translation by linear interpolation
00175         MC_v3d tr = MC_v3d_vector::sum(weights*translation_vec);
00176         res.set_block(0,2,3,3,tr);
00177         res(3,3)=1;
00178 
00179         return res;
00180 
00181     }

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MC_matrix mesh_conv::MC_quaternion::quat_interp	(	const std::vector< MC_matrix > &	matrix_vec,
		const MC_double_vector &	weights
	)			`[static]`

Generalized approximate spherical interpolation for rotation and linear one for translation.

Returns:: a 4x4 matrix

Definition at line 183 of file MC_quaternion.cpp.

References matrix(), MC_quaternion(), quat_interp(), mesh_conv::MC_matrix::set_block(), and mesh_conv::MC_double_vector::size().

00184     {
00185         if(static_cast<int>(matrix_vec.size()) !=weights.size())
00186         {std::cout<<"Error in MC_quaternion::quat_interp(vector<MC_matrix>,MC_double_vector), size are not compatible ("<<matrix_vec.size()<<","<<weights.size()<<")"<<std::endl;exit(-1);}
00187 
00188         int N=matrix_vec.size();
00189 
00190         // rotation
00191         std::vector <MC_quaternion> quaternion_vec(N);
00192         for(int k=0;k<N;k++)
00193             quaternion_vec[k] = MC_quaternion(matrix_vec[k]);
00194         MC_quaternion res = MC_quaternion::quat_interp(quaternion_vec,weights);
00195 
00196         // translation
00197         MC_v3d tr;
00198         for(int k=0;k<N;k++)
00199             tr += weights[k]*(matrix_vec[k].translation_part());
00200 
00201 
00202         MC_matrix interpolated_matrix(4,4);
00203         interpolated_matrix.set_block(0,2,0,2,res.matrix());
00204         interpolated_matrix.set_block(0,2,3,3,tr);
00205 
00206 
00207         return interpolated_matrix;
00208 
00209     }

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MC_quaternion mesh_conv::MC_quaternion::quat_interp	(	const std::vector< MC_quaternion > &	quaternion_vec,
		const MC_double_vector &	weights
	)			`[static]`

Generalized approximate spherical interpolation for rotation

Compute sum(qi)/norm(sum(qi))

Definition at line 150 of file MC_quaternion.cpp.

References mesh_conv::MC_v4d::norm(), and mesh_conv::MC_double_vector::size().

Referenced by quat_interp().

00151     {
00152         if(int(quaternion_vec.size())!=weights.size())
00153         {std::cout<<"Error in MC_quaternion::quat_interp(vector<MC_quaternion>,MC_double_vector), size are not compatible ("<<quaternion_vec.size()<<","<<weights.size()<<")"<<std::endl;exit(-1);}
00154 
00155         MC_quaternion temp(0,0,0,0);
00156         int N=quaternion_vec.size();
00157         for(int k=0;k<N;k++)
00158             temp += weights[k]*quaternion_vec[k];
00159         temp /= temp.norm();
00160         return temp;
00161     }

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MC_quaternion mesh_conv::MC_quaternion::slerp	(	const MC_quaternion &	q0,
		const MC_quaternion &	q1,
		const double &	t
	)			`[static]`

Spherical Linear Interpolation SLERP.

Use (sin((1-t) theta )q0 +sin(t theta)q1)/sin(theta) But same results with (q1 q0^{-1})^{t} q0 (q1*q0.invert()).pow_q(t)*q0)

Definition at line 98 of file MC_quaternion.cpp.

References mesh_conv::MC_v4d::dot().

00099     {
00100         double cos_theta = q0.dot(q1);
00101         double theta = acos(cos_theta);
00102         double sin_theta = sqrt(1-cos_theta*cos_theta);
00103 
00104         double epsilon=0.0001;
00105         if(fabs(sin_theta)<epsilon)
00106         {std::cout<<"Warning in Quaternion::SLERP, sin(theta) is zero"<<std::endl;return q0;}
00107 
00108         MC_quaternion interpolated = (sin((1-t)*theta)*q0 + sin(t*theta)*q1) / sin_theta;
00109         return interpolated;
00110     }

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Friends And Related Function Documentation

MC_quaternion operator*	(	const MC_quaternion &	q0,
		const MC_quaternion &	q1
	)			`[friend]`

multiplication between quaternion

The documentation for this class was generated from the following files:

/home/damien/work/2010_04_M1_info/TP/TP_glut_etudiant/src_lib/header/MC_quaternion.hpp
/home/damien/work/2010_04_M1_info/TP/TP_glut_etudiant/src_lib/src/MC_quaternion.cpp

mesh_conv::MC_quaternion Class Reference

Public Member Functions

Static Public Member Functions

Friends

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation