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/***********************************************/
/**
* @file transform3d.cpp
*
* @brief Orthogonal coordinate transformations in 3d space.
* (rotations and reflections).
*
* @author Torsten Mayer-Guerr
* @date 2019-03-03
*
*/
/***********************************************/
#include "base/importStd.h"
#include "base/ellipsoid.h"
#include "base/vector3d.h"
#include "base/tensor3d.h"
#include "base/rotary3d.h"
#include "base/transform3d.h"
/***********************************************/
/// Contructor from Rotary3d.
Transform3d::Transform3d(const Rotary3d &rot) : field(rot.field) {}
/***********************************************/
// rotary from 3x3 matrix
Transform3d::Transform3d(const_MatrixSliceRef A)
{
try
{
field[0][0] = A(0,0);
field[0][1] = A(0,1);
field[0][2] = A(0,2);
field[1][0] = A(1,0);
field[1][1] = A(1,1);
field[1][2] = A(1,2);
field[2][0] = A(2,0);
field[2][1] = A(2,1);
field[2][2] = A(2,2);
}
catch(std::exception &e)
{
GROOPS_RETHROW(e)
}
}
/***********************************************/
Transform3d::Transform3d(Vector3d x, Vector3d y)
{
// Orthonormalize
x.normalize();
Vector3d z = normalize(crossProduct(x,y));
y = crossProduct(z,x);
field[0][0] = x.x(); field[0][1] = y.x(); field[0][2] = z.x();
field[1][0] = x.y(); field[1][1] = y.y(); field[1][2] = z.y();
field[2][0] = x.z(); field[2][1] = y.z(); field[2][2] = z.z();
}
/***********************************************/
Vector3d Transform3d::transform(const Vector3d &v) const
{
Vector3d y;
for(UInt i=0; i<3; i++)
for(UInt k=0; k<3; k++)
y.field[i] += field[i][k] * v.field[k];
return y;
}
/***********************************************/
Vector3d Transform3d::inverseTransform(const Vector3d &v) const
{
Vector3d y;
for(UInt i=0; i<3; i++)
for(UInt k=0; k<3; k++)
y.field[i] += field[k][i] * v.field[k];
return y;
}
/***********************************************/
Tensor3d Transform3d::transform(const Tensor3d &t) const
{
auto rot = [&](UInt i, UInt k)
{
return field[i][0]*field[k][0] * t.xx()
+ field[i][1]*field[k][1] * t.yy()
+ field[i][2]*field[k][2] * t.zz()
+ (field[i][0]*field[k][1] + field[i][1]*field[k][0]) * t.xy()
+ (field[i][0]*field[k][2] + field[i][2]*field[k][0]) * t.xz()
+ (field[i][1]*field[k][2] + field[i][2]*field[k][1]) * t.yz();
};
Tensor3d t2;
t2.xx() = rot(0, 0);
t2.yy() = rot(1, 1);
t2.zz() = rot(2, 2);
t2.xy() = rot(0, 1);
t2.xz() = rot(0, 2);
t2.yz() = rot(1, 2);
return t2;
}
/***********************************************/
Tensor3d Transform3d::inverseTransform(const Tensor3d &t) const
{
auto rot = [&](UInt i, UInt k)
{
return field[0][i]*field[0][k] * t.xx()
+ field[1][i]*field[1][k] * t.yy()
+ field[2][i]*field[2][k] * t.zz()
+ (field[0][i]*field[1][k] + field[1][i]*field[0][k]) * t.xy()
+ (field[0][i]*field[2][k] + field[2][i]*field[0][k]) * t.xz()
+ (field[1][i]*field[2][k] + field[2][i]*field[1][k]) * t.yz();
};
Tensor3d t2;
t2.xx() = rot(0, 0);
t2.yy() = rot(1, 1);
t2.zz() = rot(2, 2);
t2.xy() = rot(0, 1);
t2.xz() = rot(0, 2);
t2.yz() = rot(1, 2);
return t2;
}
/***********************************************/
Transform3d &Transform3d::operator*= (const Transform3d &b)
{
*this = *this * b;
return *this;
}
/***********************************************/
Transform3d &Transform3d::operator*= (const Rotary3d &b)
{
*this = *this * b;
return *this;
}
/***********************************************/
Transform3d Transform3d::operator* (const Transform3d &b) const
{
Transform3d y;
for(UInt i=0; i<3; i++)
for(UInt k=0; k<3; k++)
{
y.field[i][k] = 0.0;
for(UInt l=0; l<3; l++)
y.field[i][k] += field[i][l] * b.field[l][k];
}
return y;
}
/***********************************************/
Transform3d Transform3d::operator* (const Rotary3d &b) const
{
Transform3d y;
for(UInt i=0; i<3; i++)
for(UInt k=0; k<3; k++)
{
y.field[i][k] = 0.0;
for(UInt l=0; l<3; l++)
y.field[i][k] += field[i][l] * b.field[l][k];
}
return y;
}
/***********************************************/
/***********************************************/
Transform3d inverse(const Transform3d &b)
{
Transform3d rot;
for(UInt i=0; i<3; i++)
for(UInt k=0; k<3; k++)
rot.field[i][k] = b.field[k][i];
return rot;
}
/***********************************************/
Transform3d localNorthEastUp(const Vector3d &point)
{
const Vector3d z = normalize(point); // up
const Vector3d y = normalize(crossProduct(Vector3d(0,0,1), z)); // east
const Vector3d x = normalize(crossProduct(z, y)); // north
Transform3d T;
T.field[0][0] = x.x(); T.field[0][1] = y.x(); T.field[0][2] = z.x();
T.field[1][0] = x.y(); T.field[1][1] = y.y(); T.field[1][2] = z.y();
T.field[2][0] = x.z(); T.field[2][1] = y.z(); T.field[2][2] = z.z();
return T;
}
/***********************************************/
Transform3d localNorthEastUp(const Vector3d &point, const Ellipsoid &ellipsoid)
{
Angle L, B;
Double h;
ellipsoid(point, L, B, h);
return localNorthEastUp(polar(L, B, 1.));
}
/***********************************************/
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