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transform.cpp
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transform.cpp
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#include "transform.h"
Matrix<float> Rx(float phi)
{
return Matrix<float>({{1.0f, 0.0f, 0.0f, 0.0f},
{0.0f, (float)cos(phi), (float)sin(phi), 0.0f},
{0.0f, -(float)sin(phi), (float)cos(phi), 0.0f},
{0.0f, 0.0f, 0.0f, 1.0f}});
}
Matrix<float> Ry(float theta)
{
return Matrix<float>({{(float)cos(theta), 0.0f, -(float)sin(theta), 0.0f},
{ 0.0f , 1.0f, 0.0f , 0.0f},
{(float)sin(theta), 0.0f, (float)cos(theta), 0.0f},
{ 0.0f , 0.0f, 0.0f , 1.0f}});
}
Matrix<float> Rz(float psi)
{
return Matrix<float>({{ (float)cos(psi), (float)sin(psi), 0.0f, 0.0f},
{-(float)sin(psi), (float)cos(psi), 0.0f, 0.0f},
{ 0.0f , 0.0f , 1.0f, 0.0f},
{ 0.0f , 0.0f , 0.0f, 1.0f}});
}
float angle(const Matrix<float>& v1, const Matrix<float>& v2)
{
return acos(dot(v1, v2) / (norm(v1) * norm(v2)));
}
Matrix<float> rotation(const Matrix<float>& v1, const Matrix<float>& v2)
{
Matrix<float> c = cross(v1, v2);
if(norm(c)>=1E-6)
return rotation(c, angle(v1, v2));
else
return eye(4);
}
Matrix<float> rotation(float phi, float theta, float psi)
{
return Rz(-psi) * Ry(-theta) * Rx(-phi);
}
Matrix<float> rotation(Matrix<float> axis, float theta)
{
normalize(axis);
Matrix<float> temp = (1-cos(theta)) * (axis * axis.t()) + cos(theta) * eye(3) + sin(theta) * crossmat(axis);
Matrix<float> R(4, 4, 0.0f);
for(int i = 0; i < 3; i++)
{
for(int j = 0; j < 3; j++)
{
R(i, j) = temp(i, j);
}
}
R(3, 3) = 1.0f;
return R;
}
Matrix<float> translation(const Matrix<float>& delta)
{
Matrix<float> T = eye(4);
T(0, 3) = delta(0);
T(1, 3) = delta(1);
T(2, 3) = delta(2);
return T;
}
void translate(Matrix<float>& mat, const Matrix<float>& vec)
{
mat(0, 3) += vec(0);
mat(1, 3) += vec(1);
mat(2, 3) += vec(2);
}
Matrix<float> scale(float s)
{
Matrix<float> S = eye(4);
S(0, 0) = s;
S(1, 1) = s;
S(2, 2) = s;
return S;
}
void scale(Matrix<float>& mat, float s)
{
mat(0, 0) *= s;
mat(1, 1) *= s;
mat(2, 2) *= s;
}
Matrix<float> scale(float sx, float sy, float sz)
{
Matrix<float> S = eye(4);
S(0, 0) = sx;
S(1, 1) = sy;
S(2, 2) = sz;
return S;
}
Matrix<float> sphere2xyz(const Matrix<float>& sphere_coord)
{
float r = sphere_coord(0);
float theta = sphere_coord(1);
float phi = sphere_coord(2);
Matrix<float> xyz_coord(3, 1);
float rxy = r * cos(phi);
xyz_coord(0) = rxy * cos(theta);
xyz_coord(1) = rxy * sin(theta);
xyz_coord(2) = r * sin(phi);
return xyz_coord;
}
Matrix<float> view(float AZ, float EL, float r)
{
AZ = deg2rad(AZ);
EL = deg2rad(EL);
float psi = 0.5f * PI + AZ;
float phi = 0.5f * PI - EL;
return Rx(phi) * Rz(psi) * translation(-sphere2xyz({r, AZ, EL}));
}
Matrix<float> view(const Matrix<float>& sphere_position)
{
float psi = 0.5f * PI + sphere_position(1);
float phi = 0.5f * PI - sphere_position(2);
Matrix<float> R = Rx(phi) * Rz(psi);
return R * translation(-sphere2xyz(sphere_position));
}
Matrix<float> view(const Matrix<float>& position, const Matrix<float>& point, float psi0)
{
Matrix<float> direction = point - position;
float rx = direction(0);
float ry = direction(1);
float rz = direction(2);
float r2 = rx*rx+ry*ry;
float psi = r2 > 1E-6 ? -Matrix<float>::sign(rx) * acos(ry/sqrt(r2)) : 0.0f;
r2 = rx*rx + ry*ry + rz*rz;
float phi = r2 > 1E-6 ? 0.5f * PI + asin(rz/sqrt(r2)) : 0.0f;
Matrix<float> R = Rz(-psi0) * Rx(phi) * Rz(psi);
return R * translation(-position);
}
Matrix<float> projection(float alpha, float s, float z1, float z2)
{
float t = 1.0f / tan(0.5f * alpha);
float l = z2 - z1;
return Matrix<float>({{t/s , 0.0f, 0.0f , 0.0f },
{0.0f, t , 0.0f , 0.0f },
{0.0f, 0.0f, -(z1+z2)/l, -2.0f*z1*z2/l},
{0.0f, 0.0f, -1.0f , 0.0f }});
}