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/**
* Mandelbulber v2, a 3D fractal generator ,=#MKNmMMKmmßMNWy,
* ,B" ]L,,p%%%,,,§;, "K
* Copyright (C) 2014-17 Mandelbulber Team §R-==%w["'~5]m%=L.=~5N
* ,=mm=§M ]=4 yJKA"/-Nsaj "Bw,==,,
* This file is part of Mandelbulber. §R.r= jw",M Km .mM FW ",§=ß., ,TN
* ,4R =%["w[N=7]J '"5=],""]]M,w,-; T=]M
* Mandelbulber is free software: §R.ß~-Q/M=,=5"v"]=Qf,'§"M= =,M.§ Rz]M"Kw
* you can redistribute it and/or §w "xDY.J ' -"m=====WeC=\ ""%""y=%"]"" §
* modify it under the terms of the "§M=M =D=4"N #"%==A%p M§ M6 R' #"=~.4M
* GNU General Public License as §W =, ][T"]C § § '§ e===~ U !§[Z ]N
* published by the 4M",,Jm=,"=e~ § § j]]""N BmM"py=ßM
* Free Software Foundation, ]§ T,M=& 'YmMMpM9MMM%=w=,,=MT]M m§;'§,
* either version 3 of the License, TWw [.j"5=~N[=§%=%W,T ]R,"=="Y[LFT ]N
* or (at your option) TW=,-#"%=;[ =Q:["V"" ],,M.m == ]N
* any later version. J§"mr"] ,=,," =="""J]= M"M"]==ß"
* §= "=C=4 §"eM "=B:m|4"]#F,§~
* Mandelbulber is distributed in "9w=,,]w em%wJ '"~" ,=,,ß"
* the hope that it will be useful, . "K= ,=RMMMßM"""
* but WITHOUT ANY WARRANTY; .'''
* without even the implied warranty
* of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
*
* See the GNU General Public License for more details.
* You should have received a copy of the GNU General Public License
* along with Mandelbulber. If not, see <http://www.gnu.org/licenses/>.
*
* ###########################################################################
*
* Authors: Krzysztof Marczak (buddhi1980@gmail.com)
*
* CVector2, CVector3, CVector4 and CMatrix33 classes - vector and matrix
* manipulation
*
* These classes get used throughout the program to realize 2d, 3d and 4d
* variable representation and manipulation. The class CMatrix33 is used for
* rotation in 3d space.
*/
#include "algebra.hpp"
CVector3 CVector3::RotateAroundVectorByAngle(CVector3 axis, double angle) const
{
CVector3 vector = *this * cos(angle);
vector += (axis.Cross(*this)) * sin(angle);
vector += axis * axis.Dot(*this) * (1 - cos(angle));
return vector;
}
CVector4 CVector4::RotateAroundVectorByAngle(CVector3 axis, double angle) const
{
const CVector3 oldVector = this->GetXYZ();
CVector3 vector = oldVector * cos(angle);
vector += (axis.Cross(oldVector)) * sin(angle);
vector += axis * axis.Dot(oldVector) * (1 - cos(angle));
return CVector4(vector, w);
}
double CVector3::itemByName(char item) const
{
switch (item)
{
case 'x': return x;
case 'y': return y;
case 'z': return z;
default: return 0.0;
}
}
double CVector4::itemByName(char item) const
{
switch (item)
{
case 'x': return x;
case 'y': return y;
case 'z': return z;
case 'w': return w;
default: return 0.0;
}
}
/***************** class CMatrix33 ***********************/
CMatrix33::CMatrix33()
{
m11 = 0;
m12 = 0;
m13 = 0;
m21 = 0;
m22 = 0;
m23 = 0;
m31 = 0;
m32 = 0;
m33 = 0;
}
CMatrix33::CMatrix33(const CMatrix33 &matrix)
{
m11 = matrix.m11;
m12 = matrix.m12;
m13 = matrix.m13;
m21 = matrix.m21;
m22 = matrix.m22;
m23 = matrix.m23;
m31 = matrix.m31;
m32 = matrix.m32;
m33 = matrix.m33;
}
CMatrix33::CMatrix33(const CVector3 &v1, const CVector3 &v2, const CVector3 &v3)
{
m11 = v1.x;
m12 = v2.x;
m13 = v3.x;
m21 = v1.y;
m22 = v2.y;
m23 = v3.y;
m31 = v1.z;
m32 = v2.z;
m33 = v3.z;
}
CMatrix33 &CMatrix33::operator=(const CMatrix33 &matrix) = default;
CMatrix33 CMatrix33::operator*(const CMatrix33 &matrix) const
{
CMatrix33 result;
result.m11 = m11 * matrix.m11 + m12 * matrix.m21 + m13 * matrix.m31;
result.m12 = m11 * matrix.m12 + m12 * matrix.m22 + m13 * matrix.m32;
result.m13 = m11 * matrix.m13 + m12 * matrix.m23 + m13 * matrix.m33;
result.m21 = m21 * matrix.m11 + m22 * matrix.m21 + m23 * matrix.m31;
result.m22 = m21 * matrix.m12 + m22 * matrix.m22 + m23 * matrix.m32;
result.m23 = m21 * matrix.m13 + m22 * matrix.m23 + m23 * matrix.m33;
result.m31 = m31 * matrix.m11 + m32 * matrix.m21 + m33 * matrix.m31;
result.m32 = m31 * matrix.m12 + m32 * matrix.m22 + m33 * matrix.m32;
result.m33 = m31 * matrix.m13 + m32 * matrix.m23 + m33 * matrix.m33;
return result;
}
CVector3 CMatrix33::operator*(const CVector3 &vector) const
{
CVector3 result;
result.x = m11 * vector.x + m12 * vector.y + m13 * vector.z;
result.y = m21 * vector.x + m22 * vector.y + m23 * vector.z;
result.z = m31 * vector.x + m32 * vector.y + m33 * vector.z;
return result;
}
/**************** class RotationMatrix **********************/
CRotationMatrix::CRotationMatrix()
{
matrix.m11 = 1.0;
matrix.m12 = 0.0;
matrix.m13 = 0.0;
matrix.m21 = 0.0;
matrix.m22 = 1.0;
matrix.m23 = 0.0;
matrix.m31 = 0.0;
matrix.m32 = 0.0;
matrix.m33 = 1.0;
zero = true;
}
void CRotationMatrix::RotateX(double angle)
{
if (angle != 0.0)
{
CMatrix33 rot;
const double s = sin(angle);
const double c = cos(angle);
rot.m11 = 1.0;
rot.m22 = c;
rot.m33 = c;
rot.m23 = -s;
rot.m32 = s;
matrix = matrix * rot;
zero = false;
}
}
void CRotationMatrix::RotateY(double angle)
{
if (angle != 0.0)
{
CMatrix33 rot;
const double s = sin(angle);
const double c = cos(angle);
rot.m22 = 1.0;
rot.m33 = c;
rot.m11 = c;
rot.m31 = -s;
rot.m13 = s;
matrix = matrix * rot;
zero = false;
}
}
void CRotationMatrix::RotateZ(double angle)
{
if (angle != 0.0)
{
CMatrix33 rot;
const double s = sin(angle);
const double c = cos(angle);
rot.m33 = 1.0;
rot.m11 = c;
rot.m22 = c;
rot.m12 = -s;
rot.m21 = s;
matrix = matrix * rot;
zero = false;
}
}
void CRotationMatrix::SetRotation(double angles[3])
{
Null();
RotateZ(angles[0]);
RotateX(angles[1]);
RotateY(angles[2]);
}
void CRotationMatrix::SetRotation(double alpha, double beta, double gamma)
{
Null();
RotateZ(alpha);
RotateX(beta);
RotateY(gamma);
}
void CRotationMatrix::SetRotation(CVector3 rotation)
{
Null();
RotateZ(rotation.x);
RotateX(rotation.y);
RotateY(rotation.z);
}
void CRotationMatrix::SetRotation2(CVector3 rotation)
{
Null();
RotateZ(rotation.z);
RotateY(rotation.y);
RotateX(rotation.x);
}
void CRotationMatrix::SetRotation3(CVector3 rotation)
{
Null();
RotateZ(rotation.x);
RotateY(rotation.y);
RotateX(rotation.z);
}
CVector3 CRotationMatrix::RotateVector(const CVector3 &vector) const
{
if (!zero)
{
CVector3 vector2 = matrix * vector;
return vector2;
}
else
{
return vector;
}
}
CVector4 CRotationMatrix::RotateVector(const CVector4 &vector) const
{
if (!zero)
{
CVector4 vector2 = CVector4(matrix * vector.GetXYZ(), vector.w);
return vector2;
}
else
{
return vector;
}
}
void CRotationMatrix::Null()
{
// CRotationMatrix();
matrix.m11 = 1.0;
matrix.m12 = 0.0;
matrix.m13 = 0.0;
matrix.m21 = 0.0;
matrix.m22 = 1.0;
matrix.m23 = 0.0;
matrix.m31 = 0.0;
matrix.m32 = 0.0;
matrix.m33 = 1.0;
zero = true;
}
double CRotationMatrix::GetAlfa() const
{
return atan2(matrix.m12, matrix.m22);
}
double CRotationMatrix::GetBeta() const
{
return asin(-matrix.m32);
}
double CRotationMatrix::GetGamma() const
{
return atan2(matrix.m31, matrix.m33);
}
CRotationMatrix CRotationMatrix::Transpose() const
{
CRotationMatrix m;
m.matrix.m11 = matrix.m11;
m.matrix.m12 = matrix.m21;
m.matrix.m13 = matrix.m31;
m.matrix.m21 = matrix.m12;
m.matrix.m22 = matrix.m22;
m.matrix.m23 = matrix.m32;
m.matrix.m31 = matrix.m13;
m.matrix.m32 = matrix.m23;
m.matrix.m33 = matrix.m33;
m.zero = false;
return m;
}
/***************** class CMatrix44 ***********************/
CMatrix44::CMatrix44()
{
m11 = 0;
m12 = 0;
m13 = 0;
m14 = 0;
m21 = 0;
m22 = 0;
m23 = 0;
m24 = 0;
m31 = 0;
m32 = 0;
m33 = 0;
m34 = 0;
m41 = 0;
m42 = 0;
m43 = 0;
m44 = 0;
}
CMatrix44::CMatrix44(const CMatrix44 &matrix)
{
m11 = matrix.m11;
m12 = matrix.m12;
m13 = matrix.m13;
m14 = matrix.m14;
m21 = matrix.m21;
m22 = matrix.m22;
m23 = matrix.m23;
m24 = matrix.m24;
m31 = matrix.m31;
m32 = matrix.m32;
m33 = matrix.m33;
m34 = matrix.m34;
m41 = matrix.m41;
m42 = matrix.m42;
m43 = matrix.m43;
m44 = matrix.m44;
}
CMatrix44::CMatrix44(const CVector4 &v1, const CVector4 &v2, const CVector4 &v3, const CVector4 &v4)
{
m11 = v1.x;
m12 = v2.x;
m13 = v3.x;
m14 = v4.x;
m21 = v1.y;
m22 = v2.y;
m23 = v3.y;
m24 = v4.y;
m31 = v1.z;
m32 = v2.z;
m33 = v3.z;
m34 = v4.z;
m41 = v1.w;
m42 = v2.w;
m43 = v3.w;
m44 = v4.w;
}
CMatrix44 &CMatrix44::operator=(const CMatrix44 &matrix) = default;
CMatrix44 CMatrix44::operator*(const CMatrix44 &matrix) const
{
CMatrix44 result;
result.m11 = m11 * matrix.m11 + m12 * matrix.m21 + m13 * matrix.m31 + m14 * matrix.m41;
result.m12 = m11 * matrix.m12 + m12 * matrix.m22 + m13 * matrix.m32 + m14 * matrix.m42;
result.m13 = m11 * matrix.m13 + m12 * matrix.m23 + m13 * matrix.m33 + m14 * matrix.m43;
result.m14 = m11 * matrix.m14 + m12 * matrix.m24 + m13 * matrix.m34 + m14 * matrix.m44;
result.m21 = m21 * matrix.m11 + m22 * matrix.m21 + m23 * matrix.m31 + m24 * matrix.m41;
result.m22 = m21 * matrix.m12 + m22 * matrix.m22 + m23 * matrix.m32 + m24 * matrix.m42;
result.m23 = m21 * matrix.m13 + m22 * matrix.m23 + m23 * matrix.m33 + m24 * matrix.m43;
result.m24 = m21 * matrix.m14 + m22 * matrix.m24 + m23 * matrix.m34 + m24 * matrix.m44;
result.m31 = m31 * matrix.m11 + m32 * matrix.m21 + m33 * matrix.m31 + m34 * matrix.m41;
result.m32 = m31 * matrix.m12 + m32 * matrix.m22 + m33 * matrix.m32 + m34 * matrix.m42;
result.m33 = m31 * matrix.m13 + m32 * matrix.m23 + m33 * matrix.m33 + m34 * matrix.m43;
result.m34 = m31 * matrix.m14 + m32 * matrix.m24 + m33 * matrix.m34 + m34 * matrix.m44;
result.m41 = m41 * matrix.m11 + m42 * matrix.m21 + m43 * matrix.m31 + m44 * matrix.m41;
result.m42 = m41 * matrix.m12 + m42 * matrix.m22 + m43 * matrix.m32 + m44 * matrix.m42;
result.m43 = m41 * matrix.m13 + m42 * matrix.m23 + m43 * matrix.m33 + m44 * matrix.m43;
result.m44 = m41 * matrix.m14 + m42 * matrix.m24 + m43 * matrix.m34 + m44 * matrix.m44;
return result;
}
CVector4 CMatrix44::operator*(const CVector4 &vector) const
{
CVector4 result;
result.x = m11 * vector.x + m12 * vector.y + m13 * vector.z + m14 * vector.w;
result.y = m21 * vector.x + m22 * vector.y + m23 * vector.z + m24 * vector.w;
result.z = m31 * vector.x + m32 * vector.y + m33 * vector.z + m34 * vector.w;
result.w = m41 * vector.x + m42 * vector.y + m43 * vector.z + m44 * vector.w;
return result;
}
/**************** class RotationMatrix **********************/
CRotationMatrix44::CRotationMatrix44()
{
matrix.m11 = 1.0;
matrix.m12 = 0.0;
matrix.m13 = 0.0;
matrix.m14 = 0.0;
matrix.m21 = 0.0;
matrix.m22 = 1.0;
matrix.m23 = 0.0;
matrix.m24 = 0.0;
matrix.m31 = 0.0;
matrix.m32 = 0.0;
matrix.m33 = 1.0;
matrix.m34 = 0.0;
matrix.m41 = 0.0;
matrix.m42 = 0.0;
matrix.m43 = 0.0;
matrix.m44 = 1.0;
zero = true;
}
void CRotationMatrix44::RotateXY(double angle)
{
if (angle != 0.0)
{
CMatrix44 rot;
const double s = sin(angle);
const double c = cos(angle);
rot.m11 = c;
rot.m12 = s;
rot.m21 = -s;
rot.m22 = c;
rot.m33 = 1.0;
rot.m44 = 1.0;
matrix = matrix * rot;
zero = false;
}
}
void CRotationMatrix44::RotateYZ(double angle)
{
if (angle != 0.0)
{
CMatrix44 rot;
const double s = sin(angle);
const double c = cos(angle);
rot.m22 = c;
rot.m23 = s;
rot.m11 = -s;
rot.m31 = c;
rot.m11 = 1.0;
rot.m44 = 1.0;
matrix = matrix * rot;
zero = false;
}
}
void CRotationMatrix44::RotateXZ(double angle)
{
if (angle != 0.0)
{
CMatrix44 rot;
const double s = sin(angle);
const double c = cos(angle);
rot.m11 = c;
rot.m13 = -s;
rot.m31 = s;
rot.m33 = c;
rot.m22 = 1.0;
rot.m44 = 1.0;
matrix = matrix * rot;
zero = false;
}
}
void CRotationMatrix44::RotateXW(double angle)
{
if (angle != 0.0)
{
CMatrix44 rot;
const double s = sin(angle);
const double c = cos(angle);
rot.m11 = c;
rot.m14 = s;
rot.m41 = -s;
rot.m44 = c;
rot.m22 = 1.0;
rot.m33 = 1.0;
matrix = matrix * rot;
zero = false;
}
}
void CRotationMatrix44::RotateYW(double angle)
{
if (angle != 0.0)
{
CMatrix44 rot;
const double s = sin(angle);
const double c = cos(angle);
rot.m22 = c;
rot.m24 = -s;
rot.m42 = s;
rot.m44 = c;
rot.m11 = 1.0;
rot.m33 = 1.0;
matrix = matrix * rot;
zero = false;
}
}
void CRotationMatrix44::RotateZW(double angle)
{
if (angle != 0.0)
{
CMatrix44 rot;
const double s = sin(angle);
const double c = cos(angle);
rot.m33 = c;
rot.m34 = -s;
rot.m43 = s;
rot.m44 = c;
rot.m11 = 1.0;
rot.m22 = 1.0;
matrix = matrix * rot;
zero = false;
}
}
void CRotationMatrix44::SetRotation(double angles[6])
{
Null();
RotateXY(angles[0]);
RotateYZ(angles[1]);
RotateXZ(angles[2]);
RotateXW(angles[3]);
RotateYW(angles[4]);
RotateZW(angles[5]);
}
void CRotationMatrix44::SetRotation(
double alpha, double beta, double gamma, double delta, double epsilon, double zeta)
{
Null();
RotateXY(alpha);
RotateYZ(beta);
RotateXZ(gamma);
RotateXW(delta);
RotateYW(epsilon);
RotateZW(zeta);
}
void CRotationMatrix44::SetRotation44a(CVector3 rotation)
{
Null();
RotateXY(rotation.x);
RotateYZ(rotation.y);
RotateXZ(rotation.z);
}
void CRotationMatrix44::SetRotation44b(CVector3 rotation)
{
Null();
RotateXW(rotation.x);
RotateYW(rotation.y); // ................................
RotateXZ(rotation.z); // .................................
}
/*
void CRotationMatrix44::SetRotation(CVector4 rotation)
{
Null();
RotateZ(rotation.x);
RotateX(rotation.y);
RotateY(rotation.z);
}
void CRotationMatrix44::SetRotation2(CVector4 rotation)
{
Null();
RotateZ(rotation.z);
RotateY(rotation.y);
RotateX(rotation.x);
}
void CRotationMatrix44::SetRotation3(CVector4 rotation)
{
Null();
RotateZ(rotation.x);
RotateY(rotation.y);
RotateX(rotation.z);
}
*/
CVector4 CRotationMatrix44::RotateVector(const CVector4 &vector) const
{
if (!zero)
{
CVector4 vector2 = matrix * vector;
return vector2;
}
else
{
return vector;
}
}
void CRotationMatrix44::Null()
{
// CRotationMatrix();
matrix.m11 = 1.0;
matrix.m12 = 0.0;
matrix.m13 = 0.0;
matrix.m14 = 0.0;
matrix.m21 = 0.0;
matrix.m22 = 1.0;
matrix.m23 = 0.0;
matrix.m24 = 0.0;
matrix.m31 = 0.0;
matrix.m32 = 0.0;
matrix.m33 = 1.0;
matrix.m34 = 0.0;
matrix.m41 = 0.0;
matrix.m42 = 0.0;
matrix.m43 = 0.0;
matrix.m44 = 1.0;
zero = true;
}
double CRotationMatrix44::GetAlfa() const
{
return atan2(matrix.m12, matrix.m22);
}
double CRotationMatrix44::GetBeta() const
{
return asin(-matrix.m32);
}
double CRotationMatrix44::GetGamma() const
{
return atan2(matrix.m31, matrix.m33);
}
double CRotationMatrix44::GetDelta() const
{
return atan2(matrix.m12, matrix.m22); // fix
}
double CRotationMatrix44::GetEpsilon() const
{
return asin(-matrix.m32); // fix
}
double CRotationMatrix44::GetZeta() const
{
return atan2(matrix.m31, matrix.m33); // fix
}
CRotationMatrix44 CRotationMatrix44::Transpose() const
{
CRotationMatrix44 m;
m.matrix.m11 = matrix.m11;
m.matrix.m12 = matrix.m21;
m.matrix.m13 = matrix.m31;
m.matrix.m14 = matrix.m41;
m.matrix.m21 = matrix.m12;
m.matrix.m22 = matrix.m22;
m.matrix.m23 = matrix.m32;
m.matrix.m24 = matrix.m42;
m.matrix.m31 = matrix.m13;
m.matrix.m32 = matrix.m23;
m.matrix.m33 = matrix.m33;
m.matrix.m34 = matrix.m43;
m.matrix.m41 = matrix.m14;
m.matrix.m42 = matrix.m24;
m.matrix.m43 = matrix.m34;
m.matrix.m44 = matrix.m44;
m.zero = false;
return m;
}