431 lines
10 KiB
C++
Executable File
431 lines
10 KiB
C++
Executable File
//
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// Created by Иван Ильин on 12.01.2021.
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//
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#include "Matrix4x4.h"
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#include <cassert>
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#include <cmath>
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[[nodiscard]] const std::array<double, 4>& Matrix4x4::operator[] (int i) const {
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return _arr_matrix[i];
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}
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std::array<double, 4> &Matrix4x4::operator[](int i) {
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return _arr_matrix[i];
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}
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[[nodiscard]] Matrix4x4 Matrix4x4::operator-() const {
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Matrix4x4 result(*this);
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for(int i = 0; i < 4; i++)
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for(int j = 0; j < 4; j++)
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result[i][j] = -_arr_matrix[i][j];
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return result;
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}
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[[nodiscard]] Matrix4x4 Matrix4x4::operator+() const {
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return Matrix4x4(*this);
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}
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bool Matrix4x4::operator==(const Matrix4x4 &matrix4X4) const {
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for(int i = 0; i < 4; i++)
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for(int j = 0; j < 4; j++)
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if(_arr_matrix[i][j] != matrix4X4[i][j])
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return false;
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return true;
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}
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bool Matrix4x4::operator!=(const Matrix4x4 &matrix4X4) const {
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return !(*this==matrix4X4);
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}
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Matrix4x4 Matrix4x4::operator+(const Matrix4x4 &matrix4X4) const {
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return Matrix4x4(*this) += matrix4X4;
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}
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Matrix4x4 Matrix4x4::operator-(const Matrix4x4 &matrix4X4) const {
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return Matrix4x4(*this) -= matrix4X4;
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}
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Matrix4x4 Matrix4x4::operator*(const Matrix4x4 &matrix4X4) const {
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return Matrix4x4(*this) *= matrix4X4;
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}
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Matrix4x4 Matrix4x4::operator/(const Matrix4x4 &matrix4X4) const {
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return Matrix4x4(*this) /= matrix4X4;
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}
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Matrix4x4 &Matrix4x4::operator+=(const Matrix4x4 &matrix4X4) {
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for(int i = 0; i < 4; i++)
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for(int j = 0; j < 4; j++)
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_arr_matrix[i][j] += matrix4X4[i][j];
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return *this;
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}
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Matrix4x4 &Matrix4x4::operator-=(const Matrix4x4 &matrix4X4) {
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(*this) += -matrix4X4;
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return *this;
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}
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Matrix4x4 &Matrix4x4::operator*=(const Matrix4x4 &matrix4X4) {
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Matrix4x4 copy(*this);
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this->setZero();
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for(int i = 0; i < 4; i++)
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for(int j = 0; j < 4; j++)
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for(int k = 0; k < 4; k++)
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_arr_matrix[i][j] += copy[i][k] * matrix4X4[k][j];
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return *this;
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}
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Matrix4x4 &Matrix4x4::operator/=(const Matrix4x4 &matrix4X4) {
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for(int i = 0; i < 4; i++)
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for(int j = 0; j < 4; j++) {
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assert(matrix4X4[i][j] != 0);
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_arr_matrix[i][j] /= matrix4X4[i][j];
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}
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return *this;
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}
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Matrix4x4 Matrix4x4::operator+(double number) const {
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return Matrix4x4(*this) += number;
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}
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Matrix4x4 Matrix4x4::operator-(double number) const {
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return *this+(-number);
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}
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Matrix4x4 Matrix4x4::operator*(double number) const {
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return Matrix4x4(*this) *= number;
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}
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Matrix4x4 Matrix4x4::operator/(double number) const {
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assert(number != 0);
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return *this*(1.0/number);
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}
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Matrix4x4 &Matrix4x4::operator+=(double number) {
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for(int i = 0; i < 4; i++)
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for(int j = 0; j < 4; j++)
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_arr_matrix[i][j] += number;
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return *this;
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}
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Matrix4x4 &Matrix4x4::operator-=(double number) {
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return (*this) += -number;
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}
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Matrix4x4 &Matrix4x4::operator*=(double number) {
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for(int i = 0; i < 4; i++)
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for(int j = 0; j < 4; j++)
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_arr_matrix[i][j] *= number;
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return *this;
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}
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Matrix4x4 &Matrix4x4::operator/=(double number) {
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return (*this) *= 1.0/number;
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}
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Point4D Matrix4x4::operator*(const Point4D &point4D) const {
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return Point4D(
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_arr_matrix[0][0] * point4D.x() + _arr_matrix[0][1] * point4D.y() + _arr_matrix[0][2] * point4D.z() + _arr_matrix[0][3] * point4D.w(),
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_arr_matrix[1][0] * point4D.x() + _arr_matrix[1][1] * point4D.y() + _arr_matrix[1][2] * point4D.z() + _arr_matrix[1][3] * point4D.w(),
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_arr_matrix[2][0] * point4D.x() + _arr_matrix[2][1] * point4D.y() + _arr_matrix[2][2] * point4D.z() + _arr_matrix[2][3] * point4D.w(),
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_arr_matrix[3][0] * point4D.x() + _arr_matrix[3][1] * point4D.y() + _arr_matrix[3][2] * point4D.z() + _arr_matrix[3][3] * point4D.w()
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);
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}
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double Matrix4x4::det3D() {
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return _arr_matrix[0][0] * (_arr_matrix[1][1] * _arr_matrix[2][2] - _arr_matrix[1][2] * _arr_matrix[2][1]) -
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_arr_matrix[0][1] * (_arr_matrix[1][0] * _arr_matrix[2][2] - _arr_matrix[1][2] * _arr_matrix[2][0]) +
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_arr_matrix[0][2] * (_arr_matrix[1][0] * _arr_matrix[2][1] - _arr_matrix[2][0] * _arr_matrix[1][1]);
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}
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Matrix4x4 Matrix4x4::inv3D() {
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double det = det3D();
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assert(det != 0);
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Matrix4x4 result{};
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result[3][3] = 1.0;
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result[0][0] = _arr_matrix[1][1] * _arr_matrix[2][2] - _arr_matrix[2][1] * _arr_matrix[1][2];
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result[1][0] = _arr_matrix[0][1] * _arr_matrix[2][2] - _arr_matrix[2][1] * _arr_matrix[0][2];
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result[2][0] = _arr_matrix[0][1] * _arr_matrix[1][2] - _arr_matrix[1][1] * _arr_matrix[0][2];
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result[0][1] = _arr_matrix[1][0] * _arr_matrix[2][2] - _arr_matrix[2][0] * _arr_matrix[1][2];
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result[1][1] = _arr_matrix[0][0] * _arr_matrix[2][2] - _arr_matrix[2][0] * _arr_matrix[0][2];
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result[2][1] = _arr_matrix[0][0] * _arr_matrix[1][2] - _arr_matrix[1][0] * _arr_matrix[0][2];
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result[0][2] = _arr_matrix[1][0] * _arr_matrix[2][1] - _arr_matrix[2][0] * _arr_matrix[1][1];
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result[1][2] = _arr_matrix[0][0] * _arr_matrix[2][1] - _arr_matrix[2][0] * _arr_matrix[0][1];
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result[2][2] = _arr_matrix[0][0] * _arr_matrix[1][1] - _arr_matrix[1][0] * _arr_matrix[0][1];
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return result /= det;
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}
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Matrix4x4 &Matrix4x4::transpose() {
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Matrix4x4 result{};
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for(int i = 0; i < 4; i++)
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for(int j = 0; j < 4; j++)
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result[i][j] = _arr_matrix[j][i];
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*this = result;
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return *this;
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}
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Matrix4x4 &Matrix4x4::setIdentity() {
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for(int i = 0; i < 4; i++)
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for(int j = 0; j < 4; j++)
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if(i == j)
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_arr_matrix[j][i] = 1.0;
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else
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_arr_matrix[j][i] = 0.0;
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return *this;
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}
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Matrix4x4 &Matrix4x4::setOnes() {
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setConstants(1.0);
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return *this;
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}
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Matrix4x4 &Matrix4x4::setZero() {
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setConstants(0.0);
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return *this;
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}
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Matrix4x4 &Matrix4x4::setConstants(double value) {
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for(int i = 0; i < 4; i++)
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for(int j = 0; j < 4; j++)
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_arr_matrix[j][i] = value;
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return *this;
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}
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const std::array<std::array<double, 4>, 4> &Matrix4x4::data() const {
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return _arr_matrix;
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}
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std::array<std::array<double, 4>, 4> &Matrix4x4::data() {
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return _arr_matrix;
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}
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Matrix4x4 Matrix4x4::Identity() {
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return Matrix4x4().setIdentity();
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}
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Matrix4x4 Matrix4x4::Zero() {
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return Matrix4x4();
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}
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Matrix4x4 Matrix4x4::Constant(double value) {
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return Matrix4x4().setConstants(value);
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}
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Matrix4x4 Matrix4x4::Scale(double sx, double sy, double sz) {
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Matrix4x4 s{};
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s[0][0] = sx;
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s[1][1] = sy;
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s[2][2] = sz;
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s[3][3] = 1;
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return s;
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}
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Matrix4x4 Matrix4x4::Translation(double dx, double dy, double dz) {
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Matrix4x4 t{};
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/*
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* ( 1 0 0 dx )(x) (x + dx)
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* ( 0 1 0 dy )(y) = (y + dy)
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* ( 0 0 1 dz )(z) (z + dz)
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* ( 0 0 0 1 )(1) ( 1 )
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*/
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t[0][0] = 1.0;
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t[1][1] = 1.0;
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t[2][2] = 1.0;
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t[3][3] = 1.0;
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t[0][3] = dx;
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t[1][3] = dy;
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t[2][3] = dz;
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return t;
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}
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Matrix4x4 Matrix4x4::Translation(const Point4D& v) {
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Matrix4x4 t{};
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/*
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* ( 1 0 0 dx )(x) (x + dx)
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* ( 0 1 0 dy )(y) = (y + dy)
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* ( 0 0 1 dz )(z) (z + dz)
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* ( 0 0 0 1 )(1) ( 1 )
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*/
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t[0][0] = 1.0;
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t[1][1] = 1.0;
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t[2][2] = 1.0;
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t[3][3] = 1.0;
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t[0][3] = v.x();
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t[1][3] = v.y();
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t[2][3] = v.z();
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return t;
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}
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Matrix4x4 Matrix4x4::RotationX(double rx) {
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Matrix4x4 Rx{};
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Rx[0][0] = 1.0;
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Rx[1][1] = cos(rx);
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Rx[1][2] = -sin(rx);
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Rx[2][1] = sin(rx);
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Rx[2][2] = cos(rx);
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Rx[3][3] = 1.0;
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return Rx;
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}
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Matrix4x4 Matrix4x4::RotationY(double ry) {
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Matrix4x4 Ry{};
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Ry[1][1] = 1.0;
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Ry[0][0] = cos(ry);
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Ry[0][2] = sin(ry);
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Ry[2][0] = -sin(ry);
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Ry[2][2] = cos(ry);
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Ry[3][3] = 1.0;
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return Ry;
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}
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Matrix4x4 Matrix4x4::RotationZ(double rz) {
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Matrix4x4 Rz{};
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Rz[2][2] = 1.0;
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Rz[0][0] = cos(rz);
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Rz[0][1] = -sin(rz);
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Rz[1][0] = sin(rz);
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Rz[1][1] = cos(rz);
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Rz[3][3] = 1.0;
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return Rz;
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}
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Matrix4x4 Matrix4x4::Rotation(double rx, double ry, double rz) {
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return RotationX(rx) * RotationY(ry) * RotationZ(rz);
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}
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Matrix4x4 Matrix4x4::Rotation(Point4D v, double rv) {
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Matrix4x4 Rv{};
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v.normalize();
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Rv[0][0] = cos(rv) + (1.0 - cos(rv))*v.x()*v.x();
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Rv[0][1] = (1.0 - cos(rv))*v.x()*v.y() - sin(rv)*v.z();
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Rv[0][2] = (1.0 - cos(rv))*v.x()*v.z() + sin(rv)*v.y();
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Rv[1][0] = (1.0 - cos(rv))*v.x()*v.y() + sin(rv)*v.z();
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Rv[1][1] = cos(rv) + (1.0 - cos(rv))*v.y()*v.y();
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Rv[1][2] = (1.0 - cos(rv))*v.y()*v.z() - sin(rv)*v.x();
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Rv[2][0] = (1.0 - cos(rv))*v.z()*v.x() - sin(rv)*v.y();
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Rv[2][1] = (1.0 - cos(rv))*v.z()*v.y() + sin(rv)*v.x();
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Rv[2][2] = cos(rv) + (1.0 - cos(rv))*v.z()*v.z();
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Rv[3][3] = 1.0;
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return Rv;
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}
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Matrix4x4 Matrix4x4::Projection(double fov, double aspect, double ZNear, double ZFar) {
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Matrix4x4 p{};
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p[0][0] = 1.0/(tan(M_PI*fov*0.5/180.0)*aspect);
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p[1][1] = 1.0/tan(M_PI*fov*0.5/180.0);
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p[2][2] = ZFar/(ZFar - ZNear);
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p[2][3] = -ZFar*ZNear/(ZFar - ZNear);
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p[3][2] = 1.0;
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return p;
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}
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Matrix4x4 Matrix4x4::ScreenSpace(int width, int height) {
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Matrix4x4 s{};
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s[0][0] = -0.5*width;
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s[1][1] = -0.5*height;
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s[2][2] = 1.0;
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s[0][3] = 0.5*width;
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s[1][3] = 0.5*height;
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s[3][3] = 1.0;
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return s;
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}
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Matrix4x4 Matrix4x4::View(const Point4D &left, const Point4D &up, const Point4D &lookAt, const Point4D &eye) {
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Matrix4x4 V{};
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V.setZero();
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V[0][0] = left[0];
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V[0][1] = left[1];
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V[0][2] = left[2];
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V[0][3] = -eye.dot(left);
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V[1][0] = up[0];
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V[1][1] = up[1];
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V[1][2] = up[2];
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V[1][3] = -eye.dot(up);
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V[2][0] = lookAt[0];
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V[2][1] = lookAt[1];
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V[2][2] = lookAt[2];
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V[2][3] = -eye.dot(lookAt);
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V[3][3] = 1.0;
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return V;
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}
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Matrix4x4 Matrix4x4::ViewInverse(const Point4D &left, const Point4D &up, const Point4D &lookAt, const Point4D &eye) {
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Matrix4x4 inv{};
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inv.setZero();
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inv[0][0] = left[0];
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inv[1][0] = left[1];
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inv[2][0] = left[2];
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inv[0][3] = eye[0];
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inv[0][1] = up[0];
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inv[1][1] = up[1];
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inv[2][1] = up[2];
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inv[1][3] = eye[1];
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inv[0][2] = lookAt[0];
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inv[1][2] = lookAt[1];
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inv[2][2] = lookAt[2];
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inv[2][3] = eye[2];
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inv[3][3] = 1.0;
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return inv;
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}
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Matrix4x4 Matrix4x4::Rotation(const Point4D &v) {
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return RotationX(v.x())*RotationY(v.y())*RotationZ(v.z());
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}
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Matrix4x4 Matrix4x4::Scale(const Point4D &s) {
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return Matrix4x4::Scale(s.x(), s.y(), s.z());
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}
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