mirror of
https://github.com/orange-cpp/omath.git
synced 2026-02-13 07:03:25 +00:00
Orange
75565ecf2d
Adds functions to generate left- and right-handed orthographic projection matrices. This provides more flexibility when defining a projection for rendering.
527 lines
17 KiB
C++
527 lines
17 KiB
C++
//
|
|
// Created by vlad on 9/29/2024.
|
|
//
|
|
#pragma once
|
|
#include "omath/vector3.hpp"
|
|
#include <algorithm>
|
|
#include <array>
|
|
#include <iomanip>
|
|
#include <numeric>
|
|
#include <sstream>
|
|
#include <stdexcept>
|
|
#include <utility>
|
|
|
|
#ifdef near
|
|
#undef near
|
|
#endif
|
|
|
|
#ifdef far
|
|
#undef far
|
|
#endif
|
|
|
|
namespace omath
|
|
{
|
|
struct MatSize
|
|
{
|
|
size_t rows, columns;
|
|
};
|
|
|
|
enum class MatStoreType : uint8_t
|
|
{
|
|
ROW_MAJOR = 0,
|
|
COLUMN_MAJOR
|
|
};
|
|
|
|
template<typename M1, typename M2> concept MatTemplateEqual
|
|
= (M1::rows == M2::rows) && (M1::columns == M2::columns)
|
|
&& std::is_same_v<typename M1::value_type, typename M2::value_type> && (M1::store_type == M2::store_type);
|
|
|
|
template<size_t Rows = 0, size_t Columns = 0, class Type = float, MatStoreType StoreType = MatStoreType::ROW_MAJOR>
|
|
requires std::is_arithmetic_v<Type>
|
|
class Mat final
|
|
{
|
|
public:
|
|
constexpr Mat() noexcept
|
|
{
|
|
clear();
|
|
}
|
|
|
|
[[nodiscard]]
|
|
constexpr static MatStoreType get_store_ordering() noexcept
|
|
{
|
|
return StoreType;
|
|
}
|
|
constexpr Mat(const std::initializer_list<std::initializer_list<Type>>& rows)
|
|
{
|
|
if (rows.size() != Rows)
|
|
throw std::invalid_argument("Initializer list rows size does not match template parameter Rows");
|
|
|
|
auto row_it = rows.begin();
|
|
for (size_t i = 0; i < Rows; ++i, ++row_it)
|
|
{
|
|
if (row_it->size() != Columns)
|
|
throw std::invalid_argument(
|
|
"All rows must have the same number of columns as template parameter Columns");
|
|
|
|
auto col_it = row_it->begin();
|
|
for (size_t j = 0; j < Columns; ++j, ++col_it)
|
|
{
|
|
at(i, j) = std::move(*col_it);
|
|
}
|
|
}
|
|
}
|
|
|
|
constexpr explicit Mat(const Type* raw_data)
|
|
{
|
|
std::copy_n(raw_data, Rows * Columns, m_data.begin());
|
|
}
|
|
|
|
constexpr Mat(const Mat& other) noexcept
|
|
{
|
|
m_data = other.m_data;
|
|
}
|
|
|
|
[[nodiscard]]
|
|
constexpr Type& operator[](const size_t row, const size_t col)
|
|
{
|
|
return at(row, col);
|
|
}
|
|
|
|
[[nodiscard]]
|
|
constexpr Type& operator[](const size_t row, const size_t col) const
|
|
{
|
|
return at(row, col);
|
|
}
|
|
|
|
constexpr Mat(Mat&& other) noexcept
|
|
{
|
|
m_data = std::move(other.m_data);
|
|
}
|
|
|
|
[[nodiscard]]
|
|
static constexpr size_t row_count() noexcept
|
|
{
|
|
return Rows;
|
|
}
|
|
|
|
[[nodiscard]]
|
|
static constexpr size_t columns_count() noexcept
|
|
{
|
|
return Columns;
|
|
}
|
|
|
|
[[nodiscard]]
|
|
static consteval MatSize size() noexcept
|
|
{
|
|
return {Rows, Columns};
|
|
}
|
|
|
|
[[nodiscard]]
|
|
constexpr const Type& at(const size_t row_index, const size_t column_index) const
|
|
{
|
|
#if !defined(NDEBUG) && defined(OMATH_SUPRESS_SAFETY_CHECKS)
|
|
if (row_index >= Rows || column_index >= Columns)
|
|
throw std::out_of_range("Index out of range");
|
|
#endif
|
|
if constexpr (StoreType == MatStoreType::ROW_MAJOR)
|
|
return m_data[row_index * Columns + column_index];
|
|
|
|
else if constexpr (StoreType == MatStoreType::COLUMN_MAJOR)
|
|
return m_data[row_index + column_index * Rows];
|
|
|
|
else
|
|
{
|
|
static_assert(false, "Invalid matrix access convention");
|
|
std::unreachable();
|
|
}
|
|
}
|
|
|
|
[[nodiscard]] constexpr Type& at(const size_t row_index, const size_t column_index)
|
|
{
|
|
return const_cast<Type&>(std::as_const(*this).at(row_index, column_index));
|
|
}
|
|
|
|
[[nodiscard]]
|
|
constexpr Type sum() const noexcept
|
|
{
|
|
return std::accumulate(m_data.begin(), m_data.end(), static_cast<Type>(0));
|
|
}
|
|
|
|
constexpr void clear() noexcept
|
|
{
|
|
set(static_cast<Type>(0));
|
|
}
|
|
|
|
constexpr void set(const Type& value) noexcept
|
|
{
|
|
std::ranges::fill(m_data, value);
|
|
}
|
|
|
|
// Operator overloading for multiplication with another Mat
|
|
template<size_t OtherColumns> [[nodiscard]]
|
|
constexpr Mat<Rows, OtherColumns, Type, StoreType>
|
|
operator*(const Mat<Columns, OtherColumns, Type, StoreType>& other) const
|
|
{
|
|
Mat<Rows, OtherColumns, Type, StoreType> result;
|
|
|
|
for (size_t i = 0; i < Rows; ++i)
|
|
for (size_t j = 0; j < OtherColumns; ++j)
|
|
{
|
|
Type sum = 0;
|
|
for (size_t k = 0; k < Columns; ++k)
|
|
sum += at(i, k) * other.at(k, j);
|
|
result.at(i, j) = sum;
|
|
}
|
|
return result;
|
|
}
|
|
|
|
constexpr Mat& operator*=(const Type& f) noexcept
|
|
{
|
|
std::ranges::for_each(m_data, [&f](auto& val) { val *= f; });
|
|
return *this;
|
|
}
|
|
|
|
template<size_t OtherColumns> constexpr Mat<Rows, OtherColumns, Type, StoreType>
|
|
operator*=(const Mat<Columns, OtherColumns, Type, StoreType>& other)
|
|
{
|
|
return *this = *this * other;
|
|
}
|
|
|
|
[[nodiscard]]
|
|
constexpr Mat operator*(const Type& value) const noexcept
|
|
{
|
|
Mat result(*this);
|
|
result *= value;
|
|
return result;
|
|
}
|
|
|
|
constexpr Mat& operator/=(const Type& value) noexcept
|
|
{
|
|
std::ranges::for_each(m_data, [&value](auto& val) { val /= value; });
|
|
return *this;
|
|
}
|
|
|
|
[[nodiscard]]
|
|
constexpr Mat operator/(const Type& value) const noexcept
|
|
{
|
|
Mat result(*this);
|
|
result /= value;
|
|
return result;
|
|
}
|
|
|
|
constexpr Mat& operator=(const Mat& other) noexcept
|
|
{
|
|
if (this != &other)
|
|
m_data = other.m_data;
|
|
|
|
return *this;
|
|
}
|
|
|
|
constexpr Mat& operator=(Mat&& other) noexcept
|
|
{
|
|
if (this != &other)
|
|
m_data = std::move(other.m_data);
|
|
|
|
return *this;
|
|
}
|
|
|
|
[[nodiscard]]
|
|
constexpr Mat<Columns, Rows, Type, StoreType> transposed() const noexcept
|
|
{
|
|
Mat<Columns, Rows, Type, StoreType> transposed;
|
|
for (size_t i = 0; i < Rows; ++i)
|
|
for (size_t j = 0; j < Columns; ++j)
|
|
transposed.at(j, i) = at(i, j);
|
|
|
|
return transposed;
|
|
}
|
|
|
|
[[nodiscard]]
|
|
constexpr Type determinant() const
|
|
{
|
|
static_assert(Rows == Columns, "Determinant is only defined for square matrices.");
|
|
|
|
if constexpr (Rows == 1)
|
|
return at(0, 0);
|
|
|
|
if constexpr (Rows == 2)
|
|
return at(0, 0) * at(1, 1) - at(0, 1) * at(1, 0);
|
|
|
|
if constexpr (Rows > 2)
|
|
{
|
|
Type det = 0;
|
|
for (size_t column = 0; column < Columns; ++column)
|
|
{
|
|
const Type cofactor = at(0, column) * alg_complement(0, column);
|
|
det += cofactor;
|
|
}
|
|
return det;
|
|
}
|
|
std::unreachable();
|
|
}
|
|
|
|
[[nodiscard]]
|
|
constexpr Mat<Rows - 1, Columns - 1, Type, StoreType> strip(const size_t row, const size_t column) const
|
|
{
|
|
static_assert(Rows - 1 > 0 && Columns - 1 > 0);
|
|
Mat<Rows - 1, Columns - 1, Type, StoreType> result;
|
|
for (size_t i = 0, m = 0; i < Rows; ++i)
|
|
{
|
|
if (i == row)
|
|
continue;
|
|
for (size_t j = 0, n = 0; j < Columns; ++j)
|
|
{
|
|
if (j == column)
|
|
continue;
|
|
result.at(m, n) = at(i, j);
|
|
++n;
|
|
}
|
|
++m;
|
|
}
|
|
return result;
|
|
}
|
|
|
|
[[nodiscard]]
|
|
constexpr Type minor(const size_t row, const size_t column) const
|
|
{
|
|
return strip(row, column).determinant();
|
|
}
|
|
|
|
[[nodiscard]]
|
|
constexpr Type alg_complement(const size_t row, const size_t column) const
|
|
{
|
|
const auto minor_value = minor(row, column);
|
|
return (row + column + 2) % 2 == 0 ? minor_value : -minor_value;
|
|
}
|
|
|
|
[[nodiscard]]
|
|
constexpr const std::array<Type, Rows * Columns>& raw_array() const
|
|
{
|
|
return m_data;
|
|
}
|
|
|
|
[[nodiscard]]
|
|
constexpr std::array<Type, Rows * Columns>& raw_array()
|
|
{
|
|
return m_data;
|
|
}
|
|
|
|
[[nodiscard]]
|
|
std::string to_string() const noexcept
|
|
{
|
|
std::ostringstream oss;
|
|
oss << "[[";
|
|
|
|
for (size_t i = 0; i < Rows; ++i)
|
|
{
|
|
if (i > 0)
|
|
oss << " [";
|
|
|
|
for (size_t j = 0; j < Columns; ++j)
|
|
{
|
|
oss << std::setw(9) << std::fixed << std::setprecision(3) << at(i, j);
|
|
if (j != Columns - 1)
|
|
oss << ", ";
|
|
}
|
|
oss << (i == Rows - 1 ? "]]" : "]\n");
|
|
}
|
|
return oss.str();
|
|
}
|
|
|
|
[[nodiscard]]
|
|
bool operator==(const Mat& mat) const
|
|
{
|
|
return m_data == mat.m_data;
|
|
}
|
|
|
|
[[nodiscard]]
|
|
bool operator!=(const Mat& mat) const
|
|
{
|
|
return !operator==(mat);
|
|
}
|
|
|
|
// Static methods that return fixed-size matrices
|
|
[[nodiscard]]
|
|
constexpr static Mat<4, 4> to_screen_mat(const Type& screen_width, const Type& screen_height) noexcept
|
|
{
|
|
return {
|
|
{screen_width / 2, 0, 0, 0},
|
|
{0, -screen_height / 2, 0, 0},
|
|
{0, 0, 1, 0},
|
|
{screen_width / 2, screen_height / 2, 0, 1},
|
|
};
|
|
}
|
|
|
|
[[nodiscard]]
|
|
constexpr std::optional<Mat> inverted() const
|
|
{
|
|
const auto det = determinant();
|
|
|
|
if (det == 0)
|
|
return std::nullopt;
|
|
|
|
const auto transposed_mat = transposed();
|
|
Mat result;
|
|
|
|
for (std::size_t row = 0; row < Rows; row++)
|
|
for (std::size_t column = 0; column < Rows; column++)
|
|
result.at(row, column) = transposed_mat.alg_complement(row, column);
|
|
|
|
result /= det;
|
|
|
|
return {result};
|
|
}
|
|
|
|
private:
|
|
std::array<Type, Rows * Columns> m_data;
|
|
};
|
|
|
|
template<class Type = float, MatStoreType St = MatStoreType::ROW_MAJOR> [[nodiscard]]
|
|
constexpr static Mat<1, 4, Type, St> mat_row_from_vector(const Vector3<Type>& vector) noexcept
|
|
{
|
|
return {{vector.x, vector.y, vector.z, 1}};
|
|
}
|
|
|
|
template<class Type = float, MatStoreType St = MatStoreType::ROW_MAJOR> [[nodiscard]]
|
|
constexpr static Mat<4, 1, Type, St> mat_column_from_vector(const Vector3<Type>& vector) noexcept
|
|
{
|
|
return {{vector.x}, {vector.y}, {vector.z}, {1}};
|
|
}
|
|
|
|
template<class Type = float, MatStoreType St = MatStoreType::ROW_MAJOR>
|
|
[[nodiscard]]
|
|
constexpr Mat<4, 4, Type, St> mat_translation(const Vector3<Type>& diff) noexcept
|
|
{
|
|
return
|
|
{
|
|
{1, 0, 0, diff.x},
|
|
{0, 1, 0, diff.y},
|
|
{0, 0, 1, diff.z},
|
|
{0, 0, 0, 1},
|
|
};
|
|
}
|
|
|
|
template<class Type = float, MatStoreType St = MatStoreType::ROW_MAJOR, class Angle>
|
|
[[nodiscard]]
|
|
Mat<4, 4, Type, St> mat_rotation_axis_x(const Angle& angle) noexcept
|
|
{
|
|
return
|
|
{
|
|
{1, 0, 0, 0},
|
|
{0, angle.cos(), -angle.sin(), 0},
|
|
{0, angle.sin(), angle.cos(), 0},
|
|
{0, 0, 0, 1}
|
|
};
|
|
}
|
|
|
|
template<class Type = float, MatStoreType St = MatStoreType::ROW_MAJOR, class Angle>
|
|
[[nodiscard]]
|
|
Mat<4, 4, Type, St> mat_rotation_axis_y(const Angle& angle) noexcept
|
|
{
|
|
return
|
|
{
|
|
{angle.cos(), 0, angle.sin(), 0},
|
|
{0 , 1, 0, 0},
|
|
{-angle.sin(), 0, angle.cos(), 0},
|
|
{0 , 0, 0, 1}
|
|
};
|
|
}
|
|
|
|
template<class Type = float, MatStoreType St = MatStoreType::ROW_MAJOR, class Angle>
|
|
[[nodiscard]]
|
|
Mat<4, 4, Type, St> mat_rotation_axis_z(const Angle& angle) noexcept
|
|
{
|
|
return
|
|
{
|
|
{angle.cos(), -angle.sin(), 0, 0},
|
|
{angle.sin(), angle.cos(), 0, 0},
|
|
{ 0, 0, 1, 0},
|
|
{ 0, 0, 0, 1},
|
|
};
|
|
}
|
|
|
|
template<class Type = float, MatStoreType St = MatStoreType::ROW_MAJOR>
|
|
[[nodiscard]]
|
|
static Mat<4, 4, Type, St> mat_camera_view(const Vector3<Type>& forward, const Vector3<Type>& right,
|
|
const Vector3<Type>& up, const Vector3<Type>& camera_origin) noexcept
|
|
{
|
|
return Mat<4, 4, Type, St>
|
|
{
|
|
{right.x, right.y, right.z, 0},
|
|
{up.x, up.y, up.z, 0},
|
|
{forward.x, forward.y, forward.z, 0},
|
|
{0, 0, 0, 1},
|
|
} * mat_translation<Type, St>(-camera_origin);
|
|
}
|
|
|
|
template<class Type = float, MatStoreType St = MatStoreType::ROW_MAJOR>
|
|
[[nodiscard]]
|
|
Mat<4, 4, Type, St> mat_perspective_left_handed(const float field_of_view, const float aspect_ratio,
|
|
const float near, const float far) noexcept
|
|
{
|
|
const float fov_half_tan = std::tan(angles::degrees_to_radians(field_of_view) / 2.f);
|
|
|
|
return {{1.f / (aspect_ratio * fov_half_tan), 0.f, 0.f, 0.f},
|
|
{0.f, 1.f / fov_half_tan, 0.f, 0.f},
|
|
{0.f, 0.f, (far + near) / (far - near), -(2.f * near * far) / (far - near)},
|
|
{0.f, 0.f, 1.f, 0.f}};
|
|
}
|
|
|
|
template<class Type = float, MatStoreType St = MatStoreType::ROW_MAJOR>
|
|
[[nodiscard]]
|
|
Mat<4, 4, Type, St> mat_perspective_right_handed(const float field_of_view, const float aspect_ratio,
|
|
const float near, const float far) noexcept
|
|
{
|
|
const float fov_half_tan = std::tan(angles::degrees_to_radians(field_of_view) / 2.f);
|
|
|
|
return {{1.f / (aspect_ratio * fov_half_tan), 0.f, 0.f, 0.f},
|
|
{0.f, 1.f / fov_half_tan, 0.f, 0.f},
|
|
{0.f, 0.f, -(far + near) / (far - near), -(2.f * near * far) / (far - near)},
|
|
{0.f, 0.f, -1.f, 0.f}};
|
|
}
|
|
template<class Type = float, MatStoreType St = MatStoreType::ROW_MAJOR>
|
|
[[nodiscard]]
|
|
Mat<4, 4, Type, St> mat_ortho_left_handed(const Type left, const Type right,
|
|
const Type bottom, const Type top,
|
|
const Type near, const Type far) noexcept
|
|
{
|
|
return
|
|
{
|
|
{ static_cast<Type>(2) / (right - left), 0.f, 0.f, -(right + left) / (right - left)},
|
|
{ 0.f, static_cast<Type>(2) / (top - bottom), 0.f, -(top + bottom) / (top - bottom)},
|
|
{ 0.f, 0.f, static_cast<Type>(2) / (far - near), -(far + near) / (far - near) },
|
|
{ 0.f, 0.f, 0.f, 1.f }
|
|
};
|
|
}
|
|
template<class Type = float, MatStoreType St = MatStoreType::ROW_MAJOR>
|
|
[[nodiscard]]
|
|
Mat<4, 4, Type, St> mat_ortho_right_handed(const Type left, const Type right,
|
|
const Type bottom, const Type top,
|
|
const Type near, const Type far) noexcept
|
|
{
|
|
return
|
|
{
|
|
{ static_cast<Type>(2) / (right - left), 0.f, 0.f, -(right + left) / (right - left)},
|
|
{ 0.f, static_cast<Type>(2) / (top - bottom), 0.f, -(top + bottom) / (top - bottom)},
|
|
{ 0.f, 0.f, -static_cast<Type>(2) / (far - near), -(far + near) / (far - near) },
|
|
{ 0.f, 0.f, 0.f, 1.f }
|
|
};
|
|
}
|
|
|
|
} // namespace omath
|
|
|
|
template<size_t Rows, size_t Columns, class Type, omath::MatStoreType StoreType>
|
|
struct std::formatter<omath::Mat<Rows, Columns, Type, StoreType>> // NOLINT(*-dcl58-cpp)
|
|
{
|
|
using MatType = omath::Mat<Rows, Columns, Type, StoreType>;
|
|
[[nodiscard]]
|
|
static constexpr auto parse(std::format_parse_context& ctx)
|
|
{
|
|
return ctx.begin();
|
|
}
|
|
[[nodiscard]]
|
|
static auto format(const MatType& mat, std::format_context& ctx)
|
|
{
|
|
return std::format_to(ctx.out(), "{}", mat.to_string());
|
|
}
|
|
}; |