| /* |
| * Copyright 2013 The Android Open Source Project |
| * |
| * Licensed under the Apache License, Version 2.0 (the "License"); |
| * you may not use this file except in compliance with the License. |
| * You may obtain a copy of the License at |
| * |
| * http://www.apache.org/licenses/LICENSE-2.0 |
| * |
| * Unless required by applicable law or agreed to in writing, software |
| * distributed under the License is distributed on an "AS IS" BASIS, |
| * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| * See the License for the specific language governing permissions and |
| * limitations under the License. |
| */ |
| |
| #pragma once |
| |
| #include <math/mat3.h> |
| #include <math/quat.h> |
| #include <math/TMatHelpers.h> |
| #include <math/vec3.h> |
| #include <math/vec4.h> |
| |
| #include <stdint.h> |
| #include <sys/types.h> |
| #include <limits> |
| |
| #define PURE __attribute__((pure)) |
| |
| #if __cplusplus >= 201402L |
| #define CONSTEXPR constexpr |
| #else |
| #define CONSTEXPR |
| #endif |
| |
| namespace android { |
| // ------------------------------------------------------------------------------------- |
| namespace details { |
| |
| template<typename T> |
| class TQuaternion; |
| |
| /** |
| * A 4x4 column-major matrix class. |
| * |
| * Conceptually a 4x4 matrix is a an array of 4 column double4: |
| * |
| * mat4 m = |
| * \f$ |
| * \left( |
| * \begin{array}{cccc} |
| * m[0] & m[1] & m[2] & m[3] \\ |
| * \end{array} |
| * \right) |
| * \f$ |
| * = |
| * \f$ |
| * \left( |
| * \begin{array}{cccc} |
| * m[0][0] & m[1][0] & m[2][0] & m[3][0] \\ |
| * m[0][1] & m[1][1] & m[2][1] & m[3][1] \\ |
| * m[0][2] & m[1][2] & m[2][2] & m[3][2] \\ |
| * m[0][3] & m[1][3] & m[2][3] & m[3][3] \\ |
| * \end{array} |
| * \right) |
| * \f$ |
| * = |
| * \f$ |
| * \left( |
| * \begin{array}{cccc} |
| * m(0,0) & m(0,1) & m(0,2) & m(0,3) \\ |
| * m(1,0) & m(1,1) & m(1,2) & m(1,3) \\ |
| * m(2,0) & m(2,1) & m(2,2) & m(2,3) \\ |
| * m(3,0) & m(3,1) & m(3,2) & m(3,3) \\ |
| * \end{array} |
| * \right) |
| * \f$ |
| * |
| * m[n] is the \f$ n^{th} \f$ column of the matrix and is a double4. |
| * |
| */ |
| template <typename T> |
| class TMat44 : public TVecUnaryOperators<TMat44, T>, |
| public TVecComparisonOperators<TMat44, T>, |
| public TVecAddOperators<TMat44, T>, |
| public TMatProductOperators<TMat44, T>, |
| public TMatSquareFunctions<TMat44, T>, |
| public TMatTransform<TMat44, T>, |
| public TMatHelpers<TMat44, T>, |
| public TMatDebug<TMat44, T> { |
| public: |
| enum no_init { NO_INIT }; |
| typedef T value_type; |
| typedef T& reference; |
| typedef T const& const_reference; |
| typedef size_t size_type; |
| typedef TVec4<T> col_type; |
| typedef TVec4<T> row_type; |
| |
| static constexpr size_t COL_SIZE = col_type::SIZE; // size of a column (i.e.: number of rows) |
| static constexpr size_t ROW_SIZE = row_type::SIZE; // size of a row (i.e.: number of columns) |
| static constexpr size_t NUM_ROWS = COL_SIZE; |
| static constexpr size_t NUM_COLS = ROW_SIZE; |
| |
| private: |
| /* |
| * <-- N columns --> |
| * |
| * a[0][0] a[1][0] a[2][0] ... a[N][0] ^ |
| * a[0][1] a[1][1] a[2][1] ... a[N][1] | |
| * a[0][2] a[1][2] a[2][2] ... a[N][2] M rows |
| * ... | |
| * a[0][M] a[1][M] a[2][M] ... a[N][M] v |
| * |
| * COL_SIZE = M |
| * ROW_SIZE = N |
| * m[0] = [ a[0][0] a[0][1] a[0][2] ... a[0][M] ] |
| */ |
| |
| col_type m_value[NUM_COLS]; |
| |
| public: |
| // array access |
| inline constexpr col_type const& operator[](size_t column) const { |
| #if __cplusplus >= 201402L |
| // only possible in C++0x14 with constexpr |
| assert(column < NUM_COLS); |
| #endif |
| return m_value[column]; |
| } |
| |
| inline col_type& operator[](size_t column) { |
| assert(column < NUM_COLS); |
| return m_value[column]; |
| } |
| |
| // ----------------------------------------------------------------------- |
| // we want the compiler generated versions for these... |
| TMat44(const TMat44&) = default; |
| ~TMat44() = default; |
| TMat44& operator = (const TMat44&) = default; |
| |
| /* |
| * constructors |
| */ |
| |
| // leaves object uninitialized. use with caution. |
| explicit constexpr TMat44(no_init) |
| : m_value{ col_type(col_type::NO_INIT), |
| col_type(col_type::NO_INIT), |
| col_type(col_type::NO_INIT), |
| col_type(col_type::NO_INIT) } {} |
| |
| /** initialize to identity. |
| * |
| * \f$ |
| * \left( |
| * \begin{array}{cccc} |
| * 1 & 0 & 0 & 0 \\ |
| * 0 & 1 & 0 & 0 \\ |
| * 0 & 0 & 1 & 0 \\ |
| * 0 & 0 & 0 & 1 \\ |
| * \end{array} |
| * \right) |
| * \f$ |
| */ |
| CONSTEXPR TMat44(); |
| |
| /** initialize to Identity*scalar. |
| * |
| * \f$ |
| * \left( |
| * \begin{array}{cccc} |
| * v & 0 & 0 & 0 \\ |
| * 0 & v & 0 & 0 \\ |
| * 0 & 0 & v & 0 \\ |
| * 0 & 0 & 0 & v \\ |
| * \end{array} |
| * \right) |
| * \f$ |
| */ |
| template<typename U> |
| explicit CONSTEXPR TMat44(U v); |
| |
| /** sets the diagonal to a vector. |
| * |
| * \f$ |
| * \left( |
| * \begin{array}{cccc} |
| * v[0] & 0 & 0 & 0 \\ |
| * 0 & v[1] & 0 & 0 \\ |
| * 0 & 0 & v[2] & 0 \\ |
| * 0 & 0 & 0 & v[3] \\ |
| * \end{array} |
| * \right) |
| * \f$ |
| */ |
| template <typename U> |
| explicit CONSTEXPR TMat44(const TVec4<U>& v); |
| |
| // construct from another matrix of the same size |
| template <typename U> |
| explicit CONSTEXPR TMat44(const TMat44<U>& rhs); |
| |
| /** construct from 4 column vectors. |
| * |
| * \f$ |
| * \left( |
| * \begin{array}{cccc} |
| * v0 & v1 & v2 & v3 \\ |
| * \end{array} |
| * \right) |
| * \f$ |
| */ |
| template <typename A, typename B, typename C, typename D> |
| CONSTEXPR TMat44(const TVec4<A>& v0, const TVec4<B>& v1, const TVec4<C>& v2, const TVec4<D>& v3); |
| |
| /** construct from 16 elements in column-major form. |
| * |
| * \f$ |
| * \left( |
| * \begin{array}{cccc} |
| * m[0][0] & m[1][0] & m[2][0] & m[3][0] \\ |
| * m[0][1] & m[1][1] & m[2][1] & m[3][1] \\ |
| * m[0][2] & m[1][2] & m[2][2] & m[3][2] \\ |
| * m[0][3] & m[1][3] & m[2][3] & m[3][3] \\ |
| * \end{array} |
| * \right) |
| * \f$ |
| */ |
| template < |
| typename A, typename B, typename C, typename D, |
| typename E, typename F, typename G, typename H, |
| typename I, typename J, typename K, typename L, |
| typename M, typename N, typename O, typename P> |
| CONSTEXPR TMat44( |
| A m00, B m01, C m02, D m03, |
| E m10, F m11, G m12, H m13, |
| I m20, J m21, K m22, L m23, |
| M m30, N m31, O m32, P m33); |
| |
| /** |
| * construct from a quaternion |
| */ |
| template <typename U> |
| explicit CONSTEXPR TMat44(const TQuaternion<U>& q); |
| |
| /** |
| * construct from a C array in column major form. |
| */ |
| template <typename U> |
| explicit CONSTEXPR TMat44(U const* rawArray); |
| |
| /** |
| * construct from a 3x3 matrix |
| */ |
| template <typename U> |
| explicit CONSTEXPR TMat44(const TMat33<U>& matrix); |
| |
| /** |
| * construct from a 3x3 matrix and 3d translation |
| */ |
| template <typename U, typename V> |
| CONSTEXPR TMat44(const TMat33<U>& matrix, const TVec3<V>& translation); |
| |
| /** |
| * construct from a 3x3 matrix and 4d last column. |
| */ |
| template <typename U, typename V> |
| CONSTEXPR TMat44(const TMat33<U>& matrix, const TVec4<V>& column3); |
| |
| /* |
| * helpers |
| */ |
| |
| static CONSTEXPR TMat44 ortho(T left, T right, T bottom, T top, T near, T far); |
| |
| static CONSTEXPR TMat44 frustum(T left, T right, T bottom, T top, T near, T far); |
| |
| enum class Fov { |
| HORIZONTAL, |
| VERTICAL |
| }; |
| static CONSTEXPR TMat44 perspective(T fov, T aspect, T near, T far, Fov direction = Fov::VERTICAL); |
| |
| template <typename A, typename B, typename C> |
| static CONSTEXPR TMat44 lookAt(const TVec3<A>& eye, const TVec3<B>& center, const TVec3<C>& up); |
| |
| template <typename A> |
| static CONSTEXPR TVec3<A> project(const TMat44& projectionMatrix, TVec3<A> vertice) { |
| TVec4<A> r = projectionMatrix * TVec4<A>{ vertice, 1 }; |
| return r.xyz / r.w; |
| } |
| |
| template <typename A> |
| static CONSTEXPR TVec4<A> project(const TMat44& projectionMatrix, TVec4<A> vertice) { |
| vertice = projectionMatrix * vertice; |
| return { vertice.xyz / vertice.w, 1 }; |
| } |
| |
| /** |
| * Constructs a 3x3 matrix from the upper-left corner of this 4x4 matrix |
| */ |
| inline constexpr TMat33<T> upperLeft() const { |
| return TMat33<T>(m_value[0].xyz, m_value[1].xyz, m_value[2].xyz); |
| } |
| }; |
| |
| // ---------------------------------------------------------------------------------------- |
| // Constructors |
| // ---------------------------------------------------------------------------------------- |
| |
| // Since the matrix code could become pretty big quickly, we don't inline most |
| // operations. |
| |
| template <typename T> |
| CONSTEXPR TMat44<T>::TMat44() { |
| m_value[0] = col_type(1, 0, 0, 0); |
| m_value[1] = col_type(0, 1, 0, 0); |
| m_value[2] = col_type(0, 0, 1, 0); |
| m_value[3] = col_type(0, 0, 0, 1); |
| } |
| |
| template <typename T> |
| template <typename U> |
| CONSTEXPR TMat44<T>::TMat44(U v) { |
| m_value[0] = col_type(v, 0, 0, 0); |
| m_value[1] = col_type(0, v, 0, 0); |
| m_value[2] = col_type(0, 0, v, 0); |
| m_value[3] = col_type(0, 0, 0, v); |
| } |
| |
| template<typename T> |
| template<typename U> |
| CONSTEXPR TMat44<T>::TMat44(const TVec4<U>& v) { |
| m_value[0] = col_type(v.x, 0, 0, 0); |
| m_value[1] = col_type(0, v.y, 0, 0); |
| m_value[2] = col_type(0, 0, v.z, 0); |
| m_value[3] = col_type(0, 0, 0, v.w); |
| } |
| |
| // construct from 16 scalars |
| template<typename T> |
| template < |
| typename A, typename B, typename C, typename D, |
| typename E, typename F, typename G, typename H, |
| typename I, typename J, typename K, typename L, |
| typename M, typename N, typename O, typename P> |
| CONSTEXPR TMat44<T>::TMat44( |
| A m00, B m01, C m02, D m03, |
| E m10, F m11, G m12, H m13, |
| I m20, J m21, K m22, L m23, |
| M m30, N m31, O m32, P m33) { |
| m_value[0] = col_type(m00, m01, m02, m03); |
| m_value[1] = col_type(m10, m11, m12, m13); |
| m_value[2] = col_type(m20, m21, m22, m23); |
| m_value[3] = col_type(m30, m31, m32, m33); |
| } |
| |
| template <typename T> |
| template <typename U> |
| CONSTEXPR TMat44<T>::TMat44(const TMat44<U>& rhs) { |
| for (size_t col = 0; col < NUM_COLS; ++col) { |
| m_value[col] = col_type(rhs[col]); |
| } |
| } |
| |
| // Construct from 4 column vectors. |
| template <typename T> |
| template <typename A, typename B, typename C, typename D> |
| CONSTEXPR TMat44<T>::TMat44( |
| const TVec4<A>& v0, const TVec4<B>& v1, |
| const TVec4<C>& v2, const TVec4<D>& v3) { |
| m_value[0] = col_type(v0); |
| m_value[1] = col_type(v1); |
| m_value[2] = col_type(v2); |
| m_value[3] = col_type(v3); |
| } |
| |
| // Construct from raw array, in column-major form. |
| template <typename T> |
| template <typename U> |
| CONSTEXPR TMat44<T>::TMat44(U const* rawArray) { |
| for (size_t col = 0; col < NUM_COLS; ++col) { |
| for (size_t row = 0; row < NUM_ROWS; ++row) { |
| m_value[col][row] = *rawArray++; |
| } |
| } |
| } |
| |
| template <typename T> |
| template <typename U> |
| CONSTEXPR TMat44<T>::TMat44(const TQuaternion<U>& q) { |
| const U n = q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w; |
| const U s = n > 0 ? 2/n : 0; |
| const U x = s*q.x; |
| const U y = s*q.y; |
| const U z = s*q.z; |
| const U xx = x*q.x; |
| const U xy = x*q.y; |
| const U xz = x*q.z; |
| const U xw = x*q.w; |
| const U yy = y*q.y; |
| const U yz = y*q.z; |
| const U yw = y*q.w; |
| const U zz = z*q.z; |
| const U zw = z*q.w; |
| m_value[0] = col_type(1-yy-zz, xy+zw, xz-yw, 0); |
| m_value[1] = col_type( xy-zw, 1-xx-zz, yz+xw, 0); // NOLINT |
| m_value[2] = col_type( xz+yw, yz-xw, 1-xx-yy, 0); // NOLINT |
| m_value[3] = col_type( 0, 0, 0, 1); // NOLINT |
| } |
| |
| template <typename T> |
| template <typename U> |
| CONSTEXPR TMat44<T>::TMat44(const TMat33<U>& m) { |
| m_value[0] = col_type(m[0][0], m[0][1], m[0][2], 0); |
| m_value[1] = col_type(m[1][0], m[1][1], m[1][2], 0); |
| m_value[2] = col_type(m[2][0], m[2][1], m[2][2], 0); |
| m_value[3] = col_type( 0, 0, 0, 1); // NOLINT |
| } |
| |
| template <typename T> |
| template <typename U, typename V> |
| CONSTEXPR TMat44<T>::TMat44(const TMat33<U>& m, const TVec3<V>& v) { |
| m_value[0] = col_type(m[0][0], m[0][1], m[0][2], 0); |
| m_value[1] = col_type(m[1][0], m[1][1], m[1][2], 0); |
| m_value[2] = col_type(m[2][0], m[2][1], m[2][2], 0); |
| m_value[3] = col_type( v[0], v[1], v[2], 1); // NOLINT |
| } |
| |
| template <typename T> |
| template <typename U, typename V> |
| CONSTEXPR TMat44<T>::TMat44(const TMat33<U>& m, const TVec4<V>& v) { |
| m_value[0] = col_type(m[0][0], m[0][1], m[0][2], 0); // NOLINT |
| m_value[1] = col_type(m[1][0], m[1][1], m[1][2], 0); // NOLINT |
| m_value[2] = col_type(m[2][0], m[2][1], m[2][2], 0); // NOLINT |
| m_value[3] = col_type( v[0], v[1], v[2], v[3]); // NOLINT |
| } |
| |
| // ---------------------------------------------------------------------------------------- |
| // Helpers |
| // ---------------------------------------------------------------------------------------- |
| |
| template <typename T> |
| CONSTEXPR TMat44<T> TMat44<T>::ortho(T left, T right, T bottom, T top, T near, T far) { |
| TMat44<T> m; |
| m[0][0] = 2 / (right - left); |
| m[1][1] = 2 / (top - bottom); |
| m[2][2] = -2 / (far - near); |
| m[3][0] = -(right + left) / (right - left); |
| m[3][1] = -(top + bottom) / (top - bottom); |
| m[3][2] = -(far + near) / (far - near); |
| return m; |
| } |
| |
| template <typename T> |
| CONSTEXPR TMat44<T> TMat44<T>::frustum(T left, T right, T bottom, T top, T near, T far) { |
| TMat44<T> m; |
| m[0][0] = (2 * near) / (right - left); |
| m[1][1] = (2 * near) / (top - bottom); |
| m[2][0] = (right + left) / (right - left); |
| m[2][1] = (top + bottom) / (top - bottom); |
| m[2][2] = -(far + near) / (far - near); |
| m[2][3] = -1; |
| m[3][2] = -(2 * far * near) / (far - near); |
| m[3][3] = 0; |
| return m; |
| } |
| |
| template <typename T> |
| CONSTEXPR TMat44<T> TMat44<T>::perspective(T fov, T aspect, T near, T far, TMat44::Fov direction) { |
| T h; |
| T w; |
| |
| if (direction == TMat44::Fov::VERTICAL) { |
| h = std::tan(fov * M_PI / 360.0f) * near; |
| w = h * aspect; |
| } else { |
| w = std::tan(fov * M_PI / 360.0f) * near; |
| h = w / aspect; |
| } |
| return frustum(-w, w, -h, h, near, far); |
| } |
| |
| /* |
| * Returns a matrix representing the pose of a virtual camera looking towards -Z in its |
| * local Y-up coordinate system. "eye" is where the camera is located, "center" is the points its |
| * looking at and "up" defines where the Y axis of the camera's local coordinate system is. |
| */ |
| template <typename T> |
| template <typename A, typename B, typename C> |
| CONSTEXPR TMat44<T> TMat44<T>::lookAt(const TVec3<A>& eye, const TVec3<B>& center, const TVec3<C>& up) { |
| TVec3<T> z_axis(normalize(center - eye)); |
| TVec3<T> norm_up(normalize(up)); |
| if (std::abs(dot(z_axis, norm_up)) > 0.999) { |
| // Fix up vector if we're degenerate (looking straight up, basically) |
| norm_up = { norm_up.z, norm_up.x, norm_up.y }; |
| } |
| TVec3<T> x_axis(normalize(cross(z_axis, norm_up))); |
| TVec3<T> y_axis(cross(x_axis, z_axis)); |
| return TMat44<T>( |
| TVec4<T>(x_axis, 0), |
| TVec4<T>(y_axis, 0), |
| TVec4<T>(-z_axis, 0), |
| TVec4<T>(eye, 1)); |
| } |
| |
| // ---------------------------------------------------------------------------------------- |
| // Arithmetic operators outside of class |
| // ---------------------------------------------------------------------------------------- |
| |
| /* We use non-friend functions here to prevent the compiler from using |
| * implicit conversions, for instance of a scalar to a vector. The result would |
| * not be what the caller expects. |
| * |
| * Also note that the order of the arguments in the inner loop is important since |
| * it determines the output type (only relevant when T != U). |
| */ |
| |
| // matrix * column-vector, result is a vector of the same type than the input vector |
| template <typename T, typename U> |
| CONSTEXPR typename TMat44<T>::col_type PURE operator *(const TMat44<T>& lhs, const TVec4<U>& rhs) { |
| // Result is initialized to zero. |
| typename TMat44<T>::col_type result; |
| for (size_t col = 0; col < TMat44<T>::NUM_COLS; ++col) { |
| result += lhs[col] * rhs[col]; |
| } |
| return result; |
| } |
| |
| // mat44 * vec3, result is vec3( mat44 * {vec3, 1} ) |
| template <typename T, typename U> |
| CONSTEXPR typename TMat44<T>::col_type PURE operator *(const TMat44<T>& lhs, const TVec3<U>& rhs) { |
| return lhs * TVec4<U>{ rhs, 1 }; |
| } |
| |
| |
| // row-vector * matrix, result is a vector of the same type than the input vector |
| template <typename T, typename U> |
| CONSTEXPR typename TMat44<U>::row_type PURE operator *(const TVec4<U>& lhs, const TMat44<T>& rhs) { |
| typename TMat44<U>::row_type result(TMat44<U>::row_type::NO_INIT); |
| for (size_t col = 0; col < TMat44<T>::NUM_COLS; ++col) { |
| result[col] = dot(lhs, rhs[col]); |
| } |
| return result; |
| } |
| |
| // matrix * scalar, result is a matrix of the same type than the input matrix |
| template <typename T, typename U> |
| constexpr typename std::enable_if<std::is_arithmetic<U>::value, TMat44<T>>::type PURE |
| operator *(TMat44<T> lhs, U rhs) { |
| return lhs *= rhs; |
| } |
| |
| // scalar * matrix, result is a matrix of the same type than the input matrix |
| template <typename T, typename U> |
| constexpr typename std::enable_if<std::is_arithmetic<U>::value, TMat44<T>>::type PURE |
| operator *(U lhs, const TMat44<T>& rhs) { |
| return rhs * lhs; |
| } |
| |
| // ---------------------------------------------------------------------------------------- |
| |
| /* FIXME: this should go into TMatSquareFunctions<> but for some reason |
| * BASE<T>::col_type is not accessible from there (???) |
| */ |
| template<typename T> |
| typename TMat44<T>::col_type PURE diag(const TMat44<T>& m) { |
| return matrix::diag(m); |
| } |
| |
| } // namespace details |
| |
| // ---------------------------------------------------------------------------------------- |
| |
| typedef details::TMat44<double> mat4d; |
| typedef details::TMat44<float> mat4; |
| typedef details::TMat44<float> mat4f; |
| |
| // ---------------------------------------------------------------------------------------- |
| } // namespace android |
| |
| #undef PURE |
| #undef CONSTEXPR |
