7b3475f1da
scale() -> scaling() translate() -> translation() rotate() -> rotation() These static functions create a matrix, they don't modify it. Fixes #826
512 lines
15 KiB
C++
512 lines
15 KiB
C++
/*
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* Copyright 2013 The Android Open Source Project
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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#ifndef MATH_MAT3_H_
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#define MATH_MAT3_H_
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#include <math/quat.h>
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#include <math/TMatHelpers.h>
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#include <math/vec3.h>
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#include <math/compiler.h>
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#include <limits.h>
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#include <stdint.h>
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#include <sys/types.h>
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namespace filament {
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namespace math {
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// -------------------------------------------------------------------------------------
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namespace details {
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/**
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* A 3x3 column-major matrix class.
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*
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* Conceptually a 3x3 matrix is a an array of 3 column vec3:
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*
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* mat3 m =
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* \f$
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* \left(
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* \begin{array}{ccc}
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* m[0] & m[1] & m[2] \\
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* \end{array}
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* \right)
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* \f$
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* =
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* \f$
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* \left(
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* \begin{array}{ccc}
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* m[0][0] & m[1][0] & m[2][0] \\
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* m[0][1] & m[1][1] & m[2][1] \\
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* m[0][2] & m[1][2] & m[2][2] \\
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* \end{array}
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* \right)
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* \f$
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* =
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* \f$
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* \left(
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* \begin{array}{ccc}
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* m(0,0) & m(0,1) & m(0,2) \\
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* m(1,0) & m(1,1) & m(1,2) \\
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* m(2,0) & m(2,1) & m(2,2) \\
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* \end{array}
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* \right)
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* \f$
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*
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* m[n] is the \f$ n^{th} \f$ column of the matrix and is a vec3.
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*
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*/
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template <typename T>
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class MATH_EMPTY_BASES TMat33 :
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public TVecUnaryOperators<TMat33, T>,
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public TVecComparisonOperators<TMat33, T>,
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public TVecAddOperators<TMat33, T>,
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public TMatProductOperators<TMat33, T>,
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public TMatSquareFunctions<TMat33, T>,
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public TMatTransform<TMat33, T>,
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public TMatHelpers<TMat33, T>,
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public TMatDebug<TMat33, T> {
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public:
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enum no_init { NO_INIT };
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typedef T value_type;
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typedef T& reference;
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typedef T const& const_reference;
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typedef size_t size_type;
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typedef TVec3<T> col_type;
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typedef TVec3<T> row_type;
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static constexpr size_t COL_SIZE = col_type::SIZE; // size of a column (i.e.: number of rows)
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static constexpr size_t ROW_SIZE = row_type::SIZE; // size of a row (i.e.: number of columns)
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static constexpr size_t NUM_ROWS = COL_SIZE;
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static constexpr size_t NUM_COLS = ROW_SIZE;
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private:
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/*
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* <-- N columns -->
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*
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* a[0][0] a[1][0] a[2][0] ... a[N][0] ^
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* a[0][1] a[1][1] a[2][1] ... a[N][1] |
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* a[0][2] a[1][2] a[2][2] ... a[N][2] M rows
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* ... |
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* a[0][M] a[1][M] a[2][M] ... a[N][M] v
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*
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* COL_SIZE = M
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* ROW_SIZE = N
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* m[0] = [ a[0][0] a[0][1] a[0][2] ... a[0][M] ]
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*/
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col_type m_value[NUM_COLS];
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public:
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// array access
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inline constexpr col_type const& operator[](size_t column) const {
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// only possible in C++0x14 with constexpr
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assert(column < NUM_COLS);
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return m_value[column];
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}
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inline constexpr col_type& operator[](size_t column) {
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assert(column < NUM_COLS);
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return m_value[column];
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}
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/**
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* constructors
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*/
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/**
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* leaves object uninitialized. use with caution.
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*/
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constexpr explicit TMat33(no_init) {}
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/**
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* initialize to identity.
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*
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* \f$
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* \left(
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* \begin{array}{ccc}
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* 1 & 0 & 0 \\
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* 0 & 1 & 0 \\
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* 0 & 0 & 1 \\
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* \end{array}
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* \right)
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* \f$
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*/
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constexpr TMat33();
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/**
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* initialize to Identity*scalar.
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*
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* \f$
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* \left(
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* \begin{array}{ccc}
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* v & 0 & 0 \\
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* 0 & v & 0 \\
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* 0 & 0 & v \\
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* \end{array}
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* \right)
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* \f$
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*/
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template<typename U>
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constexpr explicit TMat33(U v);
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/**
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* sets the diagonal to a vector.
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*
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* \f$
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* \left(
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* \begin{array}{ccc}
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* v[0] & 0 & 0 \\
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* 0 & v[1] & 0 \\
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* 0 & 0 & v[2] \\
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* \end{array}
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* \right)
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* \f$
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*/
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template <typename U>
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constexpr explicit TMat33(const TVec3<U>& v);
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/**
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* construct from another matrix of the same size
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*/
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template <typename U>
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constexpr explicit TMat33(const TMat33<U>& rhs);
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/**
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* construct from 3 column vectors.
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*
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* \f$
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* \left(
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* \begin{array}{ccc}
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* v0 & v1 & v2 \\
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* \end{array}
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* \right)
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* \f$
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*/
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template <typename A, typename B, typename C>
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constexpr TMat33(const TVec3<A>& v0, const TVec3<B>& v1, const TVec3<C>& v2);
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/** construct from 9 elements in column-major form.
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*
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* \f$
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* \left(
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* \begin{array}{ccc}
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* m[0][0] & m[1][0] & m[2][0] \\
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* m[0][1] & m[1][1] & m[2][1] \\
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* m[0][2] & m[1][2] & m[2][2] \\
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* \end{array}
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* \right)
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* \f$
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*/
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template <
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typename A, typename B, typename C,
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typename D, typename E, typename F,
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typename G, typename H, typename I>
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constexpr explicit TMat33(A m00, B m01, C m02,
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D m10, E m11, F m12,
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G m20, H m21, I m22);
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struct row_major_init {
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template<
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typename A, typename B, typename C,
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typename D, typename E, typename F,
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typename G, typename H, typename I>
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constexpr explicit row_major_init(A m00, B m01, C m02,
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D m10, E m11, F m12,
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G m20, H m21, I m22) noexcept
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: m(m00, m10, m20,
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m01, m11, m21,
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m02, m12, m22) {}
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private:
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friend TMat33;
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TMat33 m;
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};
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constexpr explicit TMat33(row_major_init c) : TMat33(std::move(c.m)) { }
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/**
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* construct from a quaternion
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*/
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template <typename U>
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constexpr explicit TMat33(const TQuaternion<U>& q);
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/**
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* orthogonalize only works on matrices of size 3x3
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*/
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friend inline
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constexpr TMat33 orthogonalize(const TMat33& m) {
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TMat33 ret(TMat33::NO_INIT);
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ret[0] = normalize(m[0]);
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ret[2] = normalize(cross(ret[0], m[1]));
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ret[1] = normalize(cross(ret[2], ret[0]));
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return ret;
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}
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/**
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* Packs the tangent frame represented by the specified matrix into a quaternion.
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* Reflection is preserved by encoding it as the sign of the w component in the
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* resulting quaternion. Since -0 cannot always be represented on the GPU, this
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* function computes a bias to ensure values are always either positive or negative,
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* never 0. The bias is computed based on the specified storageSize, which defaults
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* to 2 bytes, making the resulting quaternion suitable for storage into an SNORM16
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* vector.
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*/
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static constexpr TQuaternion<T> packTangentFrame(const TMat33& m,
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size_t storageSize = sizeof(int16_t));
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template <typename A>
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static constexpr TMat33 translation(const TVec3<A>& t) {
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TMat33 r;
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r[2] = t;
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return r;
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}
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template <typename A>
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static constexpr TMat33 scaling(const TVec3<A>& s) {
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return TMat33{ s };
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}
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template <typename A>
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static constexpr TMat33 scaling(A s) {
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return TMat33{ TVec3<T>{ s } };
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}
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};
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// ----------------------------------------------------------------------------------------
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// Constructors
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// ----------------------------------------------------------------------------------------
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// Since the matrix code could become pretty big quickly, we don't inline most
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// operations.
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template <typename T>
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constexpr TMat33<T>::TMat33() {
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m_value[0] = col_type(1, 0, 0);
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m_value[1] = col_type(0, 1, 0);
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m_value[2] = col_type(0, 0, 1);
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}
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template <typename T>
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template <typename U>
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constexpr TMat33<T>::TMat33(U v) {
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m_value[0] = col_type(v, 0, 0);
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m_value[1] = col_type(0, v, 0);
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m_value[2] = col_type(0, 0, v);
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}
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template<typename T>
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template<typename U>
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constexpr TMat33<T>::TMat33(const TVec3<U>& v) {
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m_value[0] = col_type(v.x, 0, 0);
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m_value[1] = col_type(0, v.y, 0);
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m_value[2] = col_type(0, 0, v.z);
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}
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// construct from 16 scalars. Note that the arrangement
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// of values in the constructor is the transpose of the matrix
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// notation.
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template<typename T>
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template <
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typename A, typename B, typename C,
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typename D, typename E, typename F,
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typename G, typename H, typename I>
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constexpr TMat33<T>::TMat33(A m00, B m01, C m02,
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D m10, E m11, F m12,
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G m20, H m21, I m22) {
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m_value[0] = col_type(m00, m01, m02);
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m_value[1] = col_type(m10, m11, m12);
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m_value[2] = col_type(m20, m21, m22);
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}
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template <typename T>
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template <typename U>
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constexpr TMat33<T>::TMat33(const TMat33<U>& rhs) {
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for (size_t col = 0; col < NUM_COLS; ++col) {
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m_value[col] = col_type(rhs[col]);
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}
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}
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// Construct from 3 column vectors.
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template <typename T>
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template <typename A, typename B, typename C>
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constexpr TMat33<T>::TMat33(const TVec3<A>& v0, const TVec3<B>& v1, const TVec3<C>& v2) {
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m_value[0] = v0;
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m_value[1] = v1;
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m_value[2] = v2;
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}
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template <typename T>
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template <typename U>
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constexpr TMat33<T>::TMat33(const TQuaternion<U>& q) {
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const U n = q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w;
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const U s = n > 0 ? 2/n : 0;
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const U x = s*q.x;
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const U y = s*q.y;
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const U z = s*q.z;
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const U xx = x*q.x;
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const U xy = x*q.y;
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const U xz = x*q.z;
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const U xw = x*q.w;
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const U yy = y*q.y;
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const U yz = y*q.z;
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const U yw = y*q.w;
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const U zz = z*q.z;
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const U zw = z*q.w;
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m_value[0] = col_type(1-yy-zz, xy+zw, xz-yw); // NOLINT
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m_value[1] = col_type( xy-zw, 1-xx-zz, yz+xw); // NOLINT
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m_value[2] = col_type( xz+yw, yz-xw, 1-xx-yy); // NOLINT
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}
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// ----------------------------------------------------------------------------------------
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// Arithmetic operators outside of class
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// ----------------------------------------------------------------------------------------
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/* We use non-friend functions here to prevent the compiler from using
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* implicit conversions, for instance of a scalar to a vector. The result would
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* not be what the caller expects.
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*
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* Also note that the order of the arguments in the inner loop is important since
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* it determines the output type (only relevant when T != U).
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*/
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// matrix * column-vector, result is a vector of the same type than the input vector
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template <typename T, typename U>
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constexpr typename TMat33<U>::col_type MATH_PURE operator *(const TMat33<T>& lhs, const TVec3<U>& rhs) {
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// Result is initialized to zero.
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typename TMat33<U>::col_type result = {};
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for (size_t col = 0; col < TMat33<T>::NUM_COLS; ++col) {
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result += lhs[col] * rhs[col];
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}
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return result;
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}
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// row-vector * matrix, result is a vector of the same type than the input vector
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template <typename T, typename U>
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constexpr typename TMat33<U>::row_type MATH_PURE operator *(const TVec3<U>& lhs, const TMat33<T>& rhs) {
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typename TMat33<U>::row_type result;
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for (size_t col = 0; col < TMat33<T>::NUM_COLS; ++col) {
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result[col] = dot(lhs, rhs[col]);
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}
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return result;
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}
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// matrix * scalar, result is a matrix of the same type than the input matrix
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template<typename T, typename U>
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constexpr typename std::enable_if<std::is_arithmetic<U>::value, TMat33<T>>::type MATH_PURE
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operator*(TMat33<T> lhs, U rhs) {
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return lhs *= rhs;
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}
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// scalar * matrix, result is a matrix of the same type than the input matrix
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template<typename T, typename U>
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constexpr typename std::enable_if<std::is_arithmetic<U>::value, TMat33<T>>::type MATH_PURE
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operator*(U lhs, const TMat33<T>& rhs) {
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return rhs * lhs;
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}
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//------------------------------------------------------------------------------
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template<typename T>
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constexpr TQuaternion<T> TMat33<T>::packTangentFrame(const TMat33<T>& m, size_t storageSize) {
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TQuaternion<T> q = TMat33<T>{m[0], cross(m[2], m[0]), m[2]}.toQuaternion();
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q = positive(normalize(q));
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// Ensure w is never 0.0
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// Bias is 2^(nb_bits - 1) - 1
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const T bias = T(1.0) / T((1 << (storageSize * CHAR_BIT - 1)) - 1);
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if (q.w < bias) {
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q.w = bias;
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const T factor = (T) (std::sqrt(1.0 - (double) bias * (double) bias));
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q.xyz *= factor;
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}
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// If there's a reflection ((n x t) . b <= 0), make sure w is negative
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if (dot(cross(m[0], m[2]), m[1]) < T(0)) {
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q = -q;
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}
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return q;
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}
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// ----------------------------------------------------------------------------------------
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/* FIXME: this should go into TMatSquareFunctions<> but for some reason
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* BASE<T>::col_type is not accessible from there (???)
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*/
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template<typename T>
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constexpr typename TMat33<T>::col_type MATH_PURE diag(const TMat33<T>& m) {
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return matrix::diag(m);
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}
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} // namespace details
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// ----------------------------------------------------------------------------------------
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typedef details::TMat33<double> mat3;
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typedef details::TMat33<float> mat3f;
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// ----------------------------------------------------------------------------------------
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} // namespace math
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} // namespace filament
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namespace std {
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template <typename T>
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constexpr void swap( filament::math::details::TMat33<T>& lhs, filament::math::details::TMat33<T>& rhs) noexcept {
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// This generates much better code than the default implementation
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// It's unclear why, I believe this is due to an optimization bug in the clang.
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//
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// filament::math::details::TMat33<T> t(lhs);
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// lhs = rhs;
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// rhs = t;
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//
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// clang always copy lhs on the stack, even if it's never using it (it's using the
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// copy it has in registers).
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const T t00 = lhs[0][0];
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const T t01 = lhs[0][1];
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const T t02 = lhs[0][2];
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const T t10 = lhs[1][0];
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const T t11 = lhs[1][1];
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const T t12 = lhs[1][2];
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const T t20 = lhs[2][0];
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const T t21 = lhs[2][1];
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const T t22 = lhs[2][2];
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lhs[0][0] = rhs[0][0];
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lhs[0][1] = rhs[0][1];
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lhs[0][2] = rhs[0][2];
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lhs[1][0] = rhs[1][0];
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lhs[1][1] = rhs[1][1];
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lhs[1][2] = rhs[1][2];
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lhs[2][0] = rhs[2][0];
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lhs[2][1] = rhs[2][1];
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lhs[2][2] = rhs[2][2];
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rhs[0][0] = t00;
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rhs[0][1] = t01;
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rhs[0][2] = t02;
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rhs[1][0] = t10;
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rhs[1][1] = t11;
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rhs[1][2] = t12;
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rhs[2][0] = t20;
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rhs[2][1] = t21;
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rhs[2][2] = t22;
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}
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}
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#endif // MATH_MAT3_H_
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