Merge Filament's math library
This math library was derived from Android's and is API compatible.
It adds new useful types (quat and half) as well as many missing
functions and optimizations.
The half type (fp16) is going to be used for HDR/color management.
Test: mat_test, quat_test, half_test and vec_test
Change-Id: I4c61efb085d6aa2cf5b43cdd194719b3e855aa9b
diff --git a/include/ui/mat3.h b/include/ui/mat3.h
new file mode 100644
index 0000000..6a071c1
--- /dev/null
+++ b/include/ui/mat3.h
@@ -0,0 +1,435 @@
+/*
+ * 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.
+ */
+
+#ifndef UI_MAT3_H_
+#define UI_MAT3_H_
+
+#include <ui/quat.h>
+#include <ui/TMatHelpers.h>
+#include <ui/vec3.h>
+#include <stdint.h>
+#include <sys/types.h>
+
+#define PURE __attribute__((pure))
+
+namespace android {
+// -------------------------------------------------------------------------------------
+namespace details {
+
+template<typename T>
+class TQuaternion;
+
+/**
+ * A 3x3 column-major matrix class.
+ *
+ * Conceptually a 3x3 matrix is a an array of 3 column vec3:
+ *
+ * mat3 m =
+ * \f$
+ * \left(
+ * \begin{array}{ccc}
+ * m[0] & m[1] & m[2] \\
+ * \end{array}
+ * \right)
+ * \f$
+ * =
+ * \f$
+ * \left(
+ * \begin{array}{ccc}
+ * m[0][0] & m[1][0] & m[2][0] \\
+ * m[0][1] & m[1][1] & m[2][1] \\
+ * m[0][2] & m[1][2] & m[2][2] \\
+ * \end{array}
+ * \right)
+ * \f$
+ * =
+ * \f$
+ * \left(
+ * \begin{array}{ccc}
+ * m(0,0) & m(0,1) & m(0,2) \\
+ * m(1,0) & m(1,1) & m(1,2) \\
+ * m(2,0) & m(2,1) & m(2,2) \\
+ * \end{array}
+ * \right)
+ * \f$
+ *
+ * m[n] is the \f$ n^{th} \f$ column of the matrix and is a vec3.
+ *
+ */
+template <typename T>
+class TMat33 : public TVecUnaryOperators<TMat33, T>,
+ public TVecComparisonOperators<TMat33, T>,
+ public TVecAddOperators<TMat33, T>,
+ public TMatProductOperators<TMat33, T>,
+ public TMatSquareFunctions<TMat33, T>,
+ public TMatTransform<TMat33, T>,
+ public TMatHelpers<TMat33, T>,
+ public TMatDebug<TMat33, 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 TVec3<T> col_type;
+ typedef TVec3<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...
+ TMat33(const TMat33&) = default;
+ ~TMat33() = default;
+ TMat33& operator = (const TMat33&) = default;
+
+ /**
+ * constructors
+ */
+
+ /**
+ * leaves object uninitialized. use with caution.
+ */
+ explicit
+ constexpr TMat33(no_init)
+ : m_value{ 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}{ccc}
+ * 1 & 0 & 0 \\
+ * 0 & 1 & 0 \\
+ * 0 & 0 & 1 \\
+ * \end{array}
+ * \right)
+ * \f$
+ */
+ TMat33();
+
+ /**
+ * initialize to Identity*scalar.
+ *
+ * \f$
+ * \left(
+ * \begin{array}{ccc}
+ * v & 0 & 0 \\
+ * 0 & v & 0 \\
+ * 0 & 0 & v \\
+ * \end{array}
+ * \right)
+ * \f$
+ */
+ template<typename U>
+ explicit TMat33(U v);
+
+ /**
+ * sets the diagonal to a vector.
+ *
+ * \f$
+ * \left(
+ * \begin{array}{ccc}
+ * v[0] & 0 & 0 \\
+ * 0 & v[1] & 0 \\
+ * 0 & 0 & v[2] \\
+ * \end{array}
+ * \right)
+ * \f$
+ */
+ template <typename U>
+ explicit TMat33(const TVec3<U>& v);
+
+ /**
+ * construct from another matrix of the same size
+ */
+ template <typename U>
+ explicit TMat33(const TMat33<U>& rhs);
+
+ /**
+ * construct from 3 column vectors.
+ *
+ * \f$
+ * \left(
+ * \begin{array}{ccc}
+ * v0 & v1 & v2 \\
+ * \end{array}
+ * \right)
+ * \f$
+ */
+ template <typename A, typename B, typename C>
+ TMat33(const TVec3<A>& v0, const TVec3<B>& v1, const TVec3<C>& v2);
+
+ /** construct from 9 elements in column-major form.
+ *
+ * \f$
+ * \left(
+ * \begin{array}{ccc}
+ * m[0][0] & m[1][0] & m[2][0] \\
+ * m[0][1] & m[1][1] & m[2][1] \\
+ * m[0][2] & m[1][2] & m[2][2] \\
+ * \end{array}
+ * \right)
+ * \f$
+ */
+ template <
+ typename A, typename B, typename C,
+ typename D, typename E, typename F,
+ typename G, typename H, typename I>
+ TMat33(A m00, B m01, C m02,
+ D m10, E m11, F m12,
+ G m20, H m21, I m22);
+
+ /**
+ * construct from a quaternion
+ */
+ template <typename U>
+ explicit TMat33(const TQuaternion<U>& q);
+
+ /**
+ * construct from a C array in column major form.
+ */
+ template <typename U>
+ explicit TMat33(U const* rawArray);
+
+ /**
+ * orthogonalize only works on matrices of size 3x3
+ */
+ friend inline
+ TMat33 orthogonalize(const TMat33& m) {
+ TMat33 ret(TMat33::NO_INIT);
+ ret[0] = normalize(m[0]);
+ ret[2] = normalize(cross(ret[0], m[1]));
+ ret[1] = normalize(cross(ret[2], ret[0]));
+ return ret;
+ }
+};
+
+// ----------------------------------------------------------------------------------------
+// Constructors
+// ----------------------------------------------------------------------------------------
+
+// Since the matrix code could become pretty big quickly, we don't inline most
+// operations.
+
+template <typename T>
+TMat33<T>::TMat33() {
+ m_value[0] = col_type(1, 0, 0);
+ m_value[1] = col_type(0, 1, 0);
+ m_value[2] = col_type(0, 0, 1);
+}
+
+template <typename T>
+template <typename U>
+TMat33<T>::TMat33(U v) {
+ m_value[0] = col_type(v, 0, 0);
+ m_value[1] = col_type(0, v, 0);
+ m_value[2] = col_type(0, 0, v);
+}
+
+template<typename T>
+template<typename U>
+TMat33<T>::TMat33(const TVec3<U>& v) {
+ m_value[0] = col_type(v.x, 0, 0);
+ m_value[1] = col_type(0, v.y, 0);
+ m_value[2] = col_type(0, 0, v.z);
+}
+
+// construct from 16 scalars. Note that the arrangement
+// of values in the constructor is the transpose of the matrix
+// notation.
+template<typename T>
+template <
+ typename A, typename B, typename C,
+ typename D, typename E, typename F,
+ typename G, typename H, typename I>
+TMat33<T>::TMat33(A m00, B m01, C m02,
+ D m10, E m11, F m12,
+ G m20, H m21, I m22) {
+ m_value[0] = col_type(m00, m01, m02);
+ m_value[1] = col_type(m10, m11, m12);
+ m_value[2] = col_type(m20, m21, m22);
+}
+
+template <typename T>
+template <typename U>
+TMat33<T>::TMat33(const TMat33<U>& rhs) {
+ for (size_t col = 0; col < NUM_COLS; ++col) {
+ m_value[col] = col_type(rhs[col]);
+ }
+}
+
+// Construct from 3 column vectors.
+template <typename T>
+template <typename A, typename B, typename C>
+TMat33<T>::TMat33(const TVec3<A>& v0, const TVec3<B>& v1, const TVec3<C>& v2) {
+ m_value[0] = v0;
+ m_value[1] = v1;
+ m_value[2] = v2;
+}
+
+// Construct from raw array, in column-major form.
+template <typename T>
+template <typename U>
+TMat33<T>::TMat33(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>
+TMat33<T>::TMat33(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); // NOLINT
+ m_value[1] = col_type( xy-zw, 1-xx-zz, yz+xw); // NOLINT
+ m_value[2] = col_type( xz+yw, yz-xw, 1-xx-yy); // NOLINT
+}
+
+// ----------------------------------------------------------------------------------------
+// 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>
+typename TMat33<U>::col_type PURE operator *(const TMat33<T>& lhs, const TVec3<U>& rhs) {
+ // Result is initialized to zero.
+ typename TMat33<U>::col_type result;
+ for (size_t col = 0; col < TMat33<T>::NUM_COLS; ++col) {
+ result += lhs[col] * rhs[col];
+ }
+ return result;
+}
+
+// row-vector * matrix, result is a vector of the same type than the input vector
+template <typename T, typename U>
+typename TMat33<U>::row_type PURE operator *(const TVec3<U>& lhs, const TMat33<T>& rhs) {
+ typename TMat33<U>::row_type result(TMat33<U>::row_type::NO_INIT);
+ for (size_t col = 0; col < TMat33<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, TMat33<T>>::type PURE
+operator*(TMat33<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, TMat33<T>>::type PURE
+operator*(U lhs, const TMat33<T>& rhs) {
+ return rhs * lhs;
+}
+
+//------------------------------------------------------------------------------
+template <typename T>
+TMat33<T> orthogonalize(const TMat33<T>& m) {
+ TMat33<T> ret(TMat33<T>::NO_INIT);
+ ret[0] = normalize(m[0]);
+ ret[2] = normalize(cross(ret[0], m[1]));
+ ret[1] = normalize(cross(ret[2], ret[0]));
+ return ret;
+}
+
+// ----------------------------------------------------------------------------------------
+
+/* FIXME: this should go into TMatSquareFunctions<> but for some reason
+ * BASE<T>::col_type is not accessible from there (???)
+ */
+template<typename T>
+typename TMat33<T>::col_type PURE diag(const TMat33<T>& m) {
+ return matrix::diag(m);
+}
+
+} // namespace details
+
+// ----------------------------------------------------------------------------------------
+
+typedef details::TMat33<double> mat3d;
+typedef details::TMat33<float> mat3;
+typedef details::TMat33<float> mat3f;
+
+// ----------------------------------------------------------------------------------------
+} // namespace android
+
+#undef PURE
+
+#endif // UI_MAT3_H_