vector and matrix classes for graphics use

- this implements vec2, vec3, vec4, which are float vectors
of size 2, 3 and 4 respectively.

the code allows easy instantiation of vectors of a different
type via the tvec{2|3|4}<T> template classes.

- this also implements mat4 which is a float 4x4 matrix. the
tmat44<T> template class allows easy instantiation of a
4x4 matrix of a different value_type.

The vector types have some minimal support for the
glsl style swizzled access; for instance:

  vec4 u;
  vec3 v = u.xyz;

only .x, .xy, .xyz and their .stpq / .rgba equivalent are
supported.

most operators are supported on both vector and matrices:
arithmetic, unary, compound assignment and comparison
(bit-wise operators NOT supported).

- operations available on vectors include:
dot, length, distance, normalize and cross

- operations available on matrices include:
transpose, inverse, trace

- and a few utilities to create matrices:
ortho, frustum, lookAt

Change-Id: I64add89ae90fa78d3f2f59985b63495575378635
diff --git a/include/ui/mat4.h b/include/ui/mat4.h
new file mode 100644
index 0000000..08a67c7
--- /dev/null
+++ b/include/ui/mat4.h
@@ -0,0 +1,473 @@
+/*
+ * 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_MAT4_H
+#define UI_MAT4_H
+
+#include <stdint.h>
+#include <sys/types.h>
+
+#include <ui/vec4.h>
+#include <utils/String8.h>
+
+#define TMAT_IMPLEMENTATION
+#include <ui/TMatHelpers.h>
+
+#define PURE __attribute__((pure))
+
+namespace android {
+// -------------------------------------------------------------------------------------
+
+template <typename T>
+class tmat44 :  public TVecUnaryOperators<tmat44, T>,
+                public TVecComparisonOperators<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;
+
+    // size of a column (i.e.: number of rows)
+    enum { COL_SIZE = col_type::SIZE };
+    static inline size_t col_size() { return COL_SIZE; }
+
+    // size of a row (i.e.: number of columns)
+    enum { ROW_SIZE = row_type::SIZE };
+    static inline size_t row_size() { return ROW_SIZE; }
+    static inline size_t size()     { return row_size(); }  // for TVec*<>
+
+private:
+
+    /*
+     *  <--  N columns  -->
+     *
+     *  a00 a10 a20 ... aN0    ^
+     *  a01 a11 a21 ... aN1    |
+     *  a02 a12 a22 ... aN2  M rows
+     *  ...                    |
+     *  a0M a1M a2M ... aNM    v
+     *
+     *  COL_SIZE = M
+     *  ROW_SIZE = N
+     *  m[0] = [a00 a01 a02 ... a01M]
+     */
+
+    col_type mValue[ROW_SIZE];
+
+public:
+    // array access
+    inline col_type const& operator [] (size_t i) const { return mValue[i]; }
+    inline col_type&       operator [] (size_t i)       { return mValue[i]; }
+
+    T const* asArray() const { return &mValue[0][0]; }
+
+    // -----------------------------------------------------------------------
+    // we don't provide copy-ctor and operator= on purpose
+    // because we want the compiler generated versions
+
+    /*
+     *  constructors
+     */
+
+    // leaves object uninitialized. use with caution.
+    explicit tmat44(no_init) { }
+
+    // initialize to identity
+    tmat44();
+
+    // initialize to Identity*scalar.
+    template<typename U>
+    explicit tmat44(U v);
+
+    // sets the diagonal to the passed vector
+    template <typename U>
+    explicit tmat44(const tvec4<U>& rhs);
+
+    // construct from another matrix of the same size
+    template <typename U>
+    explicit tmat44(const tmat44<U>& rhs);
+
+    // construct from 4 column vectors
+    template <typename A, typename B, typename C, typename D>
+    tmat44(const tvec4<A>& v0, const tvec4<B>& v1, const tvec4<C>& v2, const tvec4<D>& v3);
+
+    // construct from a C array
+    template <typename U>
+    explicit tmat44(U const* rawArray);
+
+    /*
+     *  helpers
+     */
+
+    static tmat44 ortho(T left, T right, T bottom, T top, T near, T far);
+
+    static tmat44 frustum(T left, T right, T bottom, T top, T near, T far);
+
+    template <typename A, typename B, typename C>
+    static tmat44 lookAt(const tvec3<A>& eye, const tvec3<B>& center, const tvec3<C>& up);
+
+    template <typename A>
+    static tmat44 translate(const tvec4<A>& t);
+
+    template <typename A>
+    static tmat44 scale(const tvec4<A>& s);
+
+    template <typename A, typename B>
+    static tmat44 rotate(A radian, const tvec3<B>& about);
+
+
+    /*
+     * Compound assignment arithmetic operators
+     */
+
+    // add another matrix of the same size
+    template <typename U>
+    tmat44& operator += (const tmat44<U>& v);
+
+    // subtract another matrix of the same size
+    template <typename U>
+    tmat44& operator -= (const tmat44<U>& v);
+
+    // multiply by a scalar
+    template <typename U>
+    tmat44& operator *= (U v);
+
+    // divide by a scalar
+    template <typename U>
+    tmat44& operator /= (U v);
+
+    /*
+     * debugging
+     */
+
+    String8 asString() const;
+};
+
+// ----------------------------------------------------------------------------------------
+// Constructors
+// ----------------------------------------------------------------------------------------
+
+/*
+ * Since the matrix code could become pretty big quickly, we don't inline most
+ * operations.
+ */
+
+template <typename T>
+tmat44<T>::tmat44() {
+    mValue[0] = col_type(1,0,0,0);
+    mValue[1] = col_type(0,1,0,0);
+    mValue[2] = col_type(0,0,1,0);
+    mValue[3] = col_type(0,0,0,1);
+}
+
+template <typename T>
+template <typename U>
+tmat44<T>::tmat44(U v) {
+    mValue[0] = col_type(v,0,0,0);
+    mValue[1] = col_type(0,v,0,0);
+    mValue[2] = col_type(0,0,v,0);
+    mValue[3] = col_type(0,0,0,v);
+}
+
+template<typename T>
+template<typename U>
+tmat44<T>::tmat44(const tvec4<U>& v) {
+    mValue[0] = col_type(v.x,0,0,0);
+    mValue[1] = col_type(0,v.y,0,0);
+    mValue[2] = col_type(0,0,v.z,0);
+    mValue[3] = col_type(0,0,0,v.w);
+}
+
+template <typename T>
+template <typename U>
+tmat44<T>::tmat44(const tmat44<U>& rhs) {
+    for (size_t r=0 ; r<row_size() ; r++)
+        mValue[r] = rhs[r];
+}
+
+template <typename T>
+template <typename A, typename B, typename C, typename D>
+tmat44<T>::tmat44(const tvec4<A>& v0, const tvec4<B>& v1, const tvec4<C>& v2, const tvec4<D>& v3) {
+    mValue[0] = v0;
+    mValue[1] = v1;
+    mValue[2] = v2;
+    mValue[3] = v3;
+}
+
+template <typename T>
+template <typename U>
+tmat44<T>::tmat44(U const* rawArray) {
+    for (size_t r=0 ; r<row_size() ; r++)
+        for (size_t c=0 ; c<col_size() ; c++)
+            mValue[r][c] = *rawArray++;
+}
+
+// ----------------------------------------------------------------------------------------
+// Helpers
+// ----------------------------------------------------------------------------------------
+
+template <typename T>
+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>
+tmat44<T> tmat44<T>::frustum(T left, T right, T bottom, T top, T near, T far) {
+    tmat44<T> m;
+    T A = (right + left)   / (right - left);
+    T B = (top   + bottom) / (top   - bottom);
+    T C = (far   + near)   / (far   - near);
+    T D = (2 * far * near) / (far   - near);
+    m[0][0] = (2 * near) / (right - left);
+    m[1][1] = (2 * near) / (top   - bottom);
+    m[2][0] = A;
+    m[2][1] = B;
+    m[2][2] = C;
+    m[2][3] =-1;
+    m[3][2] = D;
+    m[3][3] = 0;
+    return m;
+}
+
+template <typename T>
+template <typename A, typename B, typename C>
+tmat44<T> tmat44<T>::lookAt(const tvec3<A>& eye, const tvec3<B>& center, const tvec3<C>& up) {
+    tvec3<T> L(normalize(center - eye));
+    tvec3<T> S(normalize( cross(L, up) ));
+    tvec3<T> U(cross(S, L));
+    return tmat44<T>(
+            tvec4<T>( S, 0),
+            tvec4<T>( U, 0),
+            tvec4<T>(-L, 0),
+            tvec4<T>(-eye, 1));
+}
+
+template <typename T>
+template <typename A>
+tmat44<T> tmat44<T>::translate(const tvec4<A>& t) {
+    tmat44<T> r;
+    r[3] = t;
+    return r;
+}
+
+template <typename T>
+template <typename A>
+tmat44<T> tmat44<T>::scale(const tvec4<A>& s) {
+    tmat44<T> r;
+    r[0][0] = s[0];
+    r[1][1] = s[1];
+    r[2][2] = s[2];
+    r[3][3] = s[3];
+    return r;
+}
+
+template <typename T>
+template <typename A, typename B>
+tmat44<T> tmat44<T>::rotate(A radian, const tvec3<B>& about) {
+    tmat44<T> rotation;
+    T* r = const_cast<T*>(rotation.asArray());
+    T c = cos(radian);
+    T s = sin(radian);
+    if (about.x==1 && about.y==0 && about.z==0) {
+        r[5] = c;   r[10]= c;
+        r[6] = s;   r[9] = -s;
+    } else if (about.x==0 && about.y==1 && about.z==0) {
+        r[0] = c;   r[10]= c;
+        r[8] = s;   r[2] = -s;
+    } else if (about.x==0 && about.y==0 && about.z==1) {
+        r[0] = c;   r[5] = c;
+        r[1] = s;   r[4] = -s;
+    } else {
+        tvec3<B> nabout = normalize(about);
+        B x = nabout.x;
+        B y = nabout.y;
+        B z = nabout.z;
+        T nc = 1 - c;
+        T xy = x * y;
+        T yz = y * z;
+        T zx = z * x;
+        T xs = x * s;
+        T ys = y * s;
+        T zs = z * s;
+        r[ 0] = x*x*nc +  c;    r[ 4] =  xy*nc - zs;    r[ 8] =  zx*nc + ys;
+        r[ 1] =  xy*nc + zs;    r[ 5] = y*y*nc +  c;    r[ 9] =  yz*nc - xs;
+        r[ 2] =  zx*nc - ys;    r[ 6] =  yz*nc + xs;    r[10] = z*z*nc +  c;
+    }
+}
+
+// ----------------------------------------------------------------------------------------
+// Compound assignment arithmetic operators
+// ----------------------------------------------------------------------------------------
+
+template <typename T>
+template <typename U>
+tmat44<T>& tmat44<T>::operator += (const tmat44<U>& v) {
+    for (size_t r=0 ; r<row_size() ; r++)
+        mValue[r] += v[r];
+    return *this;
+}
+
+template <typename T>
+template <typename U>
+tmat44<T>& tmat44<T>::operator -= (const tmat44<U>& v) {
+    for (size_t r=0 ; r<row_size() ; r++)
+        mValue[r] -= v[r];
+    return *this;
+}
+
+template <typename T>
+template <typename U>
+tmat44<T>& tmat44<T>::operator *= (U v) {
+    for (size_t r=0 ; r<row_size() ; r++)
+        mValue[r] *= v;
+    return *this;
+}
+
+template <typename T>
+template <typename U>
+tmat44<T>& tmat44<T>::operator /= (U v) {
+    for (size_t r=0 ; r<row_size() ; r++)
+        mValue[r] /= v;
+    return *this;
+}
+
+// ----------------------------------------------------------------------------------------
+// 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 + matrix, result is a matrix of the same type than the lhs matrix
+template <typename T, typename U>
+tmat44<T> PURE operator +(const tmat44<T>& lhs, const tmat44<U>& rhs) {
+    tmat44<T> result(tmat44<T>::NO_INIT);
+    for (size_t r=0 ; r<tmat44<T>::row_size() ; r++)
+        result[r] = lhs[r] + rhs[r];
+    return result;
+}
+
+// matrix - matrix, result is a matrix of the same type than the lhs matrix
+template <typename T, typename U>
+tmat44<T> PURE operator -(const tmat44<T>& lhs, const tmat44<U>& rhs) {
+    tmat44<T> result(tmat44<T>::NO_INIT);
+    for (size_t r=0 ; r<tmat44<T>::row_size() ; r++)
+        result[r] = lhs[r] - rhs[r];
+    return result;
+}
+
+// matrix * vector, result is a vector of the same type than the input vector
+template <typename T, typename U>
+typename tmat44<U>::col_type PURE operator *(const tmat44<T>& lv, const tvec4<U>& rv) {
+    typename tmat44<U>::col_type result;
+    for (size_t r=0 ; r<tmat44<T>::row_size() ; r++)
+        result += rv[r]*lv[r];
+    return result;
+}
+
+// vector * matrix, result is a vector of the same type than the input vector
+template <typename T, typename U>
+typename tmat44<U>::row_type PURE operator *(const tvec4<U>& rv, const tmat44<T>& lv) {
+    typename tmat44<U>::row_type result(tmat44<U>::row_type::NO_INIT);
+    for (size_t r=0 ; r<tmat44<T>::row_size() ; r++)
+        result[r] = dot(rv, lv[r]);
+    return result;
+}
+
+// matrix * scalar, result is a matrix of the same type than the input matrix
+template <typename T, typename U>
+tmat44<T> PURE operator *(const tmat44<T>& lv, U rv) {
+    tmat44<T> result(tmat44<T>::NO_INIT);
+    for (size_t r=0 ; r<tmat44<T>::row_size() ; r++)
+        result[r] = lv[r]*rv;
+    return result;
+}
+
+// scalar * matrix, result is a matrix of the same type than the input matrix
+template <typename T, typename U>
+tmat44<T> PURE operator *(U rv, const tmat44<T>& lv) {
+    tmat44<T> result(tmat44<T>::NO_INIT);
+    for (size_t r=0 ; r<tmat44<T>::row_size() ; r++)
+        result[r] = lv[r]*rv;
+    return result;
+}
+
+// matrix * matrix, result is a matrix of the same type than the lhs matrix
+template <typename T, typename U>
+tmat44<T> PURE operator *(const tmat44<T>& lhs, const tmat44<U>& rhs) {
+    return matrix::multiply< tmat44<T> >(lhs, rhs);
+}
+
+// ----------------------------------------------------------------------------------------
+// Functions
+// ----------------------------------------------------------------------------------------
+
+// inverse a matrix
+template <typename T>
+tmat44<T> PURE inverse(const tmat44<T>& m) {
+    return matrix::inverse(m);
+}
+
+template <typename T>
+tmat44<T> PURE transpose(const tmat44<T>& m) {
+    return matrix::transpose(m);
+}
+
+template <typename T>
+T PURE trace(const tmat44<T>& m) {
+    return matrix::trace(m);
+}
+
+template <typename T>
+tvec4<T> PURE diag(const tmat44<T>& m) {
+    return matrix::diag(m);
+}
+
+// ----------------------------------------------------------------------------------------
+// Debugging
+// ----------------------------------------------------------------------------------------
+
+template <typename T>
+String8 tmat44<T>::asString() const {
+    return matrix::asString(*this);
+}
+
+// ----------------------------------------------------------------------------------------
+
+typedef tmat44<float> mat4;
+
+// ----------------------------------------------------------------------------------------
+}; // namespace android
+
+#undef PURE
+
+#endif /* UI_MAT4_H */