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++ // Copyright 2009-2021 Intel Corporation
++ // SPDX-License-Identifier: Apache-2.0
++
++ #pragma once
++
++ #include "vec2.h"
++
++ namespace embree
++ {
++ ////////////////////////////////////////////////////////////////////////////////
++ /// 2D Linear Transform (2x2 Matrix)
++ ////////////////////////////////////////////////////////////////////////////////
++
++ template<typename T> struct LinearSpace2
++ {
++ typedef T Vector;
++ typedef typename T::Scalar Scalar;
++
++ /*! default matrix constructor */
++ __forceinline LinearSpace2 ( ) {}
++ __forceinline LinearSpace2 ( const LinearSpace2& other ) { vx = other.vx; vy = other.vy; }
++ __forceinline LinearSpace2& operator=( const LinearSpace2& other ) { vx = other.vx; vy = other.vy; return *this; }
++
++ template<typename L1> __forceinline LinearSpace2( const LinearSpace2<L1>& s ) : vx(s.vx), vy(s.vy) {}
++
++ /*! matrix construction from column vectors */
++ __forceinline LinearSpace2(const Vector& vx, const Vector& vy)
++ : vx(vx), vy(vy) {}
++
++ /*! matrix construction from row mayor data */
++ __forceinline LinearSpace2(const Scalar& m00, const Scalar& m01,
++ const Scalar& m10, const Scalar& m11)
++ : vx(m00,m10), vy(m01,m11) {}
++
++ /*! compute the determinant of the matrix */
++ __forceinline const Scalar det() const { return vx.x*vy.y - vx.y*vy.x; }
++
++ /*! compute adjoint matrix */
++ __forceinline const LinearSpace2 adjoint() const { return LinearSpace2(vy.y,-vy.x,-vx.y,vx.x); }
++
++ /*! compute inverse matrix */
++ __forceinline const LinearSpace2 inverse() const { return adjoint()/det(); }
++
++ /*! compute transposed matrix */
++ __forceinline const LinearSpace2 transposed() const { return LinearSpace2(vx.x,vx.y,vy.x,vy.y); }
++
++ /*! returns first row of matrix */
++ __forceinline Vector row0() const { return Vector(vx.x,vy.x); }
++
++ /*! returns second row of matrix */
++ __forceinline Vector row1() const { return Vector(vx.y,vy.y); }
++
++ ////////////////////////////////////////////////////////////////////////////////
++ /// Constants
++ ////////////////////////////////////////////////////////////////////////////////
++
++ __forceinline LinearSpace2( ZeroTy ) : vx(zero), vy(zero) {}
++ __forceinline LinearSpace2( OneTy ) : vx(one, zero), vy(zero, one) {}
++
++ /*! return matrix for scaling */
++ static __forceinline LinearSpace2 scale(const Vector& s) {
++ return LinearSpace2(s.x, 0,
++ 0 , s.y);
++ }
++
++ /*! return matrix for rotation */
++ static __forceinline LinearSpace2 rotate(const Scalar& r) {
++ Scalar s = sin(r), c = cos(r);
++ return LinearSpace2(c, -s,
++ s, c);
++ }
++
++ /*! return closest orthogonal matrix (i.e. a general rotation including reflection) */
++ LinearSpace2 orthogonal() const
++ {
++ LinearSpace2 m = *this;
++
++ // mirrored?
++ Scalar mirror(one);
++ if (m.det() < Scalar(zero)) {
++ m.vx = -m.vx;
++ mirror = -mirror;
++ }
++
++ // rotation
++ for (int i = 0; i < 99; i++) {
++ const LinearSpace2 m_next = 0.5 * (m + m.transposed().inverse());
++ const LinearSpace2 d = m_next - m;
++ m = m_next;
++ // norm^2 of difference small enough?
++ if (max(dot(d.vx, d.vx), dot(d.vy, d.vy)) < 1e-8)
++ break;
++ }
++
++ // rotation * mirror_x
++ return LinearSpace2(mirror*m.vx, m.vy);
++ }
++
++ public:
++
++ /*! the column vectors of the matrix */
++ Vector vx,vy;
++ };
++
++ ////////////////////////////////////////////////////////////////////////////////
++ // Unary Operators
++ ////////////////////////////////////////////////////////////////////////////////
++
++ template<typename T> __forceinline LinearSpace2<T> operator -( const LinearSpace2<T>& a ) { return LinearSpace2<T>(-a.vx,-a.vy); }
++ template<typename T> __forceinline LinearSpace2<T> operator +( const LinearSpace2<T>& a ) { return LinearSpace2<T>(+a.vx,+a.vy); }
++ template<typename T> __forceinline LinearSpace2<T> rcp ( const LinearSpace2<T>& a ) { return a.inverse(); }
++
++ ////////////////////////////////////////////////////////////////////////////////
++ // Binary Operators
++ ////////////////////////////////////////////////////////////////////////////////
++
++ template<typename T> __forceinline LinearSpace2<T> operator +( const LinearSpace2<T>& a, const LinearSpace2<T>& b ) { return LinearSpace2<T>(a.vx+b.vx,a.vy+b.vy); }
++ template<typename T> __forceinline LinearSpace2<T> operator -( const LinearSpace2<T>& a, const LinearSpace2<T>& b ) { return LinearSpace2<T>(a.vx-b.vx,a.vy-b.vy); }
++
++ template<typename T> __forceinline LinearSpace2<T> operator*(const typename T::Scalar & a, const LinearSpace2<T>& b) { return LinearSpace2<T>(a*b.vx, a*b.vy); }
++ template<typename T> __forceinline T operator*(const LinearSpace2<T>& a, const T & b) { return b.x*a.vx + b.y*a.vy; }
++ template<typename T> __forceinline LinearSpace2<T> operator*(const LinearSpace2<T>& a, const LinearSpace2<T>& b) { return LinearSpace2<T>(a*b.vx, a*b.vy); }
++
++ template<typename T> __forceinline LinearSpace2<T> operator/(const LinearSpace2<T>& a, const typename T::Scalar & b) { return LinearSpace2<T>(a.vx/b, a.vy/b); }
++ template<typename T> __forceinline LinearSpace2<T> operator/(const LinearSpace2<T>& a, const LinearSpace2<T>& b) { return a * rcp(b); }
++
++ template<typename T> __forceinline LinearSpace2<T>& operator *=( LinearSpace2<T>& a, const LinearSpace2<T>& b ) { return a = a * b; }
++ template<typename T> __forceinline LinearSpace2<T>& operator /=( LinearSpace2<T>& a, const LinearSpace2<T>& b ) { return a = a / b; }
++
++ ////////////////////////////////////////////////////////////////////////////////
++ /// Comparison Operators
++ ////////////////////////////////////////////////////////////////////////////////
++
++ template<typename T> __forceinline bool operator ==( const LinearSpace2<T>& a, const LinearSpace2<T>& b ) { return a.vx == b.vx && a.vy == b.vy; }
++ template<typename T> __forceinline bool operator !=( const LinearSpace2<T>& a, const LinearSpace2<T>& b ) { return a.vx != b.vx || a.vy != b.vy; }
++
++ ////////////////////////////////////////////////////////////////////////////////
++ /// Output Operators
++ ////////////////////////////////////////////////////////////////////////////////
++
++ template<typename T> static embree_ostream operator<<(embree_ostream cout, const LinearSpace2<T>& m) {
++ return cout << "{ vx = " << m.vx << ", vy = " << m.vy << "}";
++ }
++
++ /*! Shortcuts for common linear spaces. */
++ typedef LinearSpace2<Vec2f> LinearSpace2f;
++ typedef LinearSpace2<Vec2fa> LinearSpace2fa;
++ }