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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;
}
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