--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/hostsupport/hostopenvg/src/src/riMath.h Wed Oct 06 17:59:01 2010 +0100
@@ -0,0 +1,452 @@
+#ifndef __RIMATH_H
+#define __RIMATH_H
+
+/*------------------------------------------------------------------------
+ *
+ * OpenVG 1.1 Reference Implementation
+ * -----------------------------------
+ *
+ * Copyright (c) 2007 The Khronos Group Inc.
+ * Portions copyright (c) 2010 Nokia Corporation and/or its subsidiary(-ies).
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and /or associated documentation files
+ * (the "Materials "), to deal in the Materials without restriction,
+ * including without limitation the rights to use, copy, modify, merge,
+ * publish, distribute, sublicense, and/or sell copies of the Materials,
+ * and to permit persons to whom the Materials are furnished to do so,
+ * subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included
+ * in all copies or substantial portions of the Materials.
+ *
+ * THE MATERIALS ARE PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+ * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+ * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
+ * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM,
+ * DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR
+ * OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE MATERIALS OR
+ * THE USE OR OTHER DEALINGS IN THE MATERIALS.
+ *
+ *//**
+ * \file
+ * \brief Math functions, Vector and Matrix classes.
+ * \note
+ *//*-------------------------------------------------------------------*/
+
+#ifndef __RIDEFS_H
+#include "riDefs.h"
+#endif
+
+#include <math.h>
+
+namespace OpenVGRI
+{
+
+/*-------------------------------------------------------------------*//*!
+* \brief
+* \param
+* \return
+* \note
+*//*-------------------------------------------------------------------*/
+
+RI_INLINE int RI_ISNAN(float a)
+{
+ RIfloatInt p;
+ p.f = a;
+ unsigned int exponent = (p.i>>23) & 0xff;
+ unsigned int mantissa = p.i & 0x7fffff;
+ if(exponent == 255 && mantissa)
+ return 1;
+ return 0;
+}
+
+#if (RI_MANTISSA_BITS > 23)
+#error RI_MANTISSA_BITS is greater than 23
+#elif (RI_EXPONENT_BITS > 8)
+#error RI_EXPONENT_BITS is greater than 8
+#elif (RI_MANTISSA_BITS != 23) || (RI_EXPONENT_BITS != 8)
+
+class RIfloat
+{
+public:
+ RIfloat() : v(0.0f) { removeBits(); }
+ RIfloat(float a) : v(a) { removeBits(); }
+ RIfloat(double a) : v((float)a) { removeBits(); }
+ RIfloat(int a) : v((float)a) { removeBits(); }
+ RIfloat(unsigned int a) : v((float)a) { removeBits(); }
+ RIfloat& operator=(const RIfloat &a) { v = a.v; removeBits(); return *this; }
+ RIfloat& operator+=(const RIfloat &a){ v += a.v; removeBits(); return *this; }
+ RIfloat& operator-=(const RIfloat &a){ v -= a.v; removeBits(); return *this; }
+ RIfloat& operator*=(const RIfloat &a){ v *= a.v; removeBits(); return *this; }
+ RIfloat& operator/=(const RIfloat &a){ v /= a.v; removeBits(); return *this; }
+ RIfloat operator-() const { return -v; }
+ operator float() const { return v; }
+ operator double() const { return (double)v; }
+ operator int() const { return (int)v; }
+
+ friend RIfloat operator+(const RIfloat &a, const RIfloat &b);
+ friend RIfloat operator+(float a, const RIfloat &b);
+ friend RIfloat operator+(const RIfloat &a, float b);
+ friend RIfloat operator-(const RIfloat &a, const RIfloat &b);
+ friend RIfloat operator-(float a, const RIfloat &b);
+ friend RIfloat operator-(const RIfloat &a, float b);
+ friend RIfloat operator*(const RIfloat &a, const RIfloat &b);
+ friend RIfloat operator*(float a, const RIfloat &b);
+ friend RIfloat operator*(const RIfloat &a, float b);
+ friend RIfloat operator/(const RIfloat &a, const RIfloat &b);
+ friend RIfloat operator/(float a, const RIfloat &b);
+ friend RIfloat operator/(const RIfloat &a, float b);
+
+ friend bool operator<(const RIfloat &a, const RIfloat &b);
+ friend bool operator<(float a, const RIfloat &b);
+ friend bool operator<(const RIfloat &a, float b);
+ friend bool operator>(const RIfloat &a, const RIfloat &b);
+ friend bool operator>(float a, const RIfloat &b);
+ friend bool operator>(const RIfloat &a, float b);
+ friend bool operator<=(const RIfloat &a, const RIfloat &b);
+ friend bool operator<=(float a, const RIfloat &b);
+ friend bool operator<=(const RIfloat &a, float b);
+ friend bool operator>=(const RIfloat &a, const RIfloat &b);
+ friend bool operator>=(float a, const RIfloat &b);
+ friend bool operator>=(const RIfloat &a, float b);
+ friend bool operator==(const RIfloat &a, const RIfloat &b);
+ friend bool operator==(float a, const RIfloat &b);
+ friend bool operator==(const RIfloat &a, float b);
+ friend bool operator!=(const RIfloat &a, const RIfloat &b);
+ friend bool operator!=(float a, const RIfloat &b);
+ friend bool operator!=(const RIfloat &a, float b);
+private:
+ void removeBits()
+ {
+ RIfloatInt p;
+ p.f = v;
+ unsigned int exponent = (p.i>>23) & 0xff;
+ if(exponent == 0 || exponent == 255)
+ return; //zero, denormal, infinite, or NaN
+
+ p.i &= ~((1<<(23-RI_MANTISSA_BITS))-1);
+
+#if (RI_EXPONENT_BITS != 8)
+ if (exponent > 127 + (1 << (RI_EXPONENT_BITS-1)))
+ exponent = 127 + (1 << (RI_EXPONENT_BITS-1));
+
+ if (exponent < 127 + 1 - (1 << (RI_EXPONENT_BITS-1)))
+ exponent = 127 + 1 - (1 << (RI_EXPONENT_BITS-1));
+
+ p.i &= ~(0xff<<23);
+ p.i |= exponent<<23;
+#endif
+ v = p.f;
+ }
+
+ float v;
+};
+
+RI_INLINE RIfloat operator+(const RIfloat &a, const RIfloat &b) { return RIfloat(a.v+b.v); }
+RI_INLINE RIfloat operator+(float a, const RIfloat &b) { return RIfloat(a+b.v); }
+RI_INLINE RIfloat operator+(const RIfloat &a, float b) { return RIfloat(a.v+b); }
+RI_INLINE RIfloat operator-(const RIfloat &a, const RIfloat &b) { return RIfloat(a.v-b.v); }
+RI_INLINE RIfloat operator-(float a, const RIfloat &b) { return RIfloat(a-b.v); }
+RI_INLINE RIfloat operator-(const RIfloat &a, float b) { return RIfloat(a.v-b); }
+RI_INLINE RIfloat operator*(const RIfloat &a, const RIfloat &b) { return RIfloat(a.v*b.v); }
+RI_INLINE RIfloat operator*(float a, const RIfloat &b) { return RIfloat(a*b.v); }
+RI_INLINE RIfloat operator*(const RIfloat &a, float b) { return RIfloat(a.v*b); }
+RI_INLINE RIfloat operator/(const RIfloat &a, const RIfloat &b) { return RIfloat(a.v/b.v); }
+RI_INLINE RIfloat operator/(float a, const RIfloat &b) { return RIfloat(a/b.v); }
+RI_INLINE RIfloat operator/(const RIfloat &a, float b) { return RIfloat(a.v/b); }
+
+RI_INLINE bool operator<(const RIfloat &a, const RIfloat &b) { return a.v < b.v ? true : false; }
+RI_INLINE bool operator<(float a, const RIfloat &b) { return a < b.v ? true : false; }
+RI_INLINE bool operator<(const RIfloat &a, float b) { return a.v < b ? true : false; }
+RI_INLINE bool operator>(const RIfloat &a, const RIfloat &b) { return a.v > b.v ? true : false; }
+RI_INLINE bool operator>(float a, const RIfloat &b) { return a > b.v ? true : false; }
+RI_INLINE bool operator>(const RIfloat &a, float b) { return a.v > b ? true : false; }
+RI_INLINE bool operator<=(const RIfloat &a, const RIfloat &b) { return a.v <= b.v ? true : false; }
+RI_INLINE bool operator<=(float a, const RIfloat &b) { return a <= b.v ? true : false; }
+RI_INLINE bool operator<=(const RIfloat &a, float b) { return a.v <= b ? true : false; }
+RI_INLINE bool operator>=(const RIfloat &a, const RIfloat &b) { return a.v >= b.v ? true : false; }
+RI_INLINE bool operator>=(float a, const RIfloat &b) { return a >= b.v ? true : false; }
+RI_INLINE bool operator>=(const RIfloat &a, float b) { return a.v >= b ? true : false; }
+RI_INLINE bool operator==(const RIfloat &a, const RIfloat &b) { return a.v == b.v ? true : false; }
+RI_INLINE bool operator==(float a, const RIfloat &b) { return a == b.v ? true : false; }
+RI_INLINE bool operator==(const RIfloat &a, float b) { return a.v == b ? true : false; }
+RI_INLINE bool operator!=(const RIfloat &a, const RIfloat &b) { return a.v != b.v ? true : false; }
+RI_INLINE bool operator!=(float a, const RIfloat &b) { return a != b.v ? true : false; }
+RI_INLINE bool operator!=(const RIfloat &a, float b) { return a.v != b ? true : false; }
+
+#else
+typedef float RIfloat;
+#endif
+
+#define RI_PI 3.141592654f
+
+RI_INLINE RIfloat RI_FRAC(RIfloat f) { return f - (RIfloat)(int)f; }
+RI_INLINE int RI_ROUND_TO_INT(RIfloat v) { return (v >= 0.0f) ? (int)(v+0.5f) : (int)(v-0.5f); }
+RI_INLINE RIfloat RI_MAX(RIfloat a, RIfloat b) { return (a > b) ? a : b; }
+RI_INLINE int RI_MAX(int a, int b) { return (a > b) ? a : b; }
+RI_INLINE RIfloat RI_MIN(RIfloat a, RIfloat b) { return (a < b) ? a : b; }
+RI_INLINE int RI_MIN(int a, int b) { return (a < b) ? a : b; }
+RI_INLINE RIfloat RI_CLAMP(RIfloat a, RIfloat l, RIfloat h) { if(RI_ISNAN(a)) return l; RI_ASSERT(l <= h); return (a < l) ? l : (a > h) ? h : a; }
+RI_INLINE int RI_CEIL(RIfloat a) {return (int)ceilf(a);}
+RI_INLINE int RI_FLOOR(RIfloat a) { return (int)floorf(a); }
+RI_INLINE void RI_SWAP(RIfloat &a, RIfloat &b) { RIfloat tmp = a; a = b; b = tmp; }
+RI_INLINE RIfloat RI_ABS(RIfloat a) { return (a < 0.0f) ? -a : a; }
+RI_INLINE RIfloat RI_SQR(RIfloat a) { return a * a; }
+RI_INLINE RIfloat RI_DEG_TO_RAD(RIfloat a) { return a * RI_PI / 180.0f; }
+RI_INLINE RIfloat RI_RAD_TO_DEG(RIfloat a) { return a * 180.0f/ RI_PI; }
+RI_INLINE RIfloat RI_MOD(RIfloat a, RIfloat b) { if(RI_ISNAN(a) || RI_ISNAN(b)) return 0.0f; RI_ASSERT(b >= 0.0f); if(b == 0.0f) return 0.0f; RIfloat f = (RIfloat)fmod(a, b); if(f < 0.0f) f += b; RI_ASSERT(f >= 0.0f && f <= b); return f; }
+
+#define RI_ANY_SWAP(type, a, b) {type tmp = a; a = b; b = tmp;}
+
+RI_INLINE void RI_INT16_SWAP(RIint16 &a, RIint16 &b) {RIint16 tmp = a; a = b; b = tmp;}
+RI_INLINE int RI_INT_ABS(int a) { return (a >= 0) ? a : -a; }
+RI_INLINE int RI_INT_MAX(int a, int b) { return (a > b) ? a : b; }
+RI_INLINE int RI_INT_MIN(int a, int b) { return (a < b) ? a : b; }
+RI_INLINE int RI_INT_CLAMP(int a, int l, int h) { return (a < l) ? l : (a > h) ? h : a; }
+RI_INLINE void RI_INT_SWAP(int &a, int &b) { int tmp = a; a = b; b = tmp; }
+RI_INLINE int RI_INT_MOD(int a, int b) { RI_ASSERT(b >= 0); if(!b) return 0; int i = a % b; if(i < 0) i += b; RI_ASSERT(i >= 0 && i < b); return i; }
+RI_INLINE int RI_INT_ADDSATURATE(int a, int b) { RI_ASSERT(b >= 0); int r = a + b; return (r >= a) ? r : RI_INT32_MAX; }
+
+RI_INLINE RIfloat validateFloat(RIfloat f)
+{
+ //this function is used for all floating point input values
+ if(RI_ISNAN(f)) return 0.0f; //convert NaN to zero
+ return RI_CLAMP(f, -RI_FLOAT_MAX, RI_FLOAT_MAX); //clamp +-inf to +-RIfloat max
+}
+
+
+
+RI_INLINE int RI_SHL(int a, int sh)
+{
+ RI_ASSERT(sh >= 0 && sh <= 31);
+ int r = a << sh;
+ RI_ASSERT(a >= 0 ? (r >= 0) : (r < 0));
+ return r;
+}
+
+RI_INLINE int RI_SAT_SHL(RIint32 a, int sh)
+{
+ RI_ASSERT(sh >= 0 && sh <= 31);
+
+ RIint64 r = ((RIint64)a) << sh;
+
+ if (r > 0x7fffffff)
+ return 0x7fffffff;
+ else if (r < (long long)(int)0x80000000)
+ return 0x80000000;
+
+ return (RIint32)r;
+}
+
+RI_INLINE int RI_SHR(int a, int sh)
+{
+ RI_ASSERT(sh >= 0 && sh <= 31);
+ int r = a >> sh;
+ return r;
+}
+
+RI_INLINE RIfloat RI_FLOAT_TO_FX(RIfloat f, unsigned int n) { return (RIfloat)RI_ROUND_TO_INT(f * (RIfloat)RI_SHL(1, n)); }
+
+class Matrix3x3;
+class Vector2;
+class Vector3;
+
+//==============================================================================================
+
+//MatrixRxC, R = number of rows, C = number of columns
+//indexing: matrix[row][column]
+//Matrix3x3 inline functions cannot be inside the class because Vector3 is not defined yet when Matrix3x3 is defined
+
+class Matrix3x3
+{
+public:
+ RI_INLINE Matrix3x3 (); //initialized to identity
+ RI_INLINE Matrix3x3 ( const Matrix3x3& m );
+ RI_INLINE Matrix3x3 ( RIfloat m00, RIfloat m01, RIfloat m02, RIfloat m10, RIfloat m11, RIfloat m12, RIfloat m20, RIfloat m21, RIfloat m22 );
+ RI_INLINE ~Matrix3x3 ();
+ RI_INLINE Matrix3x3& operator= ( const Matrix3x3& m );
+ RI_INLINE Vector3& operator[] ( int i ); //returns a row vector
+ RI_INLINE const Vector3& operator[] ( int i ) const;
+ RI_INLINE void set ( RIfloat m00, RIfloat m01, RIfloat m02, RIfloat m10, RIfloat m11, RIfloat m12, RIfloat m20, RIfloat m21, RIfloat m22 );
+ RI_INLINE const Vector3 getRow ( int i ) const;
+ RI_INLINE const Vector3 getColumn ( int i ) const;
+ RI_INLINE void setRow ( int i, const Vector3& v );
+ RI_INLINE void setColumn ( int i, const Vector3& v );
+ RI_INLINE void operator*= ( const Matrix3x3& m );
+ RI_INLINE void operator*= ( RIfloat f );
+ RI_INLINE void operator+= ( const Matrix3x3& m );
+ RI_INLINE void operator-= ( const Matrix3x3& m );
+ RI_INLINE const Matrix3x3 operator- () const;
+ RI_INLINE void identity ();
+ RI_INLINE void transpose ();
+ bool invert (); //if the matrix is singular, returns false and leaves it unmodified
+ RI_INLINE RIfloat det () const;
+ RI_INLINE bool isAffine () const;
+ RI_INLINE void assertValid () const;
+ RI_INLINE void validate ();
+
+private:
+ RIfloat matrix[3][3];
+};
+
+//==============================================================================================
+
+class Vector2
+{
+public:
+ RI_INLINE Vector2 () : x(0.0f), y(0.0f) {}
+ RI_INLINE Vector2 ( const Vector2& v ) : x(v.x), y(v.y) {}
+ RI_INLINE Vector2 ( RIfloat fx, RIfloat fy ) : x(fx), y(fy) {}
+ RI_INLINE ~Vector2 () {}
+ RI_INLINE Vector2& operator= ( const Vector2& v ) { x = v.x; y = v.y; return *this; }
+ RI_INLINE RIfloat& operator[] ( int i ) { RI_ASSERT(i>=0&&i<2); return (&x)[i]; }
+ RI_INLINE const RIfloat& operator[] ( int i ) const { RI_ASSERT(i>=0&&i<2); return (&x)[i]; }
+ RI_INLINE void set ( RIfloat fx, RIfloat fy ) { x = fx; y = fy; }
+ RI_INLINE void operator*= ( RIfloat f ) { x *= f; y *= f; }
+ RI_INLINE void operator+= ( const Vector2& v ) { x += v.x; y += v.y; }
+ RI_INLINE void operator-= ( const Vector2& v ) { x -= v.x; y -= v.y; }
+ RI_INLINE const Vector2 operator- () const { return Vector2(-x,-y); }
+ //if the vector is zero, returns false and leaves it unmodified
+ RI_INLINE bool normalize () { double l = (double)x*(double)x+(double)y*(double)y; if( l == 0.0 ) return false; l = 1.0 / sqrt(l); x = (RIfloat)((double)x * l); y = (RIfloat)((double)y * l); return true; }
+ RI_INLINE RIfloat length () const { return (RIfloat)sqrt((double)x*(double)x+(double)y*(double)y); }
+ RI_INLINE void scale ( const Vector2& v ) { x *= v.x; y *= v.y; } //component-wise scale
+ RI_INLINE void negate () { x = -x; y = -y; }
+
+ RIfloat x,y;
+};
+
+//==============================================================================================
+
+class Vector3
+{
+public:
+ RI_INLINE Vector3 () : x(0.0f), y(0.0f), z(0.0f) {}
+ RI_INLINE Vector3 ( const Vector3& v ) : x(v.x), y(v.y), z(v.z) {}
+ RI_INLINE Vector3 ( RIfloat fx, RIfloat fy, RIfloat fz ) : x(fx), y(fy), z(fz) {}
+ RI_INLINE ~Vector3 () {}
+ RI_INLINE Vector3& operator= ( const Vector3& v ) { x = v.x; y = v.y; z = v.z; return *this; }
+ RI_INLINE RIfloat& operator[] ( int i ) { RI_ASSERT(i>=0&&i<3); return (&x)[i]; }
+ RI_INLINE const RIfloat& operator[] ( int i ) const { RI_ASSERT(i>=0&&i<3); return (&x)[i]; }
+ RI_INLINE void set ( RIfloat fx, RIfloat fy, RIfloat fz ){ x = fx; y = fy; z = fz; }
+ RI_INLINE void operator*= ( RIfloat f ) { x *= f; y *= f; z *= f; }
+ RI_INLINE void operator+= ( const Vector3& v ) { x += v.x; y += v.y; z += v.z; }
+ RI_INLINE void operator-= ( const Vector3& v ) { x -= v.x; y -= v.y; z -= v.z; }
+ RI_INLINE const Vector3 operator- () const { return Vector3(-x,-y,-z); }
+ //if the vector is zero, returns false and leaves it unmodified
+ RI_INLINE bool normalize () { double l = (double)x*(double)x+(double)y*(double)y+(double)z*(double)z; if( l == 0.0 ) return false; l = 1.0 / sqrt(l); x = (RIfloat)((double)x * l); y = (RIfloat)((double)y * l); z = (RIfloat)((double)z * l); return true; }
+ RI_INLINE RIfloat length () const { return (RIfloat)sqrt((double)x*(double)x+(double)y*(double)y+(double)z*(double)z); }
+ RI_INLINE void scale ( const Vector3& v ) { x *= v.x; y *= v.y; z *= v.z; } //component-wise scale
+ RI_INLINE void negate () { x = -x; y = -y; z = -z; }
+
+ RIfloat x,y,z;
+};
+
+//==============================================================================================
+
+//Vector2 global functions
+RI_INLINE bool operator== ( const Vector2& v1, const Vector2& v2 ) { return (v1.x == v2.x) && (v1.y == v2.y); }
+RI_INLINE bool operator!= ( const Vector2& v1, const Vector2& v2 ) { return (v1.x != v2.x) || (v1.y != v2.y); }
+RI_INLINE bool isEqual ( const Vector2& v1, const Vector2& v2, RIfloat epsilon ) { return RI_SQR(v2.x-v1.x) + RI_SQR(v2.y-v1.y) <= epsilon*epsilon; }
+RI_INLINE bool isZero ( const Vector2& v ) { return (v.x == 0.0f) && (v.y == 0.0f); }
+RI_INLINE const Vector2 operator* ( RIfloat f, const Vector2& v ) { return Vector2(v.x*f,v.y*f); }
+RI_INLINE const Vector2 operator* ( const Vector2& v, RIfloat f ) { return Vector2(v.x*f,v.y*f); }
+RI_INLINE const Vector2 operator+ ( const Vector2& v1, const Vector2& v2 ) { return Vector2(v1.x+v2.x, v1.y+v2.y); }
+RI_INLINE const Vector2 operator- ( const Vector2& v1, const Vector2& v2 ) { return Vector2(v1.x-v2.x, v1.y-v2.y); }
+RI_INLINE RIfloat dot ( const Vector2& v1, const Vector2& v2 ) { return v1.x*v2.x+v1.y*v2.y; }
+//if v is a zero vector, returns a zero vector
+RI_INLINE const Vector2 normalize ( const Vector2& v ) { double l = (double)v.x*(double)v.x+(double)v.y*(double)v.y; if( l != 0.0 ) l = 1.0 / sqrt(l); return Vector2((RIfloat)((double)v.x * l), (RIfloat)((double)v.y * l)); }
+//if onThis is a zero vector, returns a zero vector
+RI_INLINE const Vector2 project ( const Vector2& v, const Vector2& onThis ) { RIfloat l = dot(onThis,onThis); if( l != 0.0f ) l = dot(v, onThis)/l; return onThis * l; }
+RI_INLINE const Vector2 lerp ( const Vector2& v1, const Vector2& v2, RIfloat ratio ) { return v1 + ratio * (v2 - v1); }
+RI_INLINE const Vector2 scale ( const Vector2& v1, const Vector2& v2 ) { return Vector2(v1.x*v2.x, v1.y*v2.y); }
+//matrix * column vector. The input vector2 is implicitly expanded to (x,y,1)
+RI_INLINE const Vector2 affineTransform( const Matrix3x3& m, const Vector2& v ) { RI_ASSERT(m.isAffine()); return Vector2(v.x * m[0][0] + v.y * m[0][1] + m[0][2], v.x * m[1][0] + v.y * m[1][1] + m[1][2]); }
+//matrix * column vector. The input vector2 is implicitly expanded to (x,y,0)
+RI_INLINE const Vector2 affineTangentTransform(const Matrix3x3& m, const Vector2& v) { RI_ASSERT(m.isAffine()); return Vector2(v.x * m[0][0] + v.y * m[0][1], v.x * m[1][0] + v.y * m[1][1]); }
+RI_INLINE const Vector2 perpendicularCW(const Vector2& v) { return Vector2(v.y, -v.x); }
+RI_INLINE const Vector2 perpendicularCCW(const Vector2& v) { return Vector2(-v.y, v.x); }
+RI_INLINE const Vector2 perpendicular(const Vector2& v, bool cw) { if(cw) return Vector2(v.y, -v.x); return Vector2(-v.y, v.x); }
+
+//==============================================================================================
+
+//Vector3 global functions
+RI_INLINE bool operator== ( const Vector3& v1, const Vector3& v2 ) { return (v1.x == v2.x) && (v1.y == v2.y) && (v1.z == v2.z); }
+RI_INLINE bool operator!= ( const Vector3& v1, const Vector3& v2 ) { return (v1.x != v2.x) || (v1.y != v2.y) || (v1.z != v2.z); }
+RI_INLINE bool isEqual ( const Vector3& v1, const Vector3& v2, RIfloat epsilon ) { return RI_SQR(v2.x-v1.x) + RI_SQR(v2.y-v1.y) + RI_SQR(v2.z-v1.z) <= epsilon*epsilon; }
+RI_INLINE const Vector3 operator* ( RIfloat f, const Vector3& v ) { return Vector3(v.x*f,v.y*f,v.z*f); }
+RI_INLINE const Vector3 operator* ( const Vector3& v, RIfloat f ) { return Vector3(v.x*f,v.y*f,v.z*f); }
+RI_INLINE const Vector3 operator+ ( const Vector3& v1, const Vector3& v2 ) { return Vector3(v1.x+v2.x, v1.y+v2.y, v1.z+v2.z); }
+RI_INLINE const Vector3 operator- ( const Vector3& v1, const Vector3& v2 ) { return Vector3(v1.x-v2.x, v1.y-v2.y, v1.z-v2.z); }
+RI_INLINE RIfloat dot ( const Vector3& v1, const Vector3& v2 ) { return v1.x*v2.x+v1.y*v2.y+v1.z*v2.z; }
+RI_INLINE const Vector3 cross ( const Vector3& v1, const Vector3& v2 ) { return Vector3( v1.y*v2.z-v1.z*v2.y, v1.z*v2.x-v1.x*v2.z, v1.x*v2.y-v1.y*v2.x ); }
+//if v is a zero vector, returns a zero vector
+RI_INLINE const Vector3 normalize ( const Vector3& v ) { double l = (double)v.x*(double)v.x+(double)v.y*(double)v.y+(double)v.z*(double)v.z; if( l != 0.0 ) l = 1.0 / sqrt(l); return Vector3((RIfloat)((double)v.x * l), (RIfloat)((double)v.y * l), (RIfloat)((double)v.z * l)); }
+RI_INLINE const Vector3 lerp ( const Vector3& v1, const Vector3& v2, RIfloat ratio ) { return v1 + ratio * (v2 - v1); }
+RI_INLINE const Vector3 scale ( const Vector3& v1, const Vector3& v2 ) { return Vector3(v1.x*v2.x, v1.y*v2.y, v1.z*v2.z); }
+
+//==============================================================================================
+
+//matrix * column vector
+RI_INLINE const Vector3 operator* ( const Matrix3x3& m, const Vector3& v) { return Vector3( v.x*m[0][0]+v.y*m[0][1]+v.z*m[0][2], v.x*m[1][0]+v.y*m[1][1]+v.z*m[1][2], v.x*m[2][0]+v.y*m[2][1]+v.z*m[2][2] ); }
+
+//==============================================================================================
+
+//Matrix3x3 global functions
+RI_INLINE bool operator== ( const Matrix3x3& m1, const Matrix3x3& m2 ) { for(int i=0;i<3;i++) for(int j=0;j<3;j++) if( m1[i][j] != m2[i][j] ) return false; return true; }
+RI_INLINE bool operator!= ( const Matrix3x3& m1, const Matrix3x3& m2 ) { return !(m1 == m2); }
+RI_INLINE const Matrix3x3 operator* ( const Matrix3x3& m1, const Matrix3x3& m2 ) { Matrix3x3 t; for(int i=0;i<3;i++) for(int j=0;j<3;j++) t[i][j] = m1[i][0] * m2[0][j] + m1[i][1] * m2[1][j] + m1[i][2] * m2[2][j]; return t; }
+RI_INLINE const Matrix3x3 operator* ( RIfloat f, const Matrix3x3& m ) { Matrix3x3 t(m); t *= f; return t; }
+RI_INLINE const Matrix3x3 operator* ( const Matrix3x3& m, RIfloat f ) { Matrix3x3 t(m); t *= f; return t; }
+RI_INLINE const Matrix3x3 operator+ ( const Matrix3x3& m1, const Matrix3x3& m2 ) { Matrix3x3 t(m1); t += m2; return t; }
+RI_INLINE const Matrix3x3 operator- ( const Matrix3x3& m1, const Matrix3x3& m2 ) { Matrix3x3 t(m1); t -= m2; return t; }
+RI_INLINE const Matrix3x3 transpose ( const Matrix3x3& m ) { Matrix3x3 t(m); t.transpose(); return t; }
+// if the matrix is singular, returns it unmodified
+RI_INLINE const Matrix3x3 invert ( const Matrix3x3& m ) { Matrix3x3 t(m); t.invert(); return t; }
+
+//==============================================================================================
+
+//Matrix3x3 inline functions (cannot be inside the class because Vector3 is not defined yet when Matrix3x3 is defined)
+RI_INLINE Matrix3x3::Matrix3x3 () { identity(); }
+RI_INLINE Matrix3x3::Matrix3x3 ( const Matrix3x3& m ) { *this = m; }
+RI_INLINE Matrix3x3::Matrix3x3 ( RIfloat m00, RIfloat m01, RIfloat m02, RIfloat m10, RIfloat m11, RIfloat m12, RIfloat m20, RIfloat m21, RIfloat m22 ) { set(m00,m01,m02,m10,m11,m12,m20,m21,m22); }
+RI_INLINE Matrix3x3::~Matrix3x3 () {}
+RI_INLINE Matrix3x3& Matrix3x3::operator= ( const Matrix3x3& m ) { for(int i=0;i<3;i++) for(int j=0;j<3;j++) matrix[i][j] = m.matrix[i][j]; return *this; }
+RI_INLINE Vector3& Matrix3x3::operator[] ( int i ) { RI_ASSERT(i>=0&&i<3); return (Vector3&)matrix[i][0]; }
+RI_INLINE const Vector3& Matrix3x3::operator[] ( int i ) const { RI_ASSERT(i>=0&&i<3); return (const Vector3&)matrix[i][0]; }
+RI_INLINE void Matrix3x3::set ( RIfloat m00, RIfloat m01, RIfloat m02, RIfloat m10, RIfloat m11, RIfloat m12, RIfloat m20, RIfloat m21, RIfloat m22 ) { matrix[0][0] = m00; matrix[0][1] = m01; matrix[0][2] = m02; matrix[1][0] = m10; matrix[1][1] = m11; matrix[1][2] = m12; matrix[2][0] = m20; matrix[2][1] = m21; matrix[2][2] = m22; }
+RI_INLINE const Vector3 Matrix3x3::getRow ( int i ) const { RI_ASSERT(i>=0&&i<3); return Vector3(matrix[i][0], matrix[i][1], matrix[i][2]); }
+RI_INLINE const Vector3 Matrix3x3::getColumn ( int i ) const { RI_ASSERT(i>=0&&i<3); return Vector3(matrix[0][i], matrix[1][i], matrix[2][i]); }
+RI_INLINE void Matrix3x3::setRow ( int i, const Vector3& v ) { RI_ASSERT(i>=0&&i<3); matrix[i][0] = v.x; matrix[i][1] = v.y; matrix[i][2] = v.z; }
+RI_INLINE void Matrix3x3::setColumn ( int i, const Vector3& v ) { RI_ASSERT(i>=0&&i<3); matrix[0][i] = v.x; matrix[1][i] = v.y; matrix[2][i] = v.z; }
+RI_INLINE void Matrix3x3::operator*= ( const Matrix3x3& m ) { *this = *this * m; }
+RI_INLINE void Matrix3x3::operator*= ( RIfloat f ) { for(int i=0;i<3;i++) for(int j=0;j<3;j++) matrix[i][j] *= f; }
+RI_INLINE void Matrix3x3::operator+= ( const Matrix3x3& m ) { for(int i=0;i<3;i++) for(int j=0;j<3;j++) matrix[i][j] += m.matrix[i][j]; }
+RI_INLINE void Matrix3x3::operator-= ( const Matrix3x3& m ) { for(int i=0;i<3;i++) for(int j=0;j<3;j++) matrix[i][j] -= m.matrix[i][j]; }
+RI_INLINE const Matrix3x3 Matrix3x3::operator- () const { return Matrix3x3( -matrix[0][0],-matrix[0][1],-matrix[0][2], -matrix[1][0],-matrix[1][1],-matrix[1][2], -matrix[2][0],-matrix[2][1],-matrix[2][2]); }
+RI_INLINE void Matrix3x3::identity () { for(int i=0;i<3;i++) for(int j=0;j<3;j++) matrix[i][j] = (i == j) ? 1.0f : 0.0f; }
+RI_INLINE void Matrix3x3::transpose () { RI_SWAP(matrix[1][0], matrix[0][1]); RI_SWAP(matrix[2][0], matrix[0][2]); RI_SWAP(matrix[2][1], matrix[1][2]); }
+RI_INLINE RIfloat Matrix3x3::det () const { return matrix[0][0] * (matrix[1][1]*matrix[2][2] - matrix[2][1]*matrix[1][2]) + matrix[0][1] * (matrix[2][0]*matrix[1][2] - matrix[1][0]*matrix[2][2]) + matrix[0][2] * (matrix[1][0]*matrix[2][1] - matrix[2][0]*matrix[1][1]); }
+RI_INLINE bool Matrix3x3::isAffine () const { if(matrix[2][0] == 0.0f && matrix[2][1] == 0.0f && matrix[2][2] == 1.0f) return true; return false; }
+
+RI_INLINE void Matrix3x3::validate()
+{
+ for (int i = 0; i < 3; i++)
+ for (int j = 0; j < 3; j++)
+ matrix[i][j] = validateFloat(matrix[i][j]);
+}
+
+RI_INLINE void Matrix3x3::assertValid() const
+{
+#if defined(RI_DEBUG)
+ for (int i = 0; i < 3; i++)
+ for (int j = 0; j < 3; j++)
+ RI_ASSERT(!RI_ISNAN(matrix[i][j]));
+#endif
+}
+
+//==============================================================================================
+
+} //namespace OpenVGRI
+
+#endif /* __RIMATH_H */