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+/**
+ @file Vector3.h
+
+ 3D vector class
+
+ @maintainer Morgan McGuire, http://graphics.cs.williams.edu
+
+ @created 2001-06-02
+ @edited 2009-11-01
+ Copyright 2000-2009, Morgan McGuire.
+ All rights reserved.
+ */
+
+#ifndef G3D_Vector3_h
+#define G3D_Vector3_h
+
+#include "G3D/platform.h"
+#include "G3D/g3dmath.h"
+#include "G3D/Random.h"
+#include "G3D/Vector2.h"
+#include "G3D/Table.h"
+#include "G3D/HashTrait.h"
+#include "G3D/PositionTrait.h"
+#include "G3D/Vector2.h"
+#include <iostream>
+#include <string>
+
+namespace G3D {
+
+class Vector2;
+class Vector4;
+class Vector4int8;
+class Vector3int32;
+class Any;
+
+/**
+ <B>Swizzles</B>
+ Vector classes have swizzle operators, e.g. <CODE>v.xy()</CODE>, that
+ allow selection of arbitrary sub-fields. These cannot be used as write
+ masks. Examples
+
+ <PRE>
+Vector3 v(1, 2, 3);
+Vector3 j;
+Vector2 b;
+
+b = v.xz();
+j = b.xx();
+</PRE>
+
+
+ <B>Warning</B>
+
+ Do not subclass-- this implementation makes assumptions about the
+ memory layout.
+ */
+class Vector3 {
+public:
+
+ // coordinates
+ float x, y, z;
+
+private:
+
+ // Hidden operators
+ bool operator<(const Vector3&) const;
+ bool operator>(const Vector3&) const;
+ bool operator<=(const Vector3&) const;
+ bool operator>=(const Vector3&) const;
+
+public:
+ /** Initializes to zero */
+ Vector3();
+
+ /** \param any Must either Vector3(#, #, #) or Vector3 {x = #, y = #, z = #}*/
+ Vector3(const Any& any);
+
+ /** Converts the Vector3 to an Any. */
+ operator Any() const;
+
+ /** Divides by 127 */
+ Vector3(const Vector4int8&);
+ Vector3(const class Vector3int32& v);
+ explicit Vector3(class BinaryInput& b);
+ Vector3(float _x, float _y, float _z);
+ explicit Vector3(const class Vector2& v, float _z);
+ explicit Vector3(float coordinate[3]);
+ explicit Vector3(double coordinate[3]);
+ Vector3(const class Vector3int16& v);
+ explicit Vector3(class TextInput& t);
+ explicit Vector3(const class Color3& c);
+
+ /** Format is three float32's */
+ void serialize(class BinaryOutput& b) const;
+ void deserialize(class BinaryInput& b);
+
+ /** Format is "(%f, %f, %f)" */
+ void serialize(class TextOutput& t) const;
+ void deserialize(class TextInput& t);
+
+ // access vector V as V[0] = V.x, V[1] = V.y, V[2] = V.z
+ //
+ // WARNING. These member functions rely on
+ // (1) Vector3 not having virtual functions
+ // (2) the data packed in a 3*sizeof(float) memory block
+ const float& __fastcall operator[] (int i) const;
+ float& operator[] (int i);
+
+ enum Axis {X_AXIS=0, Y_AXIS=1, Z_AXIS=2, DETECT_AXIS=-1};
+
+ /**
+ Returns the largest dimension. Particularly convenient for determining
+ which plane to project a triangle onto for point-in-polygon tests.
+ */
+ Axis primaryAxis() const;
+
+ // assignment and comparison
+ Vector3& __fastcall operator= (const Vector3& rkVector);
+ bool operator== (const Vector3& rkVector) const;
+ bool operator!= (const Vector3& rkVector) const;
+ size_t hashCode() const;
+ bool fuzzyEq(const Vector3& other) const;
+ bool fuzzyNe(const Vector3& other) const;
+
+ /** Returns true if this vector has finite length. */
+ bool isFinite() const;
+
+ /** Returns true if this vector has length ~= 0 */
+ bool isZero() const;
+
+ /** Returns true if this vector has length ~= 1 */
+ bool isUnit() const;
+
+ // arithmetic operations
+ Vector3 __fastcall operator+ (const Vector3& v) const;
+ Vector3 __fastcall operator- (const Vector3& v) const;
+ Vector3 __fastcall operator* (float s) const;
+ inline Vector3 __fastcall operator/ (float s) const {
+ return *this * (1.0f / s);
+ }
+ Vector3 __fastcall operator* (const Vector3& v) const;
+ Vector3 __fastcall operator/ (const Vector3& v) const;
+ Vector3 __fastcall operator- () const;
+
+ // arithmetic updates
+ Vector3& __fastcall operator+= (const Vector3& v);
+ Vector3& __fastcall operator-= (const Vector3& v);
+ Vector3& __fastcall operator*= (float s);
+ inline Vector3& __fastcall operator/= (float s) {
+ return (*this *= (1.0f / s));
+ }
+ Vector3& __fastcall operator*= (const Vector3& v);
+ Vector3& __fastcall operator/= (const Vector3& v);
+
+ /** Same as magnitude */
+ float length() const;
+
+ float magnitude() const;
+
+ /**
+ The result is a nan vector if the length is almost zero.
+ */
+ Vector3 direction() const;
+
+ /**
+ Potentially less accurate but faster than direction().
+ Only works if System::hasSSE is true.
+ */
+ Vector3 fastDirection() const;
+
+ /**
+ Reflect this vector about the (not necessarily unit) normal.
+ Assumes that both the before and after vectors point away from
+ the base of the normal.
+
+ Note that if used for a collision or ray reflection you
+ must negate the resulting vector to get a direction pointing
+ <I>away</I> from the collision.
+
+ <PRE>
+ V' N V
+
+ r ^ -,
+ \ | /
+ \|/
+ </PRE>
+
+ See also Vector3::reflectionDirection
+ */
+ Vector3 reflectAbout(const Vector3& normal) const;
+
+ /**
+ See also G3D::Ray::reflect.
+ The length is 1.
+ <PRE>
+ V' N V
+
+ r ^ /
+ \ | /
+ \|'-
+ </PRE>
+ */
+ Vector3 reflectionDirection(const Vector3& normal) const;
+
+
+ /**
+ Returns Vector3::zero() if the length is nearly zero, otherwise
+ returns a unit vector.
+ */
+ inline Vector3 directionOrZero() const {
+ float mag = magnitude();
+ if (G3D::fuzzyEq(mag, 0.0f)) {
+ return Vector3::zero();
+ } else if (G3D::fuzzyEq(mag, 1.0f)) {
+ return *this;
+ } else {
+ return *this * (1.0f / mag);
+ }
+ }
+
+ /**
+ Returns the direction of a refracted ray,
+ where iExit is the index of refraction for the
+ previous material and iEnter is the index of refraction
+ for the new material. Like Vector3::reflectionDirection,
+ the result has length 1 and is
+ pointed <I>away</I> from the intersection.
+
+ Returns Vector3::zero() in the case of total internal refraction.
+
+ @param iOutside The index of refraction (eta) outside
+ (on the <I>positive</I> normal side) of the surface.
+
+ @param iInside The index of refraction (eta) inside
+ (on the <I>negative</I> normal side) of the surface.
+
+ See also G3D::Ray::refract.
+ <PRE>
+ N V
+
+ ^ /
+ | /
+ |'-
+ __--
+ V'<--
+ </PRE>
+ */
+ Vector3 refractionDirection(
+ const Vector3& normal,
+ float iInside,
+ float iOutside) const;
+
+ /** Synonym for direction */
+ inline Vector3 unit() const {
+ return direction();
+ }
+
+ /** Returns a normalized vector. May be computed with lower
+ precision than unit */
+ inline Vector3 fastUnit() const {
+ return fastDirection();
+ }
+
+ /** Same as squaredMagnitude */
+ float squaredLength() const;
+
+ float squaredMagnitude () const;
+
+ float __fastcall dot(const Vector3& rkVector) const;
+
+ float unitize(float tolerance = 1e-06);
+
+ /** Cross product. Note that two cross products in a row
+ can be computed more cheaply: v1 x (v2 x v3) = (v1 dot v3) v2 - (v1 dot v2) v3.
+ */
+ Vector3 __fastcall cross(const Vector3& rkVector) const;
+ Vector3 unitCross(const Vector3& rkVector) const;
+
+ /**
+ Returns a matrix such that v.cross() * w = v.cross(w).
+ <PRE>
+ [ 0 -v.z v.y ]
+ [ v.z 0 -v.x ]
+ [ -v.y v.x 0 ]
+ </PRE>
+ */
+ class Matrix3 cross() const;
+
+ Vector3 __fastcall min(const Vector3 &v) const;
+ Vector3 __fastcall max(const Vector3 &v) const;
+
+ /** Smallest element */
+ inline float min() const {
+ return G3D::min(G3D::min(x, y), z);
+ }
+
+ /** Largest element */
+ inline float max() const {
+ return G3D::max(G3D::max(x, y), z);
+ }
+
+ std::string toString() const;
+
+ inline Vector3 clamp(const Vector3& low, const Vector3& high) const {
+ return Vector3(
+ G3D::clamp(x, low.x, high.x),
+ G3D::clamp(y, low.y, high.y),
+ G3D::clamp(z, low.z, high.z));
+ }
+
+ inline Vector3 clamp(float low, float high) const {
+ return Vector3(
+ G3D::clamp(x, low, high),
+ G3D::clamp(y, low, high),
+ G3D::clamp(z, low, high));
+ }
+
+ /**
+ Linear interpolation
+ */
+ inline Vector3 lerp(const Vector3& v, float alpha) const {
+ return (*this) + (v - *this) * alpha;
+ }
+
+ /** Gram-Schmidt orthonormalization. */
+ static void orthonormalize (Vector3 akVector[3]);
+
+ /** \brief Random unit vector, uniformly distributed on the sphere.
+
+ Distribution rendered by G3D::DirectionHistogram:
+ \image html vector3-random.png
+ */
+ static Vector3 random(Random& r = Random::common());
+
+ /** \brief Random unit vector, distributed according to \f$\max(\cos \theta,0)\f$.
+
+ That is, so that the probability of \f$\vec{V}\f$ is proportional
+ to \f$\max(\vec{v} \cdot \vec{n}, 0)\f$. Useful in photon mapping for
+ Lambertian scattering.
+
+ Distribution rendered by G3D::DirectionHistogram:
+ \image html vector3-coshemirandom.png
+
+ \param n Unit vector at the center of the distribution.
+
+ @cite Henrik Wann Jensen, Realistic Image Synthesis using Photon Mapping eqn 2.24
+ */
+ static Vector3 cosHemiRandom(const Vector3& n, Random& r = Random::common());
+
+ /** \brief Random unit vector, distributed according to \f$\max(\cos^k \theta,0)\f$.
+
+ That is, so that the probability of \f$\vec{V}\f$ is
+ proportional to \f$\max((\vec{v} \cdot \vec{n})^k, 0)\f$.
+ Useful in photon mapping for glossy scattering.
+
+ Distribution rendered by G3D::DirectionHistogram:
+ \image html vector3-cospowhemirandom.png
+
+ \param n Unit vector at the center of the distribution.
+
+ @cite Ashikhmin and Shirley, An anisotropic Phong BRDF model, Journal of Graphics Tools, 2002
+ */
+ static Vector3 cosPowHemiRandom(const Vector3& n, const float k, Random& r = Random::common());
+
+ /**
+ \brief Random vector distributed over the hemisphere about normal.
+
+ Distribution rendered by G3D::DirectionHistogram:
+ \image html vector3-hemirandom.png
+ */
+ static Vector3 hemiRandom(const Vector3& normal, Random& r = Random::common());
+
+ /** Input W must be initialize to a nonzero vector, output is {U,V,W}
+ an orthonormal basis. A hint is provided about whether or not W
+ is already unit length.
+ @deprecated Use getTangents
+ */
+ static void generateOrthonormalBasis (Vector3& rkU, Vector3& rkV,
+ Vector3& rkW, bool bUnitLengthW = true);
+
+ inline float sum() const {
+ return x + y + z;
+ }
+
+ inline float average() const {
+ return sum() / 3.0f;
+ }
+
+ // Special values.
+ static const Vector3& zero();
+ static const Vector3& one();
+ static const Vector3& unitX();
+ static const Vector3& unitY();
+ static const Vector3& unitZ();
+ static const Vector3& inf();
+ static const Vector3& nan();
+
+ /** Smallest (most negative) representable vector */
+ static const Vector3& minFinite();
+
+ /** Largest representable vector */
+ static const Vector3& maxFinite();
+
+
+ /** Creates two orthonormal tangent vectors X and Y such that
+ if Z = this, X x Y = Z.*/
+ inline void getTangents(Vector3& X, Vector3& Y) const {
+ debugAssertM(G3D::fuzzyEq(length(), 1.0f),
+ "makeAxes requires Z to have unit length");
+
+ // Choose another vector not perpendicular
+ X = (abs(x) < 0.9f) ? Vector3::unitX() : Vector3::unitY();
+
+ // Remove the part that is parallel to Z
+ X -= *this * this->dot(X);
+ X /= X.length();
+
+ Y = this->cross(X);
+ }
+
+
+ // 2-char swizzles
+
+ Vector2 xx() const;
+ Vector2 yx() const;
+ Vector2 zx() const;
+ Vector2 xy() const;
+ Vector2 yy() const;
+ Vector2 zy() const;
+ Vector2 xz() const;
+ Vector2 yz() const;
+ Vector2 zz() const;
+
+ // 3-char swizzles
+
+ Vector3 xxx() const;
+ Vector3 yxx() const;
+ Vector3 zxx() const;
+ Vector3 xyx() const;
+ Vector3 yyx() const;
+ Vector3 zyx() const;
+ Vector3 xzx() const;
+ Vector3 yzx() const;
+ Vector3 zzx() const;
+ Vector3 xxy() const;
+ Vector3 yxy() const;
+ Vector3 zxy() const;
+ Vector3 xyy() const;
+ Vector3 yyy() const;
+ Vector3 zyy() const;
+ Vector3 xzy() const;
+ Vector3 yzy() const;
+ Vector3 zzy() const;
+ Vector3 xxz() const;
+ Vector3 yxz() const;
+ Vector3 zxz() const;
+ Vector3 xyz() const;
+ Vector3 yyz() const;
+ Vector3 zyz() const;
+ Vector3 xzz() const;
+ Vector3 yzz() const;
+ Vector3 zzz() const;
+
+ // 4-char swizzles
+
+ Vector4 xxxx() const;
+ Vector4 yxxx() const;
+ Vector4 zxxx() const;
+ Vector4 xyxx() const;
+ Vector4 yyxx() const;
+ Vector4 zyxx() const;
+ Vector4 xzxx() const;
+ Vector4 yzxx() const;
+ Vector4 zzxx() const;
+ Vector4 xxyx() const;
+ Vector4 yxyx() const;
+ Vector4 zxyx() const;
+ Vector4 xyyx() const;
+ Vector4 yyyx() const;
+ Vector4 zyyx() const;
+ Vector4 xzyx() const;
+ Vector4 yzyx() const;
+ Vector4 zzyx() const;
+ Vector4 xxzx() const;
+ Vector4 yxzx() const;
+ Vector4 zxzx() const;
+ Vector4 xyzx() const;
+ Vector4 yyzx() const;
+ Vector4 zyzx() const;
+ Vector4 xzzx() const;
+ Vector4 yzzx() const;
+ Vector4 zzzx() const;
+ Vector4 xxxy() const;
+ Vector4 yxxy() const;
+ Vector4 zxxy() const;
+ Vector4 xyxy() const;
+ Vector4 yyxy() const;
+ Vector4 zyxy() const;
+ Vector4 xzxy() const;
+ Vector4 yzxy() const;
+ Vector4 zzxy() const;
+ Vector4 xxyy() const;
+ Vector4 yxyy() const;
+ Vector4 zxyy() const;
+ Vector4 xyyy() const;
+ Vector4 yyyy() const;
+ Vector4 zyyy() const;
+ Vector4 xzyy() const;
+ Vector4 yzyy() const;
+ Vector4 zzyy() const;
+ Vector4 xxzy() const;
+ Vector4 yxzy() const;
+ Vector4 zxzy() const;
+ Vector4 xyzy() const;
+ Vector4 yyzy() const;
+ Vector4 zyzy() const;
+ Vector4 xzzy() const;
+ Vector4 yzzy() const;
+ Vector4 zzzy() const;
+ Vector4 xxxz() const;
+ Vector4 yxxz() const;
+ Vector4 zxxz() const;
+ Vector4 xyxz() const;
+ Vector4 yyxz() const;
+ Vector4 zyxz() const;
+ Vector4 xzxz() const;
+ Vector4 yzxz() const;
+ Vector4 zzxz() const;
+ Vector4 xxyz() const;
+ Vector4 yxyz() const;
+ Vector4 zxyz() const;
+ Vector4 xyyz() const;
+ Vector4 yyyz() const;
+ Vector4 zyyz() const;
+ Vector4 xzyz() const;
+ Vector4 yzyz() const;
+ Vector4 zzyz() const;
+ Vector4 xxzz() const;
+ Vector4 yxzz() const;
+ Vector4 zxzz() const;
+ Vector4 xyzz() const;
+ Vector4 yyzz() const;
+ Vector4 zyzz() const;
+ Vector4 xzzz() const;
+ Vector4 yzzz() const;
+ Vector4 zzzz() const;
+
+ /** Can be passed to ignore a vector3 parameter */
+ static Vector3& ignore();
+};
+
+inline G3D::Vector3 operator*(float s, const G3D::Vector3& v) {
+ return v * s;
+}
+
+inline G3D::Vector3 operator*(double s, const G3D::Vector3& v) {
+ return v * (float)s;
+}
+
+inline G3D::Vector3 operator*(int s, const G3D::Vector3& v) {
+ return v * (float)s;
+}
+
+std::ostream& operator<<(std::ostream& os, const Vector3&);
+
+
+void serialize(const Vector3::Axis& a, class BinaryOutput& bo);
+void deserialize(Vector3::Axis& a, class BinaryInput& bo);
+
+
+//----------------------------------------------------------------------------
+inline Vector3::Vector3() : x(0.0f), y(0.0f), z(0.0f) {
+}
+
+//----------------------------------------------------------------------------
+
+inline Vector3::Vector3 (float fX, float fY, float fZ) : x(fX), y(fY), z(fZ) {
+}
+
+//----------------------------------------------------------------------------
+inline Vector3::Vector3 (float V[3]) : x(V[0]), y(V[1]), z(V[2]){
+}
+
+//----------------------------------------------------------------------------
+inline Vector3::Vector3 (double V[3]) : x((float)V[0]), y((float)V[1]), z((float)V[2]){
+}
+
+//----------------------------------------------------------------------------
+inline const float& Vector3::operator[] (int i) const {
+ return ((float*)this)[i];
+}
+
+inline float& Vector3::operator[] (int i) {
+ return ((float*)this)[i];
+}
+
+
+//----------------------------------------------------------------------------
+inline Vector3& Vector3::operator= (const Vector3& rkVector) {
+ x = rkVector.x;
+ y = rkVector.y;
+ z = rkVector.z;
+ return *this;
+}
+
+//----------------------------------------------------------------------------
+
+inline bool Vector3::fuzzyEq(const Vector3& other) const {
+ return G3D::fuzzyEq((*this - other).squaredMagnitude(), 0);
+}
+
+//----------------------------------------------------------------------------
+
+inline bool Vector3::fuzzyNe(const Vector3& other) const {
+ return G3D::fuzzyNe((*this - other).squaredMagnitude(), 0);
+}
+
+//----------------------------------------------------------------------------
+
+inline bool Vector3::isFinite() const {
+ return G3D::isFinite(x) && G3D::isFinite(y) && G3D::isFinite(z);
+}
+
+//----------------------------------------------------------------------------
+inline bool Vector3::operator== (const Vector3& rkVector) const {
+ return ( x == rkVector.x && y == rkVector.y && z == rkVector.z );
+}
+
+//----------------------------------------------------------------------------
+inline bool Vector3::operator!= (const Vector3& rkVector) const {
+ return ( x != rkVector.x || y != rkVector.y || z != rkVector.z );
+}
+
+//----------------------------------------------------------------------------
+inline Vector3 Vector3::operator+ (const Vector3& rkVector) const {
+ return Vector3(x + rkVector.x, y + rkVector.y, z + rkVector.z);
+}
+
+//----------------------------------------------------------------------------
+inline Vector3 Vector3::operator- (const Vector3& rkVector) const {
+ return Vector3(x - rkVector.x, y - rkVector.y, z - rkVector.z);
+}
+
+//----------------------------------------------------------------------------
+inline Vector3 Vector3::operator* (const Vector3& rkVector) const {
+ return Vector3(x * rkVector.x, y * rkVector.y, z * rkVector.z);
+}
+
+inline Vector3 Vector3::operator*(float f) const {
+ return Vector3(x * f, y * f, z * f);
+}
+
+//----------------------------------------------------------------------------
+inline Vector3 Vector3::operator/ (const Vector3& rkVector) const {
+ return Vector3(x / rkVector.x, y / rkVector.y, z / rkVector.z);
+}
+
+//----------------------------------------------------------------------------
+inline Vector3 Vector3::operator- () const {
+ return Vector3(-x, -y, -z);
+}
+
+//----------------------------------------------------------------------------
+inline Vector3& Vector3::operator+= (const Vector3& rkVector) {
+ x += rkVector.x;
+ y += rkVector.y;
+ z += rkVector.z;
+ return *this;
+}
+
+//----------------------------------------------------------------------------
+inline Vector3& Vector3::operator-= (const Vector3& rkVector) {
+ x -= rkVector.x;
+ y -= rkVector.y;
+ z -= rkVector.z;
+ return *this;
+}
+
+//----------------------------------------------------------------------------
+inline Vector3& Vector3::operator*= (float fScalar) {
+ x *= fScalar;
+ y *= fScalar;
+ z *= fScalar;
+ return *this;
+}
+
+//----------------------------------------------------------------------------
+inline Vector3& Vector3::operator*= (const Vector3& rkVector) {
+ x *= rkVector.x;
+ y *= rkVector.y;
+ z *= rkVector.z;
+ return *this;
+}
+
+//----------------------------------------------------------------------------
+inline Vector3& Vector3::operator/= (const Vector3& rkVector) {
+ x /= rkVector.x;
+ y /= rkVector.y;
+ z /= rkVector.z;
+ return *this;
+}
+
+//----------------------------------------------------------------------------
+inline float Vector3::squaredMagnitude () const {
+ return x*x + y*y + z*z;
+}
+
+//----------------------------------------------------------------------------
+inline float Vector3::squaredLength () const {
+ return squaredMagnitude();
+}
+
+//----------------------------------------------------------------------------
+inline float Vector3::magnitude() const {
+ return ::sqrtf(x*x + y*y + z*z);
+}
+
+//----------------------------------------------------------------------------
+inline float Vector3::length() const {
+ return magnitude();
+}
+
+//----------------------------------------------------------------------------
+inline Vector3 Vector3::direction () const {
+ const float lenSquared = squaredMagnitude();
+ const float invSqrt = 1.0f / sqrtf(lenSquared);
+ return Vector3(x * invSqrt, y * invSqrt, z * invSqrt);
+}
+
+//----------------------------------------------------------------------------
+
+inline Vector3 Vector3::fastDirection () const {
+ float lenSquared = x * x + y * y + z * z;
+ float invSqrt = rsq(lenSquared);
+ return Vector3(x * invSqrt, y * invSqrt, z * invSqrt);
+}
+
+//----------------------------------------------------------------------------
+inline float Vector3::dot (const Vector3& rkVector) const {
+ return x*rkVector.x + y*rkVector.y + z*rkVector.z;
+}
+
+//----------------------------------------------------------------------------
+inline Vector3 Vector3::cross (const Vector3& rkVector) const {
+ return Vector3(y*rkVector.z - z*rkVector.y, z*rkVector.x - x*rkVector.z,
+ x*rkVector.y - y*rkVector.x);
+}
+
+//----------------------------------------------------------------------------
+inline Vector3 Vector3::unitCross (const Vector3& rkVector) const {
+ Vector3 kCross(y*rkVector.z - z*rkVector.y, z*rkVector.x - x*rkVector.z,
+ x*rkVector.y - y*rkVector.x);
+ kCross.unitize();
+ return kCross;
+}
+
+//----------------------------------------------------------------------------
+inline Vector3 Vector3::min(const Vector3 &v) const {
+ return Vector3(G3D::min(v.x, x), G3D::min(v.y, y), G3D::min(v.z, z));
+}
+
+//----------------------------------------------------------------------------
+inline Vector3 Vector3::max(const Vector3 &v) const {
+ return Vector3(G3D::max(v.x, x), G3D::max(v.y, y), G3D::max(v.z, z));
+}
+
+//----------------------------------------------------------------------------
+inline bool Vector3::isZero() const {
+ return G3D::fuzzyEq(squaredMagnitude(), 0.0f);
+}
+
+//----------------------------------------------------------------------------
+
+inline bool Vector3::isUnit() const {
+ return G3D::fuzzyEq(squaredMagnitude(), 1.0f);
+}
+
+} // namespace G3D
+
+
+template <>
+struct HashTrait<G3D::Vector3> {
+ static size_t hashCode(const G3D::Vector3& key) {
+ return key.hashCode();
+ }
+};
+
+
+template<> struct PositionTrait<class G3D::Vector2> {
+ static void getPosition(const G3D::Vector2& v, G3D::Vector3& p) { p = G3D::Vector3(v, 0); }
+};
+
+template<> struct PositionTrait<class G3D::Vector3> {
+ static void getPosition(const G3D::Vector3& v, G3D::Vector3& p) { p = v; }
+};
+
+
+#endif