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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