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/**
@file Vector3.h
3D vector class
@maintainer Morgan McGuire, [email protected]
@created 2001-06-02
@edited 2005-08-23
Copyright 2000-2006, Morgan McGuire.
All rights reserved.
*/
#ifndef G3D_VECTOR3_H
#define G3D_VECTOR3_H
#include "G3D/platform.h"
#include "G3D/g3dmath.h"
#include "G3D/Vector2.h"
#include <iostream>
#include <string>
namespace G3D {
class Vector2;
class Vector3;
class Vector4;
/**
<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 {
private:
/**
Reflect this vector about the (not necessarily unit) 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;
// Hidden operators
bool operator<(const Vector3&) const;
bool operator>(const Vector3&) const;
bool operator<=(const Vector3&) const;
bool operator>=(const Vector3&) const;
public:
// construction
Vector3();
Vector3(float _x, float _y, float _z);
Vector3(const class Vector2& v, float _z);
Vector3(float coordinate[3]);
Vector3(double coordinate[3]);
Vector3(const Vector3& rkVector);
Vector3(const class Vector3int16& v);
// coordinates
float x, y, z;
// 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& operator[] (int i) const;
float& operator[] (int i);
inline operator float* () {
return (float*)this;
}
operator const float* () const {
return (float*)this;
}
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& operator= (const Vector3& rkVector);
bool operator== (const Vector3& rkVector) const;
bool operator!= (const Vector3& rkVector) const;
unsigned int 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 operator+ (const Vector3& v) const;
Vector3 operator- (const Vector3& v) const;
Vector3 operator* (float s) const;
Vector3 operator/ (float s) const;
Vector3 operator* (const Vector3& v) const;
Vector3 operator/ (const Vector3& v) const;
Vector3 operator- () const;
// arithmetic updates
Vector3& operator+= (const Vector3& v);
Vector3& operator-= (const Vector3& v);
Vector3& operator*= (float s);
Vector3& operator/= (float s);
Vector3& operator*= (const Vector3& v);
Vector3& operator/= (const Vector3& v);
/** @deprecated Use magnitude */
float G3D_DEPRECATED 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;
/**
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();
}
/** @deprecated Use squaredMagnitude */
float G3D_DEPRECATED squaredLength() const;
float squaredMagnitude () const;
/** @deprecated Use squaredMagnitude */
inline float G3D_DEPRECATED norm() const {
return squaredMagnitude();
}
float dot(const Vector3& rkVector) const;
float G3D_DEPRECATED unitize(float fTolerance = 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 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 min(const Vector3 &v) const;
Vector3 max(const Vector3 &v) const;
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]);
/** Random unit vector, uniformly distributed */
static Vector3 random();
/** Random unit vector, distributed
so that the probability of V is proportional
to max(V dot Normal, 0).
@cite Henrik Wann Jensen, Realistic Image Synthesis using Photon Mapping eqn 2.24
*/
static Vector3 cosRandom(const Vector3& normal);
/**
Random vector distributed over the hemisphere about normal.
*/
static Vector3 hemiRandom(const Vector3& normal);
// 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.
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.
inline static const Vector3& zero() { static Vector3 v(0, 0, 0); return v; }
inline static const Vector3& one() { static Vector3 v(1, 1, 1); return v; }
inline static const Vector3& unitX() { static Vector3 v(1, 0, 0); return v; }
inline static const Vector3& unitY() { static Vector3 v(0, 1, 0); return v; }
inline static const Vector3& unitZ() { static Vector3 v(0, 0, 1); return v; }
inline static const Vector3& inf() { static Vector3 v((float)G3D::inf(), (float)G3D::inf(), (float)G3D::inf()); return v; }
inline static const Vector3& nan() { static Vector3 v((float)G3D::nan(), (float)G3D::nan(), (float)G3D::nan()); return v; }
/** Smallest (most negative) representable vector */
inline static const Vector3& minFinite(){ static Vector3 v(-FLT_MAX, -FLT_MAX, -FLT_MAX); return v; }
/** Largest representable vector */
inline static const Vector3& maxFinite(){ static Vector3 v(FLT_MAX, FLT_MAX, FLT_MAX); return v; }
// Deprecated. See Matrix3::identity() for details.
/** @deprecated Use Vector3::zero() */
static const Vector3 ZERO;
/** @deprecated Use Vector3::zero() */
static const Vector3 ZERO3;
/** @deprecated Use Vector3::unitX() */
static const Vector3 UNIT_X;
/** @deprecated Use Vector3::unitY() */
static const Vector3 UNIT_Y;
/** @deprecated Use Vector3::unitZ() */
static const Vector3 UNIT_Z;
/** @deprecated Use Vector3::inf() */
static const Vector3 INF3;
/** @deprecated Use Vector3::nan() */
static const Vector3 NAN3;
// 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;
/** A value that can be passed to ignore a parameter. Never look at the result of dummy. */
static Vector3 dummy;
};
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&);
}
unsigned int hashCode(const G3D::Vector3& v);
#include "Vector3.inl"
#endif