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Diffstat (limited to 'dep/include/g3dlite/G3D/Quat.h')
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diff --git a/dep/include/g3dlite/G3D/Quat.h b/dep/include/g3dlite/G3D/Quat.h deleted file mode 100644 index 9ef3d57b301..00000000000 --- a/dep/include/g3dlite/G3D/Quat.h +++ /dev/null @@ -1,725 +0,0 @@ -/** - @file Quat.h - - Quaternion - - @maintainer Morgan McGuire, http://graphics.cs.williams.edu - - @created 2002-01-23 - @edited 2009-05-10 - */ - -#ifndef G3D_Quat_h -#define G3D_Quat_h - -#include "G3D/platform.h" -#include "G3D/g3dmath.h" -#include "G3D/Vector3.h" -#include "G3D/Matrix3.h" -#include <string> - -namespace G3D { - -/** - Unit quaternions are used in computer graphics to represent - rotation about an axis. Any 3x3 rotation matrix can - be stored as a quaternion. - - A quaternion represents the sum of a real scalar and - an imaginary vector: ix + jy + kz + w. A unit quaternion - representing a rotation by A about axis v has the form - [sin(A/2)*v, cos(A/2)]. For a unit quaternion, q.conj() == q.inverse() - is a rotation by -A about v. -q is the same rotation as q - (negate both the axis and angle). - - A non-unit quaterion q represents the same rotation as - q.unitize() (Dam98 pg 28). - - Although quaternion-vector operations (eg. Quat + Vector3) are - well defined, they are not supported by this class because - they typically are bugs when they appear in code. - - Do not subclass. - - <B>BETA API -- subject to change</B> - @cite Erik B. Dam, Martin Koch, Martin Lillholm, Quaternions, Interpolation and Animation. Technical Report DIKU-TR-98/5, Department of Computer Science, University of Copenhagen, Denmark. 1998. - */ -class Quat { -private: - // Hidden operators - bool operator<(const Quat&) const; - bool operator>(const Quat&) const; - bool operator<=(const Quat&) const; - bool operator>=(const Quat&) const; - -public: - - /** - q = [sin(angle / 2) * axis, cos(angle / 2)] - - In Watt & Watt's notation, s = w, v = (x, y, z) - In the Real-Time Rendering notation, u = (x, y, z), w = w - */ - float x, y, z, w; - - /** - Initializes to a zero degree rotation. - */ - inline Quat() : x(0), y(0), z(0), w(1) {} - - Quat( - const Matrix3& rot); - - inline Quat(float _x, float _y, float _z, float _w) : - x(_x), y(_y), z(_z), w(_w) {} - - /** Defaults to a pure vector quaternion */ - inline Quat(const Vector3& v, float _w = 0) : x(v.x), y(v.y), z(v.z), w(_w) { - } - - /** - The real part of the quaternion. - */ - inline const float& real() const { - return w; - } - - inline float& real() { - return w; - } - - /** Note: two quats can represent the Quat::sameRotation and not be equal. */ - bool fuzzyEq(const Quat& q) { - return G3D::fuzzyEq(x, q.x) && G3D::fuzzyEq(y, q.y) && G3D::fuzzyEq(z, q.z) && G3D::fuzzyEq(w, q.w); - } - - /** True if these quaternions represent the same rotation (note that every rotation is - represented by two values; q and -q). - */ - bool sameRotation(const Quat& q) { - return fuzzyEq(q) || fuzzyEq(-q); - } - - inline Quat operator-() const { - return Quat(-x, -y, -z, -w); - } - - /** - Returns the imaginary part (x, y, z) - */ - inline const Vector3& imag() const { - return *(reinterpret_cast<const Vector3*>(this)); - } - - inline Vector3& imag() { - return *(reinterpret_cast<Vector3*>(this)); - } - - /** q = [sin(angle/2)*axis, cos(angle/2)] */ - static Quat fromAxisAngleRotation( - const Vector3& axis, - float angle); - - /** Returns the axis and angle of rotation represented - by this quaternion (i.e. q = [sin(angle/2)*axis, cos(angle/2)]) */ - void toAxisAngleRotation( - Vector3& axis, - double& angle) const; - - void toAxisAngleRotation( - Vector3& axis, - float& angle) const { - double d; - toAxisAngleRotation(axis, d); - angle = (float)d; - } - - Matrix3 toRotationMatrix() const; - - void toRotationMatrix( - Matrix3& rot) const; - - /** - Spherical linear interpolation: linear interpolation along the - shortest (3D) great-circle route between two quaternions. - - Note: Correct rotations are expected between 0 and PI in the right order. - - @cite Based on Game Physics -- David Eberly pg 538-540 - @param threshold Critical angle between between rotations at which - the algorithm switches to normalized lerp, which is more - numerically stable in those situations. 0.0 will always slerp. - */ - Quat slerp( - const Quat& other, - float alpha, - float threshold = 0.05f) const; - - /** Normalized linear interpolation of quaternion components. */ - Quat nlerp(const Quat& other, float alpha) const; - - /** - Negates the imaginary part. - */ - inline Quat conj() const { - return Quat(-x, -y, -z, w); - } - - inline float sum() const { - return x + y + z + w; - } - - inline float average() const { - return sum() / 4.0f; - } - - inline Quat operator*(float s) const { - return Quat(x * s, y * s, z * s, w * s); - } - - inline Quat& operator*=(float s) { - x *= s; - y *= s; - z *= s; - w *= s; - return *this; - } - - /** @cite Based on Watt & Watt, page 360 */ - friend Quat operator* (float s, const Quat& q); - - inline Quat operator/(float s) const { - return Quat(x / s, y / s, z / s, w / s); - } - - inline float dot(const Quat& other) const { - return (x * other.x) + (y * other.y) + (z * other.z) + (w * other.w); - } - - /** Note that q<SUP>-1</SUP> = q.conj() for a unit quaternion. - @cite Dam99 page 13 */ - inline Quat inverse() const { - return conj() / dot(*this); - } - - Quat operator-(const Quat& other) const; - - Quat operator+(const Quat& other) const; - - /** - Quaternion multiplication (composition of rotations). - Note that this does not commute. - */ - Quat operator*(const Quat& other) const; - - /* (*this) * other.inverse() */ - Quat operator/(const Quat& other) const { - return (*this) * other.inverse(); - } - - - /** Is the magnitude nearly 1.0? */ - inline bool isUnit(float tolerance = 1e-5) const { - return abs(dot(*this) - 1.0f) < tolerance; - } - - - inline float magnitude() const { - return sqrtf(dot(*this)); - } - - inline Quat log() const { - if ((x == 0) && (y == 0) && (z == 0)) { - if (w > 0) { - return Quat(0, 0, 0, ::logf(w)); - } else if (w < 0) { - // Log of a negative number. Multivalued, any number of the form - // (PI * v, ln(-q.w)) - return Quat((float)pi(), 0, 0, ::logf(-w)); - } else { - // log of zero! - return Quat((float)nan(), (float)nan(), (float)nan(), (float)nan()); - } - } else { - // Partly imaginary. - float imagLen = sqrtf(x * x + y * y + z * z); - float len = sqrtf(imagLen * imagLen + w * w); - float theta = atan2f(imagLen, (float)w); - float t = theta / imagLen; - return Quat(t * x, t * y, t * z, ::logf(len)); - } - } - /** log q = [Av, 0] where q = [sin(A) * v, cos(A)]. - Only for unit quaternions - debugAssertM(isUnit(), "Log only defined for unit quaternions"); - // Solve for A in q = [sin(A)*v, cos(A)] - Vector3 u(x, y, z); - double len = u.magnitude(); - - if (len == 0.0) { - return - } - double A = atan2((double)w, len); - Vector3 v = u / len; - - return Quat(v * A, 0); - } - */ - - /** exp q = [sin(A) * v, cos(A)] where q = [Av, 0]. - Only defined for pure-vector quaternions */ - inline Quat exp() const { - debugAssertM(w == 0, "exp only defined for vector quaternions"); - Vector3 u(x, y, z); - float A = u.magnitude(); - Vector3 v = u / A; - return Quat(sinf(A) * v, cosf(A)); - } - - - /** - Raise this quaternion to a power. For a rotation, this is - the effect of rotating x times as much as the original - quaterion. - - Note that q.pow(a).pow(b) == q.pow(a + b) - @cite Dam98 pg 21 - */ - inline Quat pow(float x) const { - return (log() * x).exp(); - } - - inline void unitize() { - float mag2 = dot(*this); - if (! G3D::fuzzyEq(mag2, 1.0f)) { - *this *= rsq(mag2); - } - } - - /** - Returns a unit quaterion obtained by dividing through by - the magnitude. - */ - inline Quat toUnit() const { - Quat x = *this; - x.unitize(); - return x; - } - - /** - The linear algebra 2-norm, sqrt(q dot q). This matches - the value used in Dam's 1998 tech report but differs from the - n(q) value used in Eberly's 1999 paper, which is the square of the - norm. - */ - inline float norm() const { - return magnitude(); - } - - // access quaternion as q[0] = q.x, q[1] = q.y, q[2] = q.z, q[3] = q.w - // - // WARNING. These member functions rely on - // (1) Quat not having virtual functions - // (2) the data packed in a 4*sizeof(float) memory block - const float& operator[] (int i) const; - float& operator[] (int i); - - /** Generate uniform random unit quaternion (i.e. random "direction") - @cite From "Uniform Random Rotations", Ken Shoemake, Graphics Gems III. - */ - static Quat unitRandom(); - - void deserialize(class BinaryInput& b); - void serialize(class BinaryOutput& b) const; - - // 2-char swizzles - - Vector2 xx() const; - Vector2 yx() const; - Vector2 zx() const; - Vector2 wx() const; - Vector2 xy() const; - Vector2 yy() const; - Vector2 zy() const; - Vector2 wy() const; - Vector2 xz() const; - Vector2 yz() const; - Vector2 zz() const; - Vector2 wz() const; - Vector2 xw() const; - Vector2 yw() const; - Vector2 zw() const; - Vector2 ww() const; - - // 3-char swizzles - - Vector3 xxx() const; - Vector3 yxx() const; - Vector3 zxx() const; - Vector3 wxx() const; - Vector3 xyx() const; - Vector3 yyx() const; - Vector3 zyx() const; - Vector3 wyx() const; - Vector3 xzx() const; - Vector3 yzx() const; - Vector3 zzx() const; - Vector3 wzx() const; - Vector3 xwx() const; - Vector3 ywx() const; - Vector3 zwx() const; - Vector3 wwx() const; - Vector3 xxy() const; - Vector3 yxy() const; - Vector3 zxy() const; - Vector3 wxy() const; - Vector3 xyy() const; - Vector3 yyy() const; - Vector3 zyy() const; - Vector3 wyy() const; - Vector3 xzy() const; - Vector3 yzy() const; - Vector3 zzy() const; - Vector3 wzy() const; - Vector3 xwy() const; - Vector3 ywy() const; - Vector3 zwy() const; - Vector3 wwy() const; - Vector3 xxz() const; - Vector3 yxz() const; - Vector3 zxz() const; - Vector3 wxz() const; - Vector3 xyz() const; - Vector3 yyz() const; - Vector3 zyz() const; - Vector3 wyz() const; - Vector3 xzz() const; - Vector3 yzz() const; - Vector3 zzz() const; - Vector3 wzz() const; - Vector3 xwz() const; - Vector3 ywz() const; - Vector3 zwz() const; - Vector3 wwz() const; - Vector3 xxw() const; - Vector3 yxw() const; - Vector3 zxw() const; - Vector3 wxw() const; - Vector3 xyw() const; - Vector3 yyw() const; - Vector3 zyw() const; - Vector3 wyw() const; - Vector3 xzw() const; - Vector3 yzw() const; - Vector3 zzw() const; - Vector3 wzw() const; - Vector3 xww() const; - Vector3 yww() const; - Vector3 zww() const; - Vector3 www() const; - - // 4-char swizzles - - Vector4 xxxx() const; - Vector4 yxxx() const; - Vector4 zxxx() const; - Vector4 wxxx() const; - Vector4 xyxx() const; - Vector4 yyxx() const; - Vector4 zyxx() const; - Vector4 wyxx() const; - Vector4 xzxx() const; - Vector4 yzxx() const; - Vector4 zzxx() const; - Vector4 wzxx() const; - Vector4 xwxx() const; - Vector4 ywxx() const; - Vector4 zwxx() const; - Vector4 wwxx() const; - Vector4 xxyx() const; - Vector4 yxyx() const; - Vector4 zxyx() const; - Vector4 wxyx() const; - Vector4 xyyx() const; - Vector4 yyyx() const; - Vector4 zyyx() const; - Vector4 wyyx() const; - Vector4 xzyx() const; - Vector4 yzyx() const; - Vector4 zzyx() const; - Vector4 wzyx() const; - Vector4 xwyx() const; - Vector4 ywyx() const; - Vector4 zwyx() const; - Vector4 wwyx() const; - Vector4 xxzx() const; - Vector4 yxzx() const; - Vector4 zxzx() const; - Vector4 wxzx() const; - Vector4 xyzx() const; - Vector4 yyzx() const; - Vector4 zyzx() const; - Vector4 wyzx() const; - Vector4 xzzx() const; - Vector4 yzzx() const; - Vector4 zzzx() const; - Vector4 wzzx() const; - Vector4 xwzx() const; - Vector4 ywzx() const; - Vector4 zwzx() const; - Vector4 wwzx() const; - Vector4 xxwx() const; - Vector4 yxwx() const; - Vector4 zxwx() const; - Vector4 wxwx() const; - Vector4 xywx() const; - Vector4 yywx() const; - Vector4 zywx() const; - Vector4 wywx() const; - Vector4 xzwx() const; - Vector4 yzwx() const; - Vector4 zzwx() const; - Vector4 wzwx() const; - Vector4 xwwx() const; - Vector4 ywwx() const; - Vector4 zwwx() const; - Vector4 wwwx() const; - Vector4 xxxy() const; - Vector4 yxxy() const; - Vector4 zxxy() const; - Vector4 wxxy() const; - Vector4 xyxy() const; - Vector4 yyxy() const; - Vector4 zyxy() const; - Vector4 wyxy() const; - Vector4 xzxy() const; - Vector4 yzxy() const; - Vector4 zzxy() const; - Vector4 wzxy() const; - Vector4 xwxy() const; - Vector4 ywxy() const; - Vector4 zwxy() const; - Vector4 wwxy() const; - Vector4 xxyy() const; - Vector4 yxyy() const; - Vector4 zxyy() const; - Vector4 wxyy() const; - Vector4 xyyy() const; - Vector4 yyyy() const; - Vector4 zyyy() const; - Vector4 wyyy() const; - Vector4 xzyy() const; - Vector4 yzyy() const; - Vector4 zzyy() const; - Vector4 wzyy() const; - Vector4 xwyy() const; - Vector4 ywyy() const; - Vector4 zwyy() const; - Vector4 wwyy() const; - Vector4 xxzy() const; - Vector4 yxzy() const; - Vector4 zxzy() const; - Vector4 wxzy() const; - Vector4 xyzy() const; - Vector4 yyzy() const; - Vector4 zyzy() const; - Vector4 wyzy() const; - Vector4 xzzy() const; - Vector4 yzzy() const; - Vector4 zzzy() const; - Vector4 wzzy() const; - Vector4 xwzy() const; - Vector4 ywzy() const; - Vector4 zwzy() const; - Vector4 wwzy() const; - Vector4 xxwy() const; - Vector4 yxwy() const; - Vector4 zxwy() const; - Vector4 wxwy() const; - Vector4 xywy() const; - Vector4 yywy() const; - Vector4 zywy() const; - Vector4 wywy() const; - Vector4 xzwy() const; - Vector4 yzwy() const; - Vector4 zzwy() const; - Vector4 wzwy() const; - Vector4 xwwy() const; - Vector4 ywwy() const; - Vector4 zwwy() const; - Vector4 wwwy() const; - Vector4 xxxz() const; - Vector4 yxxz() const; - Vector4 zxxz() const; - Vector4 wxxz() const; - Vector4 xyxz() const; - Vector4 yyxz() const; - Vector4 zyxz() const; - Vector4 wyxz() const; - Vector4 xzxz() const; - Vector4 yzxz() const; - Vector4 zzxz() const; - Vector4 wzxz() const; - Vector4 xwxz() const; - Vector4 ywxz() const; - Vector4 zwxz() const; - Vector4 wwxz() const; - Vector4 xxyz() const; - Vector4 yxyz() const; - Vector4 zxyz() const; - Vector4 wxyz() const; - Vector4 xyyz() const; - Vector4 yyyz() const; - Vector4 zyyz() const; - Vector4 wyyz() const; - Vector4 xzyz() const; - Vector4 yzyz() const; - Vector4 zzyz() const; - Vector4 wzyz() const; - Vector4 xwyz() const; - Vector4 ywyz() const; - Vector4 zwyz() const; - Vector4 wwyz() const; - Vector4 xxzz() const; - Vector4 yxzz() const; - Vector4 zxzz() const; - Vector4 wxzz() const; - Vector4 xyzz() const; - Vector4 yyzz() const; - Vector4 zyzz() const; - Vector4 wyzz() const; - Vector4 xzzz() const; - Vector4 yzzz() const; - Vector4 zzzz() const; - Vector4 wzzz() const; - Vector4 xwzz() const; - Vector4 ywzz() const; - Vector4 zwzz() const; - Vector4 wwzz() const; - Vector4 xxwz() const; - Vector4 yxwz() const; - Vector4 zxwz() const; - Vector4 wxwz() const; - Vector4 xywz() const; - Vector4 yywz() const; - Vector4 zywz() const; - Vector4 wywz() const; - Vector4 xzwz() const; - Vector4 yzwz() const; - Vector4 zzwz() const; - Vector4 wzwz() const; - Vector4 xwwz() const; - Vector4 ywwz() const; - Vector4 zwwz() const; - Vector4 wwwz() const; - Vector4 xxxw() const; - Vector4 yxxw() const; - Vector4 zxxw() const; - Vector4 wxxw() const; - Vector4 xyxw() const; - Vector4 yyxw() const; - Vector4 zyxw() const; - Vector4 wyxw() const; - Vector4 xzxw() const; - Vector4 yzxw() const; - Vector4 zzxw() const; - Vector4 wzxw() const; - Vector4 xwxw() const; - Vector4 ywxw() const; - Vector4 zwxw() const; - Vector4 wwxw() const; - Vector4 xxyw() const; - Vector4 yxyw() const; - Vector4 zxyw() const; - Vector4 wxyw() const; - Vector4 xyyw() const; - Vector4 yyyw() const; - Vector4 zyyw() const; - Vector4 wyyw() const; - Vector4 xzyw() const; - Vector4 yzyw() const; - Vector4 zzyw() const; - Vector4 wzyw() const; - Vector4 xwyw() const; - Vector4 ywyw() const; - Vector4 zwyw() const; - Vector4 wwyw() const; - Vector4 xxzw() const; - Vector4 yxzw() const; - Vector4 zxzw() const; - Vector4 wxzw() const; - Vector4 xyzw() const; - Vector4 yyzw() const; - Vector4 zyzw() const; - Vector4 wyzw() const; - Vector4 xzzw() const; - Vector4 yzzw() const; - Vector4 zzzw() const; - Vector4 wzzw() const; - Vector4 xwzw() const; - Vector4 ywzw() const; - Vector4 zwzw() const; - Vector4 wwzw() const; - Vector4 xxww() const; - Vector4 yxww() const; - Vector4 zxww() const; - Vector4 wxww() const; - Vector4 xyww() const; - Vector4 yyww() const; - Vector4 zyww() const; - Vector4 wyww() const; - Vector4 xzww() const; - Vector4 yzww() const; - Vector4 zzww() const; - Vector4 wzww() const; - Vector4 xwww() const; - Vector4 ywww() const; - Vector4 zwww() const; - Vector4 wwww() const; -}; - -inline Quat exp(const Quat& q) { - return q.exp(); -} - -inline Quat log(const Quat& q) { - return q.log(); -} - -inline G3D::Quat operator*(double s, const G3D::Quat& q) { - return q * (float)s; -} - -inline G3D::Quat operator*(float s, const G3D::Quat& q) { - return q * s; -} - -inline float& Quat::operator[] (int i) { - debugAssert(i >= 0); - debugAssert(i < 4); - return ((float*)this)[i]; -} - -inline const float& Quat::operator[] (int i) const { - debugAssert(i >= 0); - debugAssert(i < 4); - return ((float*)this)[i]; -} - -inline Quat Quat::operator-(const Quat& other) const { - return Quat(x - other.x, y - other.y, z - other.z, w - other.w); -} - -inline Quat Quat::operator+(const Quat& other) const { - return Quat(x + other.x, y + other.y, z + other.z, w + other.w); -} - -} // Namespace G3D - -// Outside the namespace to avoid overloading confusion for C++ -inline G3D::Quat pow(const G3D::Quat& q, double x) { - return q.pow((float)x); -} - - -#endif |