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/**
\file G3D/Quat.cpp
Quaternion implementation based on Watt & Watt page 363
\uthor Morgan McGuire, graphics3d.com
\created 2002-01-23
\edited 2010-05-31
*/
#include "G3D/Quat.h"
#include "G3D/Any.h"
#include "G3D/stringutils.h"
#include "G3D/BinaryInput.h"
#include "G3D/BinaryOutput.h"
namespace G3D {
Quat Quat::fromAxisAngleRotation(
const Vector3& axis,
float angle) {
Quat q;
q.w = cos(angle / 2.0f);
q.imag() = axis.direction() * sin(angle / 2.0f);
return q;
}
Quat::Quat(const class Any& a) {
*this = Quat();
if (beginsWith(toLower(a.name()), "matrix3")) {
*this = a;
} else {
a.verifyName("Quat");
a.verifyType(Any::ARRAY);
x = a[0];
y = a[1];
z = a[2];
w = a[3];
}
}
Any Quat::toAny() const {
Any a(Any::ARRAY, "Quat");
a.append(x, y, z, w);
return a;
}
Quat::Quat(const Matrix3& rot) {
static const int plus1mod3[] = {1, 2, 0};
// Find the index of the largest diagonal component
// These ? operations hopefully compile to conditional
// move instructions instead of branches.
int i = (rot[1][1] > rot[0][0]) ? 1 : 0;
i = (rot[2][2] > rot[i][i]) ? 2 : i;
// Find the indices of the other elements
int j = plus1mod3[i];
int k = plus1mod3[j];
// Index the elements of the vector part of the quaternion as a float*
float* v = (float*)(this);
// If we attempted to pre-normalize and trusted the matrix to be
// perfectly orthonormal, the result would be:
//
// double c = sqrt((rot[i][i] - (rot[j][j] + rot[k][k])) + 1.0)
// v[i] = -c * 0.5
// v[j] = -(rot[i][j] + rot[j][i]) * 0.5 / c
// v[k] = -(rot[i][k] + rot[k][i]) * 0.5 / c
// w = (rot[j][k] - rot[k][j]) * 0.5 / c
//
// Since we're going to pay the sqrt anyway, we perform a post normalization, which also
// fixes any poorly normalized input. Multiply all elements by 2*c in the above, giving:
// nc2 = -c^2
double nc2 = ((rot[j][j] + rot[k][k]) - rot[i][i]) - 1.0;
v[i] = (float)nc2;
w = (rot[j][k] - rot[k][j]);
v[j] = -(rot[i][j] + rot[j][i]);
v[k] = -(rot[i][k] + rot[k][i]);
// We now have the correct result with the wrong magnitude, so normalize it:
float s = sqrt(x*x + y*y + z*z + w*w);
if (s > 0.00001f) {
s = 1.0f / s;
x *= s;
y *= s;
z *= s;
w *= s;
} else {
// The quaternion is nearly zero. Make it 0 0 0 1
x = 0.0f;
y = 0.0f;
z = 0.0f;
w = 1.0f;
}
}
void Quat::toAxisAngleRotation(
Vector3& axis,
double& angle) const {
// Decompose the quaternion into an angle and an axis.
axis = Vector3(x, y, z);
angle = 2 * acos(w);
float len = sqrt(1.0f - w * w);
if (fuzzyGt(abs(len), 0.0f)) {
axis /= len;
}
// Reduce the range of the angle.
if (angle < 0) {
angle = -angle;
axis = -axis;
}
while (angle > twoPi()) {
angle -= twoPi();
}
if (abs(angle) > pi()) {
angle -= twoPi();
}
// Make the angle positive.
if (angle < 0.0f) {
angle = -angle;
axis = -axis;
}
}
Matrix3 Quat::toRotationMatrix() const {
Matrix3 out = Matrix3::zero();
toRotationMatrix(out);
return out;
}
void Quat::toRotationMatrix(
Matrix3& rot) const {
rot = Matrix3(*this);
}
Quat Quat::slerp
(const Quat& _quat1,
float alpha,
float threshold,
float maxAngle) const {
// From: Game Physics -- David Eberly pg 538-540
// Modified to include lerp for small angles, which
// is a common practice.
// See also:
// http://number-none.com/product/Understanding%20Slerp,%20Then%20Not%20Using%20It/index.html
const Quat& quat0 = *this;
Quat quat1 = _quat1;
// angle between quaternion rotations
float halfPhi;
float cosHalfPhi = quat0.dot(quat1);
if (cosHalfPhi < 0) {
// Change the sign and fix the dot product; we need to
// loop the other way to get the shortest path
quat1 = -quat1;
cosHalfPhi = -cosHalfPhi;
}
// Using G3D::aCos will clamp the angle to 0 and pi
halfPhi = static_cast<float>(G3D::aCos(cosHalfPhi));
debugAssertM(halfPhi >= 0.0f, "Assumed acos returned a value >= 0");
if (halfPhi * 2.0f * alpha > maxAngle) {
// Back off alpha
alpha = maxAngle * 0.5f / halfPhi;
}
if (halfPhi >= threshold) {
// For large angles, slerp
float scale0, scale1;
scale0 = sin((1.0f - alpha) * halfPhi);
scale1 = sin(alpha * halfPhi);
return ( (quat0 * scale0) + (quat1 * scale1) ) / sin(halfPhi);
} else {
// For small angles, linear interpolate
return quat0.nlerp(quat1, alpha);
}
}
float Quat::angleBetween(const Quat& other) const {
const float d = this->dot(other);
return 2.0f * acos(fabsf(d));
}
Quat Quat::nlerp
(const Quat& quat1,
float alpha) const {
Quat result = (*this) * (1.0f - alpha) + quat1 * alpha;
return result / result.magnitude();
}
Quat Quat::operator*(const Quat& other) const {
// Following Watt & Watt, page 360
const Vector3& v1 = imag();
const Vector3& v2 = other.imag();
float s1 = w;
float s2 = other.w;
return Quat(s1*v2 + s2*v1 + v1.cross(v2), s1*s2 - v1.dot(v2));
}
// From "Uniform Random Rotations", Ken Shoemake, Graphics Gems III.
Quat Quat::unitRandom() {
float x0 = uniformRandom();
float r1 = sqrtf(1 - x0),
r2 = sqrtf(x0);
float t1 = (float)G3D::twoPi() * uniformRandom();
float t2 = (float)G3D::twoPi() * uniformRandom();
float c1 = cosf(t1),
s1 = sinf(t1);
float c2 = cosf(t2),
s2 = sinf(t2);
return Quat(s1 * r1, c1 * r1, s2 * r2, c2 * r2);
}
void Quat::deserialize(class BinaryInput& b) {
x = b.readFloat32();
y = b.readFloat32();
z = b.readFloat32();
w = b.readFloat32();
}
void Quat::serialize(class BinaryOutput& b) const {
b.writeFloat32(x);
b.writeFloat32(y);
b.writeFloat32(z);
b.writeFloat32(w);
}
// 2-char swizzles
Vector2 Quat::xx() const { return Vector2 (x, x); }
Vector2 Quat::yx() const { return Vector2 (y, x); }
Vector2 Quat::zx() const { return Vector2 (z, x); }
Vector2 Quat::wx() const { return Vector2 (w, x); }
Vector2 Quat::xy() const { return Vector2 (x, y); }
Vector2 Quat::yy() const { return Vector2 (y, y); }
Vector2 Quat::zy() const { return Vector2 (z, y); }
Vector2 Quat::wy() const { return Vector2 (w, y); }
Vector2 Quat::xz() const { return Vector2 (x, z); }
Vector2 Quat::yz() const { return Vector2 (y, z); }
Vector2 Quat::zz() const { return Vector2 (z, z); }
Vector2 Quat::wz() const { return Vector2 (w, z); }
Vector2 Quat::xw() const { return Vector2 (x, w); }
Vector2 Quat::yw() const { return Vector2 (y, w); }
Vector2 Quat::zw() const { return Vector2 (z, w); }
Vector2 Quat::ww() const { return Vector2 (w, w); }
// 3-char swizzles
Vector3 Quat::xxx() const { return Vector3 (x, x, x); }
Vector3 Quat::yxx() const { return Vector3 (y, x, x); }
Vector3 Quat::zxx() const { return Vector3 (z, x, x); }
Vector3 Quat::wxx() const { return Vector3 (w, x, x); }
Vector3 Quat::xyx() const { return Vector3 (x, y, x); }
Vector3 Quat::yyx() const { return Vector3 (y, y, x); }
Vector3 Quat::zyx() const { return Vector3 (z, y, x); }
Vector3 Quat::wyx() const { return Vector3 (w, y, x); }
Vector3 Quat::xzx() const { return Vector3 (x, z, x); }
Vector3 Quat::yzx() const { return Vector3 (y, z, x); }
Vector3 Quat::zzx() const { return Vector3 (z, z, x); }
Vector3 Quat::wzx() const { return Vector3 (w, z, x); }
Vector3 Quat::xwx() const { return Vector3 (x, w, x); }
Vector3 Quat::ywx() const { return Vector3 (y, w, x); }
Vector3 Quat::zwx() const { return Vector3 (z, w, x); }
Vector3 Quat::wwx() const { return Vector3 (w, w, x); }
Vector3 Quat::xxy() const { return Vector3 (x, x, y); }
Vector3 Quat::yxy() const { return Vector3 (y, x, y); }
Vector3 Quat::zxy() const { return Vector3 (z, x, y); }
Vector3 Quat::wxy() const { return Vector3 (w, x, y); }
Vector3 Quat::xyy() const { return Vector3 (x, y, y); }
Vector3 Quat::yyy() const { return Vector3 (y, y, y); }
Vector3 Quat::zyy() const { return Vector3 (z, y, y); }
Vector3 Quat::wyy() const { return Vector3 (w, y, y); }
Vector3 Quat::xzy() const { return Vector3 (x, z, y); }
Vector3 Quat::yzy() const { return Vector3 (y, z, y); }
Vector3 Quat::zzy() const { return Vector3 (z, z, y); }
Vector3 Quat::wzy() const { return Vector3 (w, z, y); }
Vector3 Quat::xwy() const { return Vector3 (x, w, y); }
Vector3 Quat::ywy() const { return Vector3 (y, w, y); }
Vector3 Quat::zwy() const { return Vector3 (z, w, y); }
Vector3 Quat::wwy() const { return Vector3 (w, w, y); }
Vector3 Quat::xxz() const { return Vector3 (x, x, z); }
Vector3 Quat::yxz() const { return Vector3 (y, x, z); }
Vector3 Quat::zxz() const { return Vector3 (z, x, z); }
Vector3 Quat::wxz() const { return Vector3 (w, x, z); }
Vector3 Quat::xyz() const { return Vector3 (x, y, z); }
Vector3 Quat::yyz() const { return Vector3 (y, y, z); }
Vector3 Quat::zyz() const { return Vector3 (z, y, z); }
Vector3 Quat::wyz() const { return Vector3 (w, y, z); }
Vector3 Quat::xzz() const { return Vector3 (x, z, z); }
Vector3 Quat::yzz() const { return Vector3 (y, z, z); }
Vector3 Quat::zzz() const { return Vector3 (z, z, z); }
Vector3 Quat::wzz() const { return Vector3 (w, z, z); }
Vector3 Quat::xwz() const { return Vector3 (x, w, z); }
Vector3 Quat::ywz() const { return Vector3 (y, w, z); }
Vector3 Quat::zwz() const { return Vector3 (z, w, z); }
Vector3 Quat::wwz() const { return Vector3 (w, w, z); }
Vector3 Quat::xxw() const { return Vector3 (x, x, w); }
Vector3 Quat::yxw() const { return Vector3 (y, x, w); }
Vector3 Quat::zxw() const { return Vector3 (z, x, w); }
Vector3 Quat::wxw() const { return Vector3 (w, x, w); }
Vector3 Quat::xyw() const { return Vector3 (x, y, w); }
Vector3 Quat::yyw() const { return Vector3 (y, y, w); }
Vector3 Quat::zyw() const { return Vector3 (z, y, w); }
Vector3 Quat::wyw() const { return Vector3 (w, y, w); }
Vector3 Quat::xzw() const { return Vector3 (x, z, w); }
Vector3 Quat::yzw() const { return Vector3 (y, z, w); }
Vector3 Quat::zzw() const { return Vector3 (z, z, w); }
Vector3 Quat::wzw() const { return Vector3 (w, z, w); }
Vector3 Quat::xww() const { return Vector3 (x, w, w); }
Vector3 Quat::yww() const { return Vector3 (y, w, w); }
Vector3 Quat::zww() const { return Vector3 (z, w, w); }
Vector3 Quat::www() const { return Vector3 (w, w, w); }
// 4-char swizzles
Vector4 Quat::xxxx() const { return Vector4 (x, x, x, x); }
Vector4 Quat::yxxx() const { return Vector4 (y, x, x, x); }
Vector4 Quat::zxxx() const { return Vector4 (z, x, x, x); }
Vector4 Quat::wxxx() const { return Vector4 (w, x, x, x); }
Vector4 Quat::xyxx() const { return Vector4 (x, y, x, x); }
Vector4 Quat::yyxx() const { return Vector4 (y, y, x, x); }
Vector4 Quat::zyxx() const { return Vector4 (z, y, x, x); }
Vector4 Quat::wyxx() const { return Vector4 (w, y, x, x); }
Vector4 Quat::xzxx() const { return Vector4 (x, z, x, x); }
Vector4 Quat::yzxx() const { return Vector4 (y, z, x, x); }
Vector4 Quat::zzxx() const { return Vector4 (z, z, x, x); }
Vector4 Quat::wzxx() const { return Vector4 (w, z, x, x); }
Vector4 Quat::xwxx() const { return Vector4 (x, w, x, x); }
Vector4 Quat::ywxx() const { return Vector4 (y, w, x, x); }
Vector4 Quat::zwxx() const { return Vector4 (z, w, x, x); }
Vector4 Quat::wwxx() const { return Vector4 (w, w, x, x); }
Vector4 Quat::xxyx() const { return Vector4 (x, x, y, x); }
Vector4 Quat::yxyx() const { return Vector4 (y, x, y, x); }
Vector4 Quat::zxyx() const { return Vector4 (z, x, y, x); }
Vector4 Quat::wxyx() const { return Vector4 (w, x, y, x); }
Vector4 Quat::xyyx() const { return Vector4 (x, y, y, x); }
Vector4 Quat::yyyx() const { return Vector4 (y, y, y, x); }
Vector4 Quat::zyyx() const { return Vector4 (z, y, y, x); }
Vector4 Quat::wyyx() const { return Vector4 (w, y, y, x); }
Vector4 Quat::xzyx() const { return Vector4 (x, z, y, x); }
Vector4 Quat::yzyx() const { return Vector4 (y, z, y, x); }
Vector4 Quat::zzyx() const { return Vector4 (z, z, y, x); }
Vector4 Quat::wzyx() const { return Vector4 (w, z, y, x); }
Vector4 Quat::xwyx() const { return Vector4 (x, w, y, x); }
Vector4 Quat::ywyx() const { return Vector4 (y, w, y, x); }
Vector4 Quat::zwyx() const { return Vector4 (z, w, y, x); }
Vector4 Quat::wwyx() const { return Vector4 (w, w, y, x); }
Vector4 Quat::xxzx() const { return Vector4 (x, x, z, x); }
Vector4 Quat::yxzx() const { return Vector4 (y, x, z, x); }
Vector4 Quat::zxzx() const { return Vector4 (z, x, z, x); }
Vector4 Quat::wxzx() const { return Vector4 (w, x, z, x); }
Vector4 Quat::xyzx() const { return Vector4 (x, y, z, x); }
Vector4 Quat::yyzx() const { return Vector4 (y, y, z, x); }
Vector4 Quat::zyzx() const { return Vector4 (z, y, z, x); }
Vector4 Quat::wyzx() const { return Vector4 (w, y, z, x); }
Vector4 Quat::xzzx() const { return Vector4 (x, z, z, x); }
Vector4 Quat::yzzx() const { return Vector4 (y, z, z, x); }
Vector4 Quat::zzzx() const { return Vector4 (z, z, z, x); }
Vector4 Quat::wzzx() const { return Vector4 (w, z, z, x); }
Vector4 Quat::xwzx() const { return Vector4 (x, w, z, x); }
Vector4 Quat::ywzx() const { return Vector4 (y, w, z, x); }
Vector4 Quat::zwzx() const { return Vector4 (z, w, z, x); }
Vector4 Quat::wwzx() const { return Vector4 (w, w, z, x); }
Vector4 Quat::xxwx() const { return Vector4 (x, x, w, x); }
Vector4 Quat::yxwx() const { return Vector4 (y, x, w, x); }
Vector4 Quat::zxwx() const { return Vector4 (z, x, w, x); }
Vector4 Quat::wxwx() const { return Vector4 (w, x, w, x); }
Vector4 Quat::xywx() const { return Vector4 (x, y, w, x); }
Vector4 Quat::yywx() const { return Vector4 (y, y, w, x); }
Vector4 Quat::zywx() const { return Vector4 (z, y, w, x); }
Vector4 Quat::wywx() const { return Vector4 (w, y, w, x); }
Vector4 Quat::xzwx() const { return Vector4 (x, z, w, x); }
Vector4 Quat::yzwx() const { return Vector4 (y, z, w, x); }
Vector4 Quat::zzwx() const { return Vector4 (z, z, w, x); }
Vector4 Quat::wzwx() const { return Vector4 (w, z, w, x); }
Vector4 Quat::xwwx() const { return Vector4 (x, w, w, x); }
Vector4 Quat::ywwx() const { return Vector4 (y, w, w, x); }
Vector4 Quat::zwwx() const { return Vector4 (z, w, w, x); }
Vector4 Quat::wwwx() const { return Vector4 (w, w, w, x); }
Vector4 Quat::xxxy() const { return Vector4 (x, x, x, y); }
Vector4 Quat::yxxy() const { return Vector4 (y, x, x, y); }
Vector4 Quat::zxxy() const { return Vector4 (z, x, x, y); }
Vector4 Quat::wxxy() const { return Vector4 (w, x, x, y); }
Vector4 Quat::xyxy() const { return Vector4 (x, y, x, y); }
Vector4 Quat::yyxy() const { return Vector4 (y, y, x, y); }
Vector4 Quat::zyxy() const { return Vector4 (z, y, x, y); }
Vector4 Quat::wyxy() const { return Vector4 (w, y, x, y); }
Vector4 Quat::xzxy() const { return Vector4 (x, z, x, y); }
Vector4 Quat::yzxy() const { return Vector4 (y, z, x, y); }
Vector4 Quat::zzxy() const { return Vector4 (z, z, x, y); }
Vector4 Quat::wzxy() const { return Vector4 (w, z, x, y); }
Vector4 Quat::xwxy() const { return Vector4 (x, w, x, y); }
Vector4 Quat::ywxy() const { return Vector4 (y, w, x, y); }
Vector4 Quat::zwxy() const { return Vector4 (z, w, x, y); }
Vector4 Quat::wwxy() const { return Vector4 (w, w, x, y); }
Vector4 Quat::xxyy() const { return Vector4 (x, x, y, y); }
Vector4 Quat::yxyy() const { return Vector4 (y, x, y, y); }
Vector4 Quat::zxyy() const { return Vector4 (z, x, y, y); }
Vector4 Quat::wxyy() const { return Vector4 (w, x, y, y); }
Vector4 Quat::xyyy() const { return Vector4 (x, y, y, y); }
Vector4 Quat::yyyy() const { return Vector4 (y, y, y, y); }
Vector4 Quat::zyyy() const { return Vector4 (z, y, y, y); }
Vector4 Quat::wyyy() const { return Vector4 (w, y, y, y); }
Vector4 Quat::xzyy() const { return Vector4 (x, z, y, y); }
Vector4 Quat::yzyy() const { return Vector4 (y, z, y, y); }
Vector4 Quat::zzyy() const { return Vector4 (z, z, y, y); }
Vector4 Quat::wzyy() const { return Vector4 (w, z, y, y); }
Vector4 Quat::xwyy() const { return Vector4 (x, w, y, y); }
Vector4 Quat::ywyy() const { return Vector4 (y, w, y, y); }
Vector4 Quat::zwyy() const { return Vector4 (z, w, y, y); }
Vector4 Quat::wwyy() const { return Vector4 (w, w, y, y); }
Vector4 Quat::xxzy() const { return Vector4 (x, x, z, y); }
Vector4 Quat::yxzy() const { return Vector4 (y, x, z, y); }
Vector4 Quat::zxzy() const { return Vector4 (z, x, z, y); }
Vector4 Quat::wxzy() const { return Vector4 (w, x, z, y); }
Vector4 Quat::xyzy() const { return Vector4 (x, y, z, y); }
Vector4 Quat::yyzy() const { return Vector4 (y, y, z, y); }
Vector4 Quat::zyzy() const { return Vector4 (z, y, z, y); }
Vector4 Quat::wyzy() const { return Vector4 (w, y, z, y); }
Vector4 Quat::xzzy() const { return Vector4 (x, z, z, y); }
Vector4 Quat::yzzy() const { return Vector4 (y, z, z, y); }
Vector4 Quat::zzzy() const { return Vector4 (z, z, z, y); }
Vector4 Quat::wzzy() const { return Vector4 (w, z, z, y); }
Vector4 Quat::xwzy() const { return Vector4 (x, w, z, y); }
Vector4 Quat::ywzy() const { return Vector4 (y, w, z, y); }
Vector4 Quat::zwzy() const { return Vector4 (z, w, z, y); }
Vector4 Quat::wwzy() const { return Vector4 (w, w, z, y); }
Vector4 Quat::xxwy() const { return Vector4 (x, x, w, y); }
Vector4 Quat::yxwy() const { return Vector4 (y, x, w, y); }
Vector4 Quat::zxwy() const { return Vector4 (z, x, w, y); }
Vector4 Quat::wxwy() const { return Vector4 (w, x, w, y); }
Vector4 Quat::xywy() const { return Vector4 (x, y, w, y); }
Vector4 Quat::yywy() const { return Vector4 (y, y, w, y); }
Vector4 Quat::zywy() const { return Vector4 (z, y, w, y); }
Vector4 Quat::wywy() const { return Vector4 (w, y, w, y); }
Vector4 Quat::xzwy() const { return Vector4 (x, z, w, y); }
Vector4 Quat::yzwy() const { return Vector4 (y, z, w, y); }
Vector4 Quat::zzwy() const { return Vector4 (z, z, w, y); }
Vector4 Quat::wzwy() const { return Vector4 (w, z, w, y); }
Vector4 Quat::xwwy() const { return Vector4 (x, w, w, y); }
Vector4 Quat::ywwy() const { return Vector4 (y, w, w, y); }
Vector4 Quat::zwwy() const { return Vector4 (z, w, w, y); }
Vector4 Quat::wwwy() const { return Vector4 (w, w, w, y); }
Vector4 Quat::xxxz() const { return Vector4 (x, x, x, z); }
Vector4 Quat::yxxz() const { return Vector4 (y, x, x, z); }
Vector4 Quat::zxxz() const { return Vector4 (z, x, x, z); }
Vector4 Quat::wxxz() const { return Vector4 (w, x, x, z); }
Vector4 Quat::xyxz() const { return Vector4 (x, y, x, z); }
Vector4 Quat::yyxz() const { return Vector4 (y, y, x, z); }
Vector4 Quat::zyxz() const { return Vector4 (z, y, x, z); }
Vector4 Quat::wyxz() const { return Vector4 (w, y, x, z); }
Vector4 Quat::xzxz() const { return Vector4 (x, z, x, z); }
Vector4 Quat::yzxz() const { return Vector4 (y, z, x, z); }
Vector4 Quat::zzxz() const { return Vector4 (z, z, x, z); }
Vector4 Quat::wzxz() const { return Vector4 (w, z, x, z); }
Vector4 Quat::xwxz() const { return Vector4 (x, w, x, z); }
Vector4 Quat::ywxz() const { return Vector4 (y, w, x, z); }
Vector4 Quat::zwxz() const { return Vector4 (z, w, x, z); }
Vector4 Quat::wwxz() const { return Vector4 (w, w, x, z); }
Vector4 Quat::xxyz() const { return Vector4 (x, x, y, z); }
Vector4 Quat::yxyz() const { return Vector4 (y, x, y, z); }
Vector4 Quat::zxyz() const { return Vector4 (z, x, y, z); }
Vector4 Quat::wxyz() const { return Vector4 (w, x, y, z); }
Vector4 Quat::xyyz() const { return Vector4 (x, y, y, z); }
Vector4 Quat::yyyz() const { return Vector4 (y, y, y, z); }
Vector4 Quat::zyyz() const { return Vector4 (z, y, y, z); }
Vector4 Quat::wyyz() const { return Vector4 (w, y, y, z); }
Vector4 Quat::xzyz() const { return Vector4 (x, z, y, z); }
Vector4 Quat::yzyz() const { return Vector4 (y, z, y, z); }
Vector4 Quat::zzyz() const { return Vector4 (z, z, y, z); }
Vector4 Quat::wzyz() const { return Vector4 (w, z, y, z); }
Vector4 Quat::xwyz() const { return Vector4 (x, w, y, z); }
Vector4 Quat::ywyz() const { return Vector4 (y, w, y, z); }
Vector4 Quat::zwyz() const { return Vector4 (z, w, y, z); }
Vector4 Quat::wwyz() const { return Vector4 (w, w, y, z); }
Vector4 Quat::xxzz() const { return Vector4 (x, x, z, z); }
Vector4 Quat::yxzz() const { return Vector4 (y, x, z, z); }
Vector4 Quat::zxzz() const { return Vector4 (z, x, z, z); }
Vector4 Quat::wxzz() const { return Vector4 (w, x, z, z); }
Vector4 Quat::xyzz() const { return Vector4 (x, y, z, z); }
Vector4 Quat::yyzz() const { return Vector4 (y, y, z, z); }
Vector4 Quat::zyzz() const { return Vector4 (z, y, z, z); }
Vector4 Quat::wyzz() const { return Vector4 (w, y, z, z); }
Vector4 Quat::xzzz() const { return Vector4 (x, z, z, z); }
Vector4 Quat::yzzz() const { return Vector4 (y, z, z, z); }
Vector4 Quat::zzzz() const { return Vector4 (z, z, z, z); }
Vector4 Quat::wzzz() const { return Vector4 (w, z, z, z); }
Vector4 Quat::xwzz() const { return Vector4 (x, w, z, z); }
Vector4 Quat::ywzz() const { return Vector4 (y, w, z, z); }
Vector4 Quat::zwzz() const { return Vector4 (z, w, z, z); }
Vector4 Quat::wwzz() const { return Vector4 (w, w, z, z); }
Vector4 Quat::xxwz() const { return Vector4 (x, x, w, z); }
Vector4 Quat::yxwz() const { return Vector4 (y, x, w, z); }
Vector4 Quat::zxwz() const { return Vector4 (z, x, w, z); }
Vector4 Quat::wxwz() const { return Vector4 (w, x, w, z); }
Vector4 Quat::xywz() const { return Vector4 (x, y, w, z); }
Vector4 Quat::yywz() const { return Vector4 (y, y, w, z); }
Vector4 Quat::zywz() const { return Vector4 (z, y, w, z); }
Vector4 Quat::wywz() const { return Vector4 (w, y, w, z); }
Vector4 Quat::xzwz() const { return Vector4 (x, z, w, z); }
Vector4 Quat::yzwz() const { return Vector4 (y, z, w, z); }
Vector4 Quat::zzwz() const { return Vector4 (z, z, w, z); }
Vector4 Quat::wzwz() const { return Vector4 (w, z, w, z); }
Vector4 Quat::xwwz() const { return Vector4 (x, w, w, z); }
Vector4 Quat::ywwz() const { return Vector4 (y, w, w, z); }
Vector4 Quat::zwwz() const { return Vector4 (z, w, w, z); }
Vector4 Quat::wwwz() const { return Vector4 (w, w, w, z); }
Vector4 Quat::xxxw() const { return Vector4 (x, x, x, w); }
Vector4 Quat::yxxw() const { return Vector4 (y, x, x, w); }
Vector4 Quat::zxxw() const { return Vector4 (z, x, x, w); }
Vector4 Quat::wxxw() const { return Vector4 (w, x, x, w); }
Vector4 Quat::xyxw() const { return Vector4 (x, y, x, w); }
Vector4 Quat::yyxw() const { return Vector4 (y, y, x, w); }
Vector4 Quat::zyxw() const { return Vector4 (z, y, x, w); }
Vector4 Quat::wyxw() const { return Vector4 (w, y, x, w); }
Vector4 Quat::xzxw() const { return Vector4 (x, z, x, w); }
Vector4 Quat::yzxw() const { return Vector4 (y, z, x, w); }
Vector4 Quat::zzxw() const { return Vector4 (z, z, x, w); }
Vector4 Quat::wzxw() const { return Vector4 (w, z, x, w); }
Vector4 Quat::xwxw() const { return Vector4 (x, w, x, w); }
Vector4 Quat::ywxw() const { return Vector4 (y, w, x, w); }
Vector4 Quat::zwxw() const { return Vector4 (z, w, x, w); }
Vector4 Quat::wwxw() const { return Vector4 (w, w, x, w); }
Vector4 Quat::xxyw() const { return Vector4 (x, x, y, w); }
Vector4 Quat::yxyw() const { return Vector4 (y, x, y, w); }
Vector4 Quat::zxyw() const { return Vector4 (z, x, y, w); }
Vector4 Quat::wxyw() const { return Vector4 (w, x, y, w); }
Vector4 Quat::xyyw() const { return Vector4 (x, y, y, w); }
Vector4 Quat::yyyw() const { return Vector4 (y, y, y, w); }
Vector4 Quat::zyyw() const { return Vector4 (z, y, y, w); }
Vector4 Quat::wyyw() const { return Vector4 (w, y, y, w); }
Vector4 Quat::xzyw() const { return Vector4 (x, z, y, w); }
Vector4 Quat::yzyw() const { return Vector4 (y, z, y, w); }
Vector4 Quat::zzyw() const { return Vector4 (z, z, y, w); }
Vector4 Quat::wzyw() const { return Vector4 (w, z, y, w); }
Vector4 Quat::xwyw() const { return Vector4 (x, w, y, w); }
Vector4 Quat::ywyw() const { return Vector4 (y, w, y, w); }
Vector4 Quat::zwyw() const { return Vector4 (z, w, y, w); }
Vector4 Quat::wwyw() const { return Vector4 (w, w, y, w); }
Vector4 Quat::xxzw() const { return Vector4 (x, x, z, w); }
Vector4 Quat::yxzw() const { return Vector4 (y, x, z, w); }
Vector4 Quat::zxzw() const { return Vector4 (z, x, z, w); }
Vector4 Quat::wxzw() const { return Vector4 (w, x, z, w); }
Vector4 Quat::xyzw() const { return Vector4 (x, y, z, w); }
Vector4 Quat::yyzw() const { return Vector4 (y, y, z, w); }
Vector4 Quat::zyzw() const { return Vector4 (z, y, z, w); }
Vector4 Quat::wyzw() const { return Vector4 (w, y, z, w); }
Vector4 Quat::xzzw() const { return Vector4 (x, z, z, w); }
Vector4 Quat::yzzw() const { return Vector4 (y, z, z, w); }
Vector4 Quat::zzzw() const { return Vector4 (z, z, z, w); }
Vector4 Quat::wzzw() const { return Vector4 (w, z, z, w); }
Vector4 Quat::xwzw() const { return Vector4 (x, w, z, w); }
Vector4 Quat::ywzw() const { return Vector4 (y, w, z, w); }
Vector4 Quat::zwzw() const { return Vector4 (z, w, z, w); }
Vector4 Quat::wwzw() const { return Vector4 (w, w, z, w); }
Vector4 Quat::xxww() const { return Vector4 (x, x, w, w); }
Vector4 Quat::yxww() const { return Vector4 (y, x, w, w); }
Vector4 Quat::zxww() const { return Vector4 (z, x, w, w); }
Vector4 Quat::wxww() const { return Vector4 (w, x, w, w); }
Vector4 Quat::xyww() const { return Vector4 (x, y, w, w); }
Vector4 Quat::yyww() const { return Vector4 (y, y, w, w); }
Vector4 Quat::zyww() const { return Vector4 (z, y, w, w); }
Vector4 Quat::wyww() const { return Vector4 (w, y, w, w); }
Vector4 Quat::xzww() const { return Vector4 (x, z, w, w); }
Vector4 Quat::yzww() const { return Vector4 (y, z, w, w); }
Vector4 Quat::zzww() const { return Vector4 (z, z, w, w); }
Vector4 Quat::wzww() const { return Vector4 (w, z, w, w); }
Vector4 Quat::xwww() const { return Vector4 (x, w, w, w); }
Vector4 Quat::ywww() const { return Vector4 (y, w, w, w); }
Vector4 Quat::zwww() const { return Vector4 (z, w, w, w); }
Vector4 Quat::wwww() const { return Vector4 (w, w, w, w); }
}
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