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+/**
+ @file Quat.cpp
+
+ Quaternion implementation based on Watt & Watt page 363
+
+ @author Morgan McGuire, graphics3d.com
+
+ @created 2002-01-23
+ @edited 2006-01-31
+ */
+
+#include "G3D/Quat.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 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] = 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) 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 phi;
+ float cosphi = quat0.dot(quat1);
+
+
+ if (cosphi < 0) {
+ // Change the sign and fix the dot product; we need to
+ // loop the other way to get the shortest path
+ quat1 = -quat1;
+ cosphi = -cosphi;
+ }
+
+ // Using G3D::aCos will clamp the angle to 0 and pi
+ phi = static_cast<float>(G3D::aCos(cosphi));
+
+ if (phi >= threshold) {
+ // For large angles, slerp
+ float scale0, scale1;
+
+ scale0 = sin((1.0f - alpha) * phi);
+ scale1 = sin(alpha * phi);
+
+ return ( (quat0 * scale0) + (quat1 * scale1) ) / sin(phi);
+ } else {
+ // For small angles, linear interpolate
+ return quat0.nlerp(quat1, alpha);
+ }
+}
+
+
+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); }
+}
+