31 #ifndef OPENVDB_MATH_QUAT_H_HAS_BEEN_INCLUDED
32 #define OPENVDB_MATH_QUAT_H_HAS_BEEN_INCLUDED
49 template<
typename T>
class Quat;
59 if (fabs(qdot) >= 1.0) {
64 sineAngle =
sin(angle);
73 if (sineAngle <= tolerance) {
76 Quat<T> qtemp(s * q1[0] + t * q2[0], s * q1[1] + t * q2[1],
77 s * q1[2] + t * q2[2], s * q1[3] + t * q2[3]);
84 double lengthSquared = qtemp.
dot(qtemp);
86 if (lengthSquared <= tolerance * tolerance) {
87 qtemp = (t < 0.5) ? q1 : q2;
89 qtemp *= 1.0 / sqrt(lengthSquared);
94 T sine = 1.0 / sineAngle;
95 T a =
sin((1.0 - t) * angle) * sine;
96 T b =
sin(t * angle) * sine;
97 return Quat<T>(a * q1[0] + b * q2[0], a * q1[1] + b * q2[1],
98 a * q1[2] + b * q2[2], a * q1[3] + b * q2[3]);
136 T s =
T(
sin(angle*
T(0.5)));
138 mm[0] = axis.
x() * s;
139 mm[1] = axis.
y() * s;
140 mm[2] = axis.
z() * s;
149 T s =
T(
sin(angle*
T(0.5)));
159 template<
typename T1>
165 "A non-rotation matrix can not be used to construct a quaternion");
169 "A reflection matrix can not be used to construct a quaternion");
175 T q_w = 0.5 * std::sqrt(trace+1);
176 T factor = 0.25 / q_w;
178 mm[0] = factor * (
rot(1,2) -
rot(2,1));
179 mm[1] = factor * (
rot(2,0) -
rot(0,2));
180 mm[2] = factor * (
rot(0,1) -
rot(1,0));
182 }
else if (
rot(0,0) >
rot(1,1) &&
rot(0,0) >
rot(2,2)) {
184 T q_x = 0.5 * sqrt(
rot(0,0)-
rot(1,1)-
rot(2,2)+1);
185 T factor = 0.25 / q_x;
188 mm[1] = factor * (
rot(0,1) +
rot(1,0));
189 mm[2] = factor * (
rot(2,0) +
rot(0,2));
190 mm[3] = factor * (
rot(1,2) -
rot(2,1));
191 }
else if (
rot(1,1) >
rot(2,2)) {
193 T q_y = 0.5 * sqrt(
rot(1,1)-
rot(0,0)-
rot(2,2)+1);
194 T factor = 0.25 / q_y;
196 mm[0] = factor * (
rot(0,1) +
rot(1,0));
198 mm[2] = factor * (
rot(1,2) +
rot(2,1));
199 mm[3] = factor * (
rot(2,0) -
rot(0,2));
202 T q_z = 0.5 * sqrt(
rot(2,2)-
rot(0,0)-
rot(1,1)+1);
203 T factor = 0.25 / q_z;
205 mm[0] = factor * (
rot(2,0) +
rot(0,2));
206 mm[1] = factor * (
rot(1,2) +
rot(2,1));
208 mm[3] = factor * (
rot(0,1) -
rot(1,0));
244 operator T*() {
return mm; }
245 operator const T*()
const {
return mm; }
258 if ( sqrLength > 1.0e-8 ) {
260 return T(
T(2.0) *
acos(mm[3]));
273 if ( sqrLength > 1.0e-8 ) {
275 T invLength =
T(
T(1)/sqrt(sqrLength));
277 return Vec3<T>( mm[0]*invLength, mm[1]*invLength, mm[2]*invLength );
300 T s =
T(
sin(angle*
T(0.5)));
302 mm[0] = axis.
x() * s;
303 mm[1] = axis.
y() * s;
304 mm[2] = axis.
z() * s;
321 mm[0] =
mm[1] =
mm[2] = 0;
351 bool eq(
const Quat &q, T eps=1.0e-7)
const
426 return Quat<T>(
mm[0]*scalar,
mm[1]*scalar,
mm[2]*scalar,
mm[3]*scalar);
432 return Quat<T>(
mm[0]/scalar,
mm[1]/scalar,
mm[2]/scalar,
mm[3]/scalar);
437 {
return Quat<T>(-
mm[0], -mm[1], -mm[2], -mm[3]); }
443 mm[0] = q1.
mm[0] + q2.
mm[0];
444 mm[1] = q1.
mm[1] + q2.
mm[1];
445 mm[2] = q1.
mm[2] + q2.
mm[2];
446 mm[3] = q1.
mm[3] + q2.
mm[3];
455 mm[0] = q1.
mm[0] - q2.
mm[0];
456 mm[1] = q1.
mm[1] - q2.
mm[1];
457 mm[2] = q1.
mm[2] - q2.
mm[2];
458 mm[3] = q1.
mm[3] - q2.
mm[3];
467 mm[0] = q1.
mm[3]*q2.
mm[0] + q1.
mm[0]*q2.
mm[3] +
468 q1.
mm[1]*q2.
mm[2] - q1.
mm[2]*q2.
mm[1];
469 mm[1] = q1.
mm[3]*q2.
mm[1] + q1.
mm[1]*q2.
mm[3] +
470 q1.
mm[2]*q2.
mm[0] - q1.
mm[0]*q2.
mm[2];
471 mm[2] = q1.
mm[3]*q2.
mm[2] + q1.
mm[2]*q2.
mm[3] +
472 q1.
mm[0]*q2.
mm[1] - q1.
mm[1]*q2.
mm[0];
473 mm[3] = q1.
mm[3]*q2.
mm[3] - q1.
mm[0]*q2.
mm[0] -
474 q1.
mm[1]*q2.
mm[1] - q1.
mm[2]*q2.
mm[2];
483 mm[0] = scale * q.
mm[0];
484 mm[1] = scale * q.
mm[1];
485 mm[2] = scale * q.
mm[2];
486 mm[3] = scale * q.
mm[3];
501 return Quat<T>( +
w()*omega.
x() -
z()*omega.
y() +
y()*omega.
z() ,
502 +
z()*omega.
x() +
w()*omega.
y() -
x()*omega.
z() ,
503 -
y()*omega.
x() +
x()*omega.
y() +
w()*omega.
z() ,
504 -
x()*omega.
x() -
y()*omega.
y() -
z()*omega.
z() );
522 "Normalizing degenerate quaternion");
532 "Cannot invert degenerate quaternion");
533 Quat result = *
this/-d;
534 result.
mm[3] = -result.
mm[3];
543 return Quat<T>(-
mm[0], -mm[1], -mm[2], mm[3]);
560 std::ostringstream
buffer;
565 for (
unsigned j(0); j < 4; j++) {
566 if (j) buffer <<
", ";
582 friend Quat slerp<>(
const Quat &q1,
const Quat &q2,
T t,
T tolerance);
584 void write(std::ostream& os)
const { os.write(static_cast<char*>(&
mm),
sizeof(
T) * 4); }
585 void read(std::istream& is) { is.read(static_cast<char*>(&
mm),
sizeof(
T) * 4); }
592 template <
typename S,
typename T>
599 template <
typename T,
typename T0>
607 if (q1.
dot(q2) < 0) q2 *= -1;
609 Quat<T> qslerp = slerp<T>(q1, q2,
static_cast<T>(t));
610 MatType m = rotation<MatType>(qslerp);
624 template <
typename T,
typename T0>
629 Mat3<T> m00, m01, m02, m10, m11;
631 m00 =
slerp(m1, m2, t);
632 m01 =
slerp(m2, m3, t);
633 m02 =
slerp(m3, m4, t);
635 m10 =
slerp(m00, m01, t);
636 m11 =
slerp(m01, m02, t);
638 return slerp(m10, m11, t);
653 #endif //OPENVDB_MATH_QUAT_H_HAS_BEEN_INCLUDED
Quat operator*(T scalar) const
Return (this*scalar), e.g. q = q1 * scalar;.
SYS_API double cos(double x)
Quat(T x, T y, T z, T w)
Constructor with four arguments, e.g. Quatf q(1,2,3,4);.
Vec3< T > axis() const
Return axis of rotation.
Quat & sub(const Quat &q1, const Quat &q2)
T operator[](int i) const
Array style constant reference to the components, e.g. float f = q[1];.
bool isExactlyEqual(const T0 &a, const T1 &b)
Return true if a is exactly equal to b.
Quat derivative(const Vec3< T > &omega) const
Quat & scale(T scale, const Quat &q)
GLsizei const GLchar *const * string
Quat operator*(const Quat &q) const
Return (this*q), e.g. q = q1 * q2;.
GA_API const UT_StringHolder rot
GLdouble GLdouble GLdouble z
Mat3< typename promote< T0, T1 >::type > operator*(const Mat3< T0 > &m0, const Mat3< T1 > &m1)
Matrix multiplication.
GLboolean GLboolean GLboolean GLboolean a
bool operator==(const Quat &q) const
Equality operator, does exact floating point comparisons.
Quat unit() const
this = normalized this
Quat & init(T x, T y, T z, T w)
"this" quaternion gets initialized to [x, y, z, w]
Quat & operator=(const Quat &q)
Assignment operator.
Vec3< typename MatType::value_type > eulerAngles(const MatType &mat, RotationOrder rotationOrder, typename MatType::value_type eps=static_cast< typename MatType::value_type >(1.0e-8))
Return the Euler angles composing the given rotation matrix.
Quat operator-(const Quat &q) const
Return (this-q), e.g. q = q1 - q2;.
Quat operator+(const Quat &q) const
Return (this+q), e.g. q = q1 + q2;.
Vec3< T0 > transform(const Vec3< T0 > &v) const
Quat operator*=(const Quat &q)
Assigns this to (this*q), e.g. q *= q1;.
Quat operator/(T scalar) const
Return (this/scalar), e.g. q = q1 / scalar;.
Quat inverse(T tolerance=T(0))
returns inverse of this
Mat3< T > bezLerp(const Mat3< T0 > &m1, const Mat3< T0 > &m2, const Mat3< T0 > &m3, const Mat3< T0 > &m4, T t)
Quat(T *a)
Constructor with array argument, e.g. float a[4]; Quatf q(a);.
Quat(const Mat3< T1 > &rot)
Constructor given a rotation matrix.
Quat & operator-=(const Quat &q)
Subtract quaternion q from "this" quaternion, e.g. q -= q1;.
bool eq(const Quat &q, T eps=1.0e-7) const
Test if "this" is equivalent to q with tolerance of eps value.
void read(std::istream &is)
Quat(math::Axis axis, T angle)
Constructor given rotation as axis and angle.
#define OPENVDB_VERSION_NAME
General-purpose arithmetic and comparison routines, most of which accept arbitrary value types (or at...
bool normalize(T eps=T(1.0e-8))
this = normalized this
Vec3< T > rotateVector(const Vec3< T > &v) const
Return rotated vector by "this" quaternion.
Quat(const Quat &q)
Copy constructor.
T angle(const Vec2< T > &v1, const Vec2< T > &v2)
bool isUnitary(const MatType &m)
Determine if a matrix is unitary (i.e., rotation or reflection).
Quat operator-() const
Negation operator, e.g. q = -q;.
Vec3< T > eulerAngles(RotationOrder rotationOrder) const
Returns vector of x,y,z rotational components.
T det() const
Determinant of matrix.
SYS_API double acos(double x)
GLboolean GLboolean GLboolean b
static unsigned numElements()
Quat & setIdentity()
Set "this" vector to identity.
Quat()
Trivial constructor, the quaternion is NOT initialized.
bool isApproxEqual(const Type &a, const Type &b)
Return true if a is equal to b to within the default floating-point comparison tolerance.
Quat & init()
"this" quaternion gets initialized to identity, same as setIdentity()
T dot(const Quat &q) const
Dot product.
T & operator()(int i)
Alternative indexed reference to the elements.
T & x()
Reference to the component, e.g. v.x() = 4.5f;.
T & operator[](int i)
Array style reference to the components, e.g. q[3] = 1.34f;.
T trace() const
Trace of matrix.
T & x()
Reference to the component, e.g. q.x() = 4.5f;.
T angle() const
Return angle of rotation.
void write(std::ostream &os) const
Quat & setAxisAngle(const Vec3< T > &axis, T angle)
T x() const
Get the component, e.g. float f = q.w();.
GLubyte GLubyte GLubyte GLubyte w
Quat & operator*=(T scalar)
Scale "this" quaternion by scalar, e.g. q *= scalar;.
Quat & add(const Quat &q1, const Quat &q2)
Quat< T > slerp(const Quat< T > &q1, const Quat< T > &q2, T t, T tolerance=0.00001)
Linear interpolation between the two quaternions.
#define OPENVDB_USE_VERSION_NAMESPACE
static Quat zero()
Predefined constants, e.g. Quat q = Quat::identity();.
Quat & mult(const Quat &q1, const Quat &q2)
Quat & setZero()
Set "this" vector to zero.
Quat(const Vec3< T > &axis, T angle)
SYS_API double sin(double x)
Quat & operator+=(const Quat &q)
Add quaternion q to "this" quaternion, e.g. q += q1;.
#define OPENVDB_THROW(exception, message)
T operator()(int i) const
Alternative indexed constant reference to the elements,.
friend std::ostream & operator<<(std::ostream &stream, const Quat &q)
Output to the stream, e.g. std::cout << q << std::endl;.