-// Copyright (C) 2006 Mathias Froehlich - Mathias.Froehlich@web.de
+// Copyright (C) 2006-2009 Mathias Froehlich - Mathias.Froehlich@web.de
//
// This library is free software; you can redistribute it and/or
// modify it under the terms of the GNU Library General Public
#ifndef SGQuat_H
#define SGQuat_H
-/// 3D Vector Class
+#ifdef min
+#undef min
+#endif
+
+#ifdef max
+#undef max
+#endif
+
+#ifndef NO_OPENSCENEGRAPH_INTERFACE
+#include <osg/Quat>
+#endif
+
+/// Quaternion Class
template<typename T>
class SGQuat {
public:
/// uninitialized values in the debug build very fast ...
#ifndef NDEBUG
for (unsigned i = 0; i < 4; ++i)
- _data[i] = SGLimits<T>::quiet_NaN();
+ data()[i] = SGLimits<T>::quiet_NaN();
#endif
}
/// Constructor. Initialize by the given values
/// Constructor. Initialize by the content of a plain array,
/// make sure it has at least 4 elements
explicit SGQuat(const T* d)
- { _data[0] = d[0]; _data[1] = d[1]; _data[2] = d[2]; _data[3] = d[3]; }
+ { data()[0] = d[0]; data()[1] = d[1]; data()[2] = d[2]; data()[3] = d[3]; }
/// Return a unit quaternion
static SGQuat unit(void)
- { return fromRealImag(1, SGVec3<T>(0)); }
+ { return fromRealImag(1, SGVec3<T>(0, 0, 0)); }
/// Return a quaternion from euler angles
static SGQuat fromEulerRad(T z, T y, T x)
static SGQuat fromHeadAttBankDeg(T h, T a, T b)
{ return fromEulerDeg(h, a, b); }
- /// Return a quaternion rotation the the horizontal local frame from given
- /// longitude and latitude
+ /// Return a quaternion rotation from the earth centered to the
+ /// simulation usual horizontal local frame from given
+ /// longitude and latitude.
+ /// The horizontal local frame used in simulations is the frame with x-axis
+ /// pointing north, the y-axis pointing eastwards and the z axis
+ /// pointing downwards.
static SGQuat fromLonLatRad(T lon, T lat)
{
SGQuat q;
T zd2 = T(0.5)*lon;
- T yd2 = T(-0.25)*SGMisc<value_type>::pi() - T(0.5)*lat;
+ T yd2 = T(-0.25)*SGMisc<T>::pi() - T(0.5)*lat;
T Szd2 = sin(zd2);
T Syd2 = sin(yd2);
T Czd2 = cos(zd2);
q.z() = Szd2*Cyd2;
return q;
}
-
- /// Return a quaternion rotation the the horizontal local frame from given
- /// longitude and latitude
+ /// Like the above provided for convenience
static SGQuat fromLonLatDeg(T lon, T lat)
{ return fromLonLatRad(SGMisc<T>::deg2rad(lon), SGMisc<T>::deg2rad(lat)); }
-
- /// Return a quaternion rotation the the horizontal local frame from given
- /// longitude and latitude
+ /// Like the above provided for convenience
static SGQuat fromLonLat(const SGGeod& geod)
{ return fromLonLatRad(geod.getLongitudeRad(), geod.getLatitudeRad()); }
+
/// Create a quaternion from the angle axis representation
static SGQuat fromAngleAxis(T angle, const SGVec3<T>& axis)
{
- T angle2 = 0.5*angle;
+ T angle2 = T(0.5)*angle;
return fromRealImag(cos(angle2), T(sin(angle2))*axis);
}
{
T nAxis = norm(axis);
if (nAxis <= SGLimits<T>::min())
- return SGQuat(1, 0, 0, 0);
- T angle2 = 0.5*nAxis;
+ return SGQuat::unit();
+ T angle2 = T(0.5)*nAxis;
return fromRealImag(cos(angle2), T(sin(angle2)/nAxis)*axis);
}
+ /// Return a quaternion that rotates the from vector onto the to vector.
+ static SGQuat fromRotateTo(const SGVec3<T>& from, const SGVec3<T>& to)
+ {
+ T nfrom = norm(from);
+ T nto = norm(to);
+ if (nfrom <= SGLimits<T>::min() || nto <= SGLimits<T>::min())
+ return SGQuat::unit();
+
+ return SGQuat::fromRotateToNorm((1/nfrom)*from, (1/nto)*to);
+ }
+
+ /// Return a quaternion that rotates v1 onto the i1-th unit vector
+ /// and v2 into a plane that is spanned by the i2-th and i1-th unit vector.
+ static SGQuat fromRotateTo(const SGVec3<T>& v1, unsigned i1,
+ const SGVec3<T>& v2, unsigned i2)
+ {
+ T nrmv1 = norm(v1);
+ T nrmv2 = norm(v2);
+ if (nrmv1 <= SGLimits<T>::min() || nrmv2 <= SGLimits<T>::min())
+ return SGQuat::unit();
+
+ SGVec3<T> nv1 = (1/nrmv1)*v1;
+ SGVec3<T> nv2 = (1/nrmv2)*v2;
+ T dv1v2 = dot(nv1, nv2);
+ if (fabs(fabs(dv1v2)-1) <= SGLimits<T>::epsilon())
+ return SGQuat::unit();
+
+ // The target vector for the first rotation
+ SGVec3<T> nto1 = SGVec3<T>::zeros();
+ SGVec3<T> nto2 = SGVec3<T>::zeros();
+ nto1[i1] = 1;
+ nto2[i2] = 1;
+
+ // The first rotation can be done with the usual routine.
+ SGQuat q = SGQuat::fromRotateToNorm(nv1, nto1);
+
+ // The rotation axis for the second rotation is the
+ // target for the first one, so the rotation axis is nto1
+ // We need to get the angle.
+
+ // Make nv2 exactly orthogonal to nv1.
+ nv2 = normalize(nv2 - dv1v2*nv1);
+
+ SGVec3<T> tnv2 = q.transform(nv2);
+ T cosang = dot(nto2, tnv2);
+ T cos05ang = T(0.5)+T(0.5)*cosang;
+ if (cos05ang <= 0)
+ cosang = 0;
+ cos05ang = sqrt(cos05ang);
+ T sig = dot(nto1, cross(nto2, tnv2));
+ T sin05ang = T(0.5)-T(0.5)*cosang;
+ if (sin05ang <= 0)
+ sin05ang = 0;
+ sin05ang = copysign(sqrt(sin05ang), sig);
+ q *= SGQuat::fromRealImag(cos05ang, sin05ang*nto1);
+
+ return q;
+ }
+
+
+ // Return a quaternion which rotates the vector given by v
+ // to the vector -v. Other directions are *not* preserved.
+ static SGQuat fromChangeSign(const SGVec3<T>& v)
+ {
+ // The vector from points to the oposite direction than to.
+ // Find a vector perpendicular to the vector to.
+ T absv1 = fabs(v(0));
+ T absv2 = fabs(v(1));
+ T absv3 = fabs(v(2));
+
+ SGVec3<T> axis;
+ if (absv2 < absv1 && absv3 < absv1) {
+ T quot = v(1)/v(0);
+ axis = (1/sqrt(1+quot*quot))*SGVec3<T>(quot, -1, 0);
+ } else if (absv1 < absv2 && absv3 < absv2) {
+ T quot = v(2)/v(1);
+ axis = (1/sqrt(1+quot*quot))*SGVec3<T>(0, quot, -1);
+ } else if (absv1 < absv3 && absv2 < absv3) {
+ T quot = v(0)/v(2);
+ axis = (1/sqrt(1+quot*quot))*SGVec3<T>(-1, 0, quot);
+ } else {
+ // The all zero case.
+ return SGQuat::unit();
+ }
+
+ return SGQuat::fromRealImag(0, axis);
+ }
+
/// Return a quaternion from real and imaginary part
static SGQuat fromRealImag(T r, const SGVec3<T>& i)
{
SGQuat q;
q.w() = r;
- q.x() = i(0);
- q.y() = i(1);
- q.z() = i(2);
+ q.x() = i.x();
+ q.y() = i.y();
+ q.z() = i.z();
return q;
}
/// write the euler angles into the references
void getEulerRad(T& zRad, T& yRad, T& xRad) const
{
- value_type sqrQW = w()*w();
- value_type sqrQX = x()*x();
- value_type sqrQY = y()*y();
- value_type sqrQZ = z()*z();
-
- value_type num = 2*(y()*z() + w()*x());
- value_type den = sqrQW - sqrQX - sqrQY + sqrQZ;
- if (fabs(den) < SGLimits<value_type>::min() &&
- fabs(num) < SGLimits<value_type>::min())
+ T sqrQW = w()*w();
+ T sqrQX = x()*x();
+ T sqrQY = y()*y();
+ T sqrQZ = z()*z();
+
+ T num = 2*(y()*z() + w()*x());
+ T den = sqrQW - sqrQX - sqrQY + sqrQZ;
+ if (fabs(den) <= SGLimits<T>::min() &&
+ fabs(num) <= SGLimits<T>::min())
xRad = 0;
else
xRad = atan2(num, den);
- value_type tmp = 2*(x()*z() - w()*y());
- if (tmp < -1)
- yRad = 0.5*SGMisc<value_type>::pi();
- else if (1 < tmp)
- yRad = -0.5*SGMisc<value_type>::pi();
+ T tmp = 2*(x()*z() - w()*y());
+ if (tmp <= -1)
+ yRad = T(0.5)*SGMisc<T>::pi();
+ else if (1 <= tmp)
+ yRad = -T(0.5)*SGMisc<T>::pi();
else
yRad = -asin(tmp);
num = 2*(x()*y() + w()*z());
den = sqrQW + sqrQX - sqrQY - sqrQZ;
- if (fabs(den) < SGLimits<value_type>::min() &&
- fabs(num) < SGLimits<value_type>::min())
+ if (fabs(den) <= SGLimits<T>::min() &&
+ fabs(num) <= SGLimits<T>::min())
zRad = 0;
else {
- value_type psi = atan2(num, den);
+ T psi = atan2(num, den);
if (psi < 0)
- psi += 2*SGMisc<value_type>::pi();
+ psi += 2*SGMisc<T>::pi();
zRad = psi;
}
}
void getAngleAxis(T& angle, SGVec3<T>& axis) const
{
T nrm = norm(*this);
- if (nrm < SGLimits<T>::min()) {
+ if (nrm <= SGLimits<T>::min()) {
angle = 0;
axis = SGVec3<T>(0, 0, 0);
} else {
T rNrm = 1/nrm;
angle = acos(SGMisc<T>::max(-1, SGMisc<T>::min(1, rNrm*w())));
T sAng = sin(angle);
- if (fabs(sAng) < SGLimits<T>::min())
+ if (fabs(sAng) <= SGLimits<T>::min())
axis = SGVec3<T>(1, 0, 0);
else
axis = (rNrm/sAng)*imag(*this);
/// Access by index, the index is unchecked
const T& operator()(unsigned i) const
- { return _data[i]; }
+ { return data()[i]; }
/// Access by index, the index is unchecked
T& operator()(unsigned i)
- { return _data[i]; }
+ { return data()[i]; }
/// Access raw data by index, the index is unchecked
const T& operator[](unsigned i) const
- { return _data[i]; }
+ { return data()[i]; }
/// Access raw data by index, the index is unchecked
T& operator[](unsigned i)
- { return _data[i]; }
+ { return data()[i]; }
/// Access the x component
const T& x(void) const
- { return _data[0]; }
+ { return data()[0]; }
/// Access the x component
T& x(void)
- { return _data[0]; }
+ { return data()[0]; }
/// Access the y component
const T& y(void) const
- { return _data[1]; }
+ { return data()[1]; }
/// Access the y component
T& y(void)
- { return _data[1]; }
+ { return data()[1]; }
/// Access the z component
const T& z(void) const
- { return _data[2]; }
+ { return data()[2]; }
/// Access the z component
T& z(void)
- { return _data[2]; }
+ { return data()[2]; }
/// Access the w component
const T& w(void) const
- { return _data[3]; }
+ { return data()[3]; }
/// Access the w component
T& w(void)
- { return _data[3]; }
+ { return data()[3]; }
- /// Get the data pointer, usefull for interfacing with plib's sg*Vec
- const T* data(void) const
+ /// Get the data pointer
+ const T (&data(void) const)[4]
{ return _data; }
- /// Get the data pointer, usefull for interfacing with plib's sg*Vec
- T* data(void)
- { return _data; }
-
- /// Readonly interface function to ssg's sgQuat/sgdQuat
- const T (&sg(void) const)[4]
- { return _data; }
- /// Interface function to ssg's sgQuat/sgdQuat
- T (&sg(void))[4]
+ /// Get the data pointer
+ T (&data(void))[4]
{ return _data; }
/// Inplace addition
SGQuat& operator+=(const SGQuat& v)
- { _data[0]+=v(0);_data[1]+=v(1);_data[2]+=v(2);_data[3]+=v(3);return *this; }
+ { data()[0]+=v(0);data()[1]+=v(1);data()[2]+=v(2);data()[3]+=v(3);return *this; }
/// Inplace subtraction
SGQuat& operator-=(const SGQuat& v)
- { _data[0]-=v(0);_data[1]-=v(1);_data[2]-=v(2);_data[3]-=v(3);return *this; }
+ { data()[0]-=v(0);data()[1]-=v(1);data()[2]-=v(2);data()[3]-=v(3);return *this; }
/// Inplace scalar multiplication
template<typename S>
SGQuat& operator*=(S s)
- { _data[0] *= s; _data[1] *= s; _data[2] *= s; _data[3] *= s; return *this; }
+ { data()[0] *= s; data()[1] *= s; data()[2] *= s; data()[3] *= s; return *this; }
/// Inplace scalar multiplication by 1/s
template<typename S>
SGQuat& operator/=(S s)
/// frame rotated with the quaternion
SGVec3<T> transform(const SGVec3<T>& v) const
{
- value_type r = 2/dot(*this, *this);
+ T r = 2/dot(*this, *this);
SGVec3<T> qimag = imag(*this);
- value_type qr = real(*this);
+ T qr = real(*this);
return (r*qr*qr - 1)*v + (r*dot(qimag, v))*qimag - (r*qr)*cross(qimag, v);
}
/// Transform a vector from the coordinate frame rotated with the quaternion
/// to the current coordinate frame
SGVec3<T> backTransform(const SGVec3<T>& v) const
{
- value_type r = 2/dot(*this, *this);
+ T r = 2/dot(*this, *this);
SGVec3<T> qimag = imag(*this);
- value_type qr = real(*this);
+ T qr = real(*this);
return (r*qr*qr - 1)*v + (r*dot(qimag, v))*qimag + (r*qr)*cross(qimag, v);
}
/// Return the time derivative of the quaternion given the angular velocity
SGQuat
- derivative(const SGVec3<T>& angVel)
+ derivative(const SGVec3<T>& angVel) const
{
SGQuat deriv;
- deriv.w() = 0.5*(-x()*angVel(0) - y()*angVel(1) - z()*angVel(2));
- deriv.x() = 0.5*( w()*angVel(0) - z()*angVel(1) + y()*angVel(2));
- deriv.y() = 0.5*( z()*angVel(0) + w()*angVel(1) - x()*angVel(2));
- deriv.z() = 0.5*(-y()*angVel(0) + x()*angVel(1) + w()*angVel(2));
+ deriv.w() = T(0.5)*(-x()*angVel(0) - y()*angVel(1) - z()*angVel(2));
+ deriv.x() = T(0.5)*( w()*angVel(0) - z()*angVel(1) + y()*angVel(2));
+ deriv.y() = T(0.5)*( z()*angVel(0) + w()*angVel(1) - x()*angVel(2));
+ deriv.z() = T(0.5)*(-y()*angVel(0) + x()*angVel(1) + w()*angVel(2));
return deriv;
}
private:
- /// The actual data
+
+ // Private because it assumes normalized inputs.
+ static SGQuat
+ fromRotateToSmaller90Deg(T cosang,
+ const SGVec3<T>& from, const SGVec3<T>& to)
+ {
+ // In this function we assume that the angle required to rotate from
+ // the vector from to the vector to is <= 90 deg.
+ // That is done so because of possible instabilities when we rotate more
+ // then 90deg.
+
+ // Note that the next comment does actually cover a *more* *general* case
+ // than we need in this function. That shows that this formula is even
+ // valid for rotations up to 180deg.
+
+ // Because of the signs in the axis, it is sufficient to care for angles
+ // in the interval [-pi,pi]. That means that 0.5*angle is in the interval
+ // [-pi/2,pi/2]. But in that range the cosine is allways >= 0.
+ // So we do not need to care for egative roots in the following equation:
+ T cos05ang = sqrt(T(0.5)+T(0.5)*cosang);
+
+
+ // Now our assumption of angles <= 90 deg comes in play.
+ // For that reason, we know that cos05ang is not zero.
+ // It is even more, we can see from the above formula that
+ // sqrt(0.5) < cos05ang.
+
+
+ // Compute the rotation axis, that is
+ // sin(angle)*normalized rotation axis
+ SGVec3<T> axis = cross(to, from);
+
+ // We need sin(0.5*angle)*normalized rotation axis.
+ // So rescale with sin(0.5*x)/sin(x).
+ // To do that we use the equation:
+ // sin(x) = 2*sin(0.5*x)*cos(0.5*x)
+ return SGQuat::fromRealImag( cos05ang, (1/(2*cos05ang))*axis);
+ }
+
+ // Private because it assumes normalized inputs.
+ static SGQuat
+ fromRotateToNorm(const SGVec3<T>& from, const SGVec3<T>& to)
+ {
+ // To avoid instabilities with roundoff, we distinguish between rotations
+ // with more then 90deg and rotations with less than 90deg.
+
+ // Compute the cosine of the angle.
+ T cosang = dot(from, to);
+
+ // For the small ones do direct computation
+ if (T(-0.5) < cosang)
+ return SGQuat::fromRotateToSmaller90Deg(cosang, from, to);
+
+ // For larger rotations. first rotate from to -from.
+ // Past that we will have a smaller angle again.
+ SGQuat q1 = SGQuat::fromChangeSign(from);
+ SGQuat q2 = SGQuat::fromRotateToSmaller90Deg(-cosang, -from, to);
+ return q1*q2;
+ }
+
T _data[4];
};
// need the scales now, if the angle is very small, do linear interpolation
// to avoid instabilities
T scale0, scale1;
- if (fabs(o) < SGLimits<T>::epsilon()) {
+ if (fabs(o) <= SGLimits<T>::epsilon()) {
scale0 = 1 - t;
scale1 = t;
} else {
toQuatd(const SGQuatf& v)
{ return SGQuatd(v(0), v(1), v(2), v(3)); }
+#ifndef NO_OPENSCENEGRAPH_INTERFACE
+inline
+SGQuatd
+toSG(const osg::Quat& q)
+{ return SGQuatd(q[0], q[1], q[2], q[3]); }
+
+inline
+osg::Quat
+toOsg(const SGQuatd& q)
+{ return osg::Quat(q[0], q[1], q[2], q[3]); }
+#endif
+
#endif
projects / simgear.git / blobdiff