1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     1.2 +++ b/vmath/quat.cc	Sun Nov 09 13:03:36 2014 +0200
     1.3 @@ -0,0 +1,191 @@
     1.4 +#include "quat.h"
     1.5 +#include "vmath.h"
     1.6 +
     1.7 +Quaternion::Quaternion() {
     1.8 +	s = 1.0;
     1.9 +	v.x = v.y = v.z = 0.0;
    1.10 +}
    1.11 +
    1.12 +Quaternion::Quaternion(scalar_t s, const Vector3 &v) {
    1.13 +	this->s = s;
    1.14 +	this->v = v;
    1.15 +}
    1.16 +
    1.17 +Quaternion::Quaternion(scalar_t s, scalar_t x, scalar_t y, scalar_t z) {
    1.18 +	v.x = x;
    1.19 +	v.y = y;
    1.20 +	v.z = z;
    1.21 +	this->s = s;
    1.22 +}
    1.23 +
    1.24 +Quaternion::Quaternion(const Vector3 &axis, scalar_t angle) {
    1.25 +	set_rotation(axis, angle);
    1.26 +}
    1.27 +
    1.28 +Quaternion::Quaternion(const quat_t &quat)
    1.29 +{
    1.30 +	v.x = quat.x;
    1.31 +	v.y = quat.y;
    1.32 +	v.z = quat.z;
    1.33 +	s = quat.w;
    1.34 +}
    1.35 +
    1.36 +Quaternion Quaternion::operator +(const Quaternion &quat) const
    1.37 +{
    1.38 +	return Quaternion(s + quat.s, v + quat.v);
    1.39 +}
    1.40 +
    1.41 +Quaternion Quaternion::operator -(const Quaternion &quat) const
    1.42 +{
    1.43 +	return Quaternion(s - quat.s, v - quat.v);
    1.44 +}
    1.45 +
    1.46 +Quaternion Quaternion::operator -() const
    1.47 +{
    1.48 +	return Quaternion(-s, -v);
    1.49 +}
    1.50 +
    1.51 +/** Quaternion Multiplication:
    1.52 + * Q1*Q2 = [s1*s2 - v1.v2,  s1*v2 + s2*v1 + v1(x)v2]
    1.53 + */
    1.54 +Quaternion Quaternion::operator *(const Quaternion &quat) const {
    1.55 +	Quaternion newq;
    1.56 +	newq.s = s * quat.s - dot_product(v, quat.v);
    1.57 +	newq.v = quat.v * s + v * quat.s + cross_product(v, quat.v);
    1.58 +	return newq;
    1.59 +}
    1.60 +
    1.61 +void Quaternion::operator +=(const Quaternion &quat) {
    1.62 +	*this = Quaternion(s + quat.s, v + quat.v);
    1.63 +}
    1.64 +
    1.65 +void Quaternion::operator -=(const Quaternion &quat) {
    1.66 +	*this = Quaternion(s - quat.s, v - quat.v);
    1.67 +}
    1.68 +
    1.69 +void Quaternion::operator *=(const Quaternion &quat) {
    1.70 +	*this = *this * quat;
    1.71 +}
    1.72 +
    1.73 +void Quaternion::reset_identity() {
    1.74 +	s = 1.0;
    1.75 +	v.x = v.y = v.z = 0.0;
    1.76 +}
    1.77 +
    1.78 +Quaternion Quaternion::conjugate() const {
    1.79 +	return Quaternion(s, -v);
    1.80 +}
    1.81 +
    1.82 +scalar_t Quaternion::length() const {
    1.83 +	return (scalar_t)sqrt(v.x*v.x + v.y*v.y + v.z*v.z + s*s);
    1.84 +}
    1.85 +
    1.86 +/** Q * ~Q = ||Q||^2 */
    1.87 +scalar_t Quaternion::length_sq() const {
    1.88 +	return v.x*v.x + v.y*v.y + v.z*v.z + s*s;
    1.89 +}
    1.90 +
    1.91 +void Quaternion::normalize() {
    1.92 +	scalar_t len = (scalar_t)sqrt(v.x*v.x + v.y*v.y + v.z*v.z + s*s);
    1.93 +	v.x /= len;
    1.94 +	v.y /= len;
    1.95 +	v.z /= len;
    1.96 +	s /= len;
    1.97 +}
    1.98 +
    1.99 +Quaternion Quaternion::normalized() const {
   1.100 +	Quaternion nq = *this;
   1.101 +	scalar_t len = (scalar_t)sqrt(v.x*v.x + v.y*v.y + v.z*v.z + s*s);
   1.102 +	nq.v.x /= len;
   1.103 +	nq.v.y /= len;
   1.104 +	nq.v.z /= len;
   1.105 +	nq.s /= len;
   1.106 +	return nq;
   1.107 +}
   1.108 +
   1.109 +/** Quaternion Inversion: Q^-1 = ~Q / ||Q||^2 */
   1.110 +Quaternion Quaternion::inverse() const {
   1.111 +	Quaternion inv = conjugate();
   1.112 +	scalar_t lensq = length_sq();
   1.113 +	inv.v /= lensq;
   1.114 +	inv.s /= lensq;
   1.115 +
   1.116 +	return inv;
   1.117 +}
   1.118 +
   1.119 +
   1.120 +void Quaternion::set_rotation(const Vector3 &axis, scalar_t angle) {
   1.121 +	scalar_t half_angle = angle / 2.0;
   1.122 +	s = cos(half_angle);
   1.123 +	v = axis * sin(half_angle);
   1.124 +}
   1.125 +
   1.126 +void Quaternion::rotate(const Vector3 &axis, scalar_t angle) {
   1.127 +	Quaternion q;
   1.128 +	scalar_t half_angle = angle / 2.0;
   1.129 +	q.s = cos(half_angle);
   1.130 +	q.v = axis * sin(half_angle);
   1.131 +
   1.132 +	*this *= q;
   1.133 +}
   1.134 +
   1.135 +void Quaternion::rotate(const Quaternion &q) {
   1.136 +	*this = q * *this * q.conjugate();
   1.137 +}
   1.138 +
   1.139 +Matrix3x3 Quaternion::get_rotation_matrix() const {
   1.140 +	return Matrix3x3(
   1.141 +			1.0 - 2.0 * v.y*v.y - 2.0 * v.z*v.z,	2.0 * v.x * v.y - 2.0 * s * v.z,		2.0 * v.z * v.x + 2.0 * s * v.y,
   1.142 +			2.0 * v.x * v.y + 2.0 * s * v.z,		1.0 - 2.0 * v.x*v.x - 2.0 * v.z*v.z,	2.0 * v.y * v.z - 2.0 * s * v.x,
   1.143 +			2.0 * v.z * v.x - 2.0 * s * v.y,		2.0 * v.y * v.z + 2.0 * s * v.x,		1.0 - 2.0 * v.x*v.x - 2.0 * v.y*v.y);
   1.144 +}
   1.145 +
   1.146 +
   1.147 +/** Spherical linear interpolation (slerp) */
   1.148 +Quaternion slerp(const Quaternion &quat1, const Quaternion &q2, scalar_t t) {
   1.149 +	Quaternion q1;
   1.150 +	scalar_t dot = q1.s * q2.s + q1.v.x * q2.v.x + q1.v.y * q2.v.y + q1.v.z * q2.v.z;
   1.151 +
   1.152 +	if(dot < 0.0) {
   1.153 +		/* make sure we interpolate across the shortest arc */
   1.154 +		q1 = -quat1;
   1.155 +		dot = -dot;
   1.156 +	} else {
   1.157 +		q1 = quat1;
   1.158 +	}
   1.159 +
   1.160 +	/* clamp dot to [-1, 1] in order to avoid domain errors in acos due to
   1.161 +	 * floating point imprecisions
   1.162 +	 */
   1.163 +	if(dot < -1.0) dot = -1.0;
   1.164 +	if(dot > 1.0) dot = 1.0;
   1.165 +
   1.166 +	scalar_t angle = acos(dot);
   1.167 +	scalar_t a, b;
   1.168 +
   1.169 +	scalar_t sin_angle = sin(angle);
   1.170 +	if(fabs(sin_angle) < SMALL_NUMBER) {
   1.171 +		/* for very small angles or completely opposite orientations
   1.172 +		 * use linear interpolation to avoid div/zero (in the first case it makes sense,
   1.173 +		 * the second case is pretty much undefined anyway I guess ...
   1.174 +		 */
   1.175 +		a = 1.0f - t;
   1.176 +		b = t;
   1.177 +	} else {
   1.178 +		a = sin((1.0f - t) * angle) / sin_angle;
   1.179 +		b = sin(t * angle) / sin_angle;
   1.180 +	}
   1.181 +
   1.182 +	scalar_t x = q1.v.x * a + q2.v.x * b;
   1.183 +	scalar_t y = q1.v.y * a + q2.v.y * b;
   1.184 +	scalar_t z = q1.v.z * a + q2.v.z * b;
   1.185 +	scalar_t s = q1.s * a + q2.s * b;
   1.186 +
   1.187 +	return Quaternion(s, Vector3(x, y, z));
   1.188 +}
   1.189 +
   1.190 +
   1.191 +std::ostream &operator <<(std::ostream &out, const Quaternion &q) {
   1.192 +	out << "(" << q.s << ", " << q.v << ")";
   1.193 +	return out;
   1.194 +}