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annotate libs/vmath/quat.cc @ 0:b2f14e535253

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initial commit
author John Tsiombikas <nuclear@member.fsf.org>
date Sat, 01 Feb 2014 19:58:19 +0200
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nuclear@0 1 #include "quat.h"
nuclear@0 2 #include "vmath.h"
nuclear@0 3
nuclear@0 4 Quaternion::Quaternion()
nuclear@0 5 {
nuclear@0 6 s = 1.0;
nuclear@0 7 v.x = v.y = v.z = 0.0;
nuclear@0 8 }
nuclear@0 9
nuclear@0 10 Quaternion::Quaternion(scalar_t s, const Vector3 &v)
nuclear@0 11 {
nuclear@0 12 this->s = s;
nuclear@0 13 this->v = v;
nuclear@0 14 }
nuclear@0 15
nuclear@0 16 Quaternion::Quaternion(scalar_t s, scalar_t x, scalar_t y, scalar_t z)
nuclear@0 17 {
nuclear@0 18 v.x = x;
nuclear@0 19 v.y = y;
nuclear@0 20 v.z = z;
nuclear@0 21 this->s = s;
nuclear@0 22 }
nuclear@0 23
nuclear@0 24 Quaternion::Quaternion(const Vector3 &axis, scalar_t angle)
nuclear@0 25 {
nuclear@0 26 set_rotation(axis, angle);
nuclear@0 27 }
nuclear@0 28
nuclear@0 29 Quaternion::Quaternion(const quat_t &quat)
nuclear@0 30 {
nuclear@0 31 v.x = quat.x;
nuclear@0 32 v.y = quat.y;
nuclear@0 33 v.z = quat.z;
nuclear@0 34 s = quat.w;
nuclear@0 35 }
nuclear@0 36
nuclear@0 37 Quaternion Quaternion::operator +(const Quaternion &quat) const
nuclear@0 38 {
nuclear@0 39 return Quaternion(s + quat.s, v + quat.v);
nuclear@0 40 }
nuclear@0 41
nuclear@0 42 Quaternion Quaternion::operator -(const Quaternion &quat) const
nuclear@0 43 {
nuclear@0 44 return Quaternion(s - quat.s, v - quat.v);
nuclear@0 45 }
nuclear@0 46
nuclear@0 47 Quaternion Quaternion::operator -() const
nuclear@0 48 {
nuclear@0 49 return Quaternion(-s, -v);
nuclear@0 50 }
nuclear@0 51
nuclear@0 52 /** Quaternion Multiplication:
nuclear@0 53 * Q1*Q2 = [s1*s2 - v1.v2, s1*v2 + s2*v1 + v1(x)v2]
nuclear@0 54 */
nuclear@0 55 Quaternion Quaternion::operator *(const Quaternion &quat) const
nuclear@0 56 {
nuclear@0 57 Quaternion newq;
nuclear@0 58 newq.s = s * quat.s - dot_product(v, quat.v);
nuclear@0 59 newq.v = quat.v * s + v * quat.s + cross_product(v, quat.v);
nuclear@0 60 return newq;
nuclear@0 61 }
nuclear@0 62
nuclear@0 63 void Quaternion::operator +=(const Quaternion &quat)
nuclear@0 64 {
nuclear@0 65 *this = Quaternion(s + quat.s, v + quat.v);
nuclear@0 66 }
nuclear@0 67
nuclear@0 68 void Quaternion::operator -=(const Quaternion &quat)
nuclear@0 69 {
nuclear@0 70 *this = Quaternion(s - quat.s, v - quat.v);
nuclear@0 71 }
nuclear@0 72
nuclear@0 73 void Quaternion::operator *=(const Quaternion &quat)
nuclear@0 74 {
nuclear@0 75 *this = *this * quat;
nuclear@0 76 }
nuclear@0 77
nuclear@0 78 void Quaternion::reset_identity()
nuclear@0 79 {
nuclear@0 80 s = 1.0;
nuclear@0 81 v.x = v.y = v.z = 0.0;
nuclear@0 82 }
nuclear@0 83
nuclear@0 84 Quaternion Quaternion::conjugate() const
nuclear@0 85 {
nuclear@0 86 return Quaternion(s, -v);
nuclear@0 87 }
nuclear@0 88
nuclear@0 89 scalar_t Quaternion::length() const
nuclear@0 90 {
nuclear@0 91 return (scalar_t)sqrt(v.x*v.x + v.y*v.y + v.z*v.z + s*s);
nuclear@0 92 }
nuclear@0 93
nuclear@0 94 /** Q * ~Q = ||Q||^2 */
nuclear@0 95 scalar_t Quaternion::length_sq() const
nuclear@0 96 {
nuclear@0 97 return v.x*v.x + v.y*v.y + v.z*v.z + s*s;
nuclear@0 98 }
nuclear@0 99
nuclear@0 100 void Quaternion::normalize()
nuclear@0 101 {
nuclear@0 102 scalar_t len = (scalar_t)sqrt(v.x*v.x + v.y*v.y + v.z*v.z + s*s);
nuclear@0 103 v.x /= len;
nuclear@0 104 v.y /= len;
nuclear@0 105 v.z /= len;
nuclear@0 106 s /= len;
nuclear@0 107 }
nuclear@0 108
nuclear@0 109 Quaternion Quaternion::normalized() const
nuclear@0 110 {
nuclear@0 111 Quaternion nq = *this;
nuclear@0 112 scalar_t len = (scalar_t)sqrt(v.x*v.x + v.y*v.y + v.z*v.z + s*s);
nuclear@0 113 nq.v.x /= len;
nuclear@0 114 nq.v.y /= len;
nuclear@0 115 nq.v.z /= len;
nuclear@0 116 nq.s /= len;
nuclear@0 117 return nq;
nuclear@0 118 }
nuclear@0 119
nuclear@0 120 /** Quaternion Inversion: Q^-1 = ~Q / ||Q||^2 */
nuclear@0 121 Quaternion Quaternion::inverse() const
nuclear@0 122 {
nuclear@0 123 Quaternion inv = conjugate();
nuclear@0 124 scalar_t lensq = length_sq();
nuclear@0 125 inv.v /= lensq;
nuclear@0 126 inv.s /= lensq;
nuclear@0 127
nuclear@0 128 return inv;
nuclear@0 129 }
nuclear@0 130
nuclear@0 131
nuclear@0 132 void Quaternion::set_rotation(const Vector3 &axis, scalar_t angle)
nuclear@0 133 {
nuclear@0 134 scalar_t half_angle = angle / 2.0;
nuclear@0 135 s = cos(half_angle);
nuclear@0 136 v = axis * sin(half_angle);
nuclear@0 137 }
nuclear@0 138
nuclear@0 139 void Quaternion::rotate(const Vector3 &axis, scalar_t angle)
nuclear@0 140 {
nuclear@0 141 Quaternion q;
nuclear@0 142 scalar_t half_angle = angle / 2.0;
nuclear@0 143 q.s = cos(half_angle);
nuclear@0 144 q.v = axis * sin(half_angle);
nuclear@0 145
nuclear@0 146 *this *= q;
nuclear@0 147 }
nuclear@0 148
nuclear@0 149 void Quaternion::rotate(const Quaternion &q)
nuclear@0 150 {
nuclear@0 151 *this = q * *this * q.conjugate();
nuclear@0 152 }
nuclear@0 153
nuclear@0 154 Matrix3x3 Quaternion::get_rotation_matrix() const
nuclear@0 155 {
nuclear@0 156 return Matrix3x3(
nuclear@0 157 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,
nuclear@0 158 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,
nuclear@0 159 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);
nuclear@0 160 }
nuclear@0 161
nuclear@0 162
nuclear@0 163 /** Spherical linear interpolation (slerp) */
nuclear@0 164 Quaternion slerp(const Quaternion &quat1, const Quaternion &q2, scalar_t t)
nuclear@0 165 {
nuclear@0 166 Quaternion q1;
nuclear@0 167 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;
nuclear@0 168
nuclear@0 169 if(dot < 0.0) {
nuclear@0 170 /* make sure we interpolate across the shortest arc */
nuclear@0 171 q1 = -quat1;
nuclear@0 172 dot = -dot;
nuclear@0 173 } else {
nuclear@0 174 q1 = quat1;
nuclear@0 175 }
nuclear@0 176
nuclear@0 177 /* clamp dot to [-1, 1] in order to avoid domain errors in acos due to
nuclear@0 178 * floating point imprecisions
nuclear@0 179 */
nuclear@0 180 if(dot < -1.0) dot = -1.0;
nuclear@0 181 if(dot > 1.0) dot = 1.0;
nuclear@0 182
nuclear@0 183 scalar_t angle = acos(dot);
nuclear@0 184 scalar_t a, b;
nuclear@0 185
nuclear@0 186 scalar_t sin_angle = sin(angle);
nuclear@0 187 if(fabs(sin_angle) < SMALL_NUMBER) {
nuclear@0 188 /* for very small angles or completely opposite orientations
nuclear@0 189 * use linear interpolation to avoid div/zero (in the first case it makes sense,
nuclear@0 190 * the second case is pretty much undefined anyway I guess ...
nuclear@0 191 */
nuclear@0 192 a = 1.0f - t;
nuclear@0 193 b = t;
nuclear@0 194 } else {
nuclear@0 195 a = sin((1.0f - t) * angle) / sin_angle;
nuclear@0 196 b = sin(t * angle) / sin_angle;
nuclear@0 197 }
nuclear@0 198
nuclear@0 199 scalar_t x = q1.v.x * a + q2.v.x * b;
nuclear@0 200 scalar_t y = q1.v.y * a + q2.v.y * b;
nuclear@0 201 scalar_t z = q1.v.z * a + q2.v.z * b;
nuclear@0 202 scalar_t s = q1.s * a + q2.s * b;
nuclear@0 203
nuclear@0 204 return Quaternion(s, Vector3(x, y, z));
nuclear@0 205 }
nuclear@0 206
nuclear@0 207
nuclear@0 208 std::ostream &operator <<(std::ostream &out, const Quaternion &q)
nuclear@0 209 {
nuclear@0 210 out << "(" << q.s << ", " << q.v << ")";
nuclear@0 211 return out;
nuclear@0 212 }