2 // Copyright (c) 2014 Samsung Electronics Co., Ltd.
4 // Licensed under the Flora License, Version 1.0 (the License);
5 // you may not use this file except in compliance with the License.
6 // You may obtain a copy of the License at
8 // http://floralicense.org/license/
10 // Unless required by applicable law or agreed to in writing, software
11 // distributed under the License is distributed on an AS IS BASIS,
12 // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
13 // See the License for the specific language governing permissions and
14 // limitations under the License.
18 #include <dali/public-api/math/quaternion.h>
21 #include <dali/public-api/common/constants.h>
22 #include <dali/public-api/math/degree.h>
23 #include <dali/public-api/math/matrix.h>
24 #include <dali/public-api/math/radian.h>
25 #include <dali/internal/render/common/performance-monitor.h>
29 using Internal::PerformanceMonitor;
31 const Quaternion Quaternion::IDENTITY;
37 Quaternion::Quaternion()
38 : mVector(0.0f, 0.0f, 0.0f, 1.0f)
42 Quaternion::Quaternion(float cosThetaBy2, float iBySineTheta, float jBySineTheta, float kBySineTheta) :
43 mVector(iBySineTheta, jBySineTheta, kBySineTheta, cosThetaBy2)
47 Quaternion::Quaternion(const Vector4& vector)
52 Quaternion::Quaternion(float angle, const Vector3 &axis)
54 MATH_INCREASE_BY(PerformanceMonitor::FLOAT_POINT_MULTIPLY,4);
56 Vector3 tmpAxis = axis;
58 const float halfAngle = angle * 0.5f;
59 const float sinThetaByTwo = sinf(halfAngle);
60 const float cosThetaByTwo = cosf(halfAngle);
61 mVector.x = tmpAxis.x * sinThetaByTwo;
62 mVector.y = tmpAxis.y * sinThetaByTwo;
63 mVector.z = tmpAxis.z * sinThetaByTwo;
64 mVector.w = cosThetaByTwo;
67 Quaternion::Quaternion(float theta, const Vector4 &axis)
69 MATH_INCREASE_BY(PerformanceMonitor::FLOAT_POINT_MULTIPLY,4);
71 Vector4 tmpAxis = axis;
73 const float halfTheta = theta * 0.5f;
74 const float sinThetaByTwo = sinf(halfTheta);
75 const float cosThetaByTwo = cosf(halfTheta);
76 mVector.x = tmpAxis.x * sinThetaByTwo;
77 mVector.y = tmpAxis.y * sinThetaByTwo;
78 mVector.z = tmpAxis.z * sinThetaByTwo;
79 mVector.w = cosThetaByTwo;
82 Quaternion::Quaternion(float x, float y, float z)
87 Quaternion::Quaternion(const Matrix& matrix)
89 Vector3 xAxis( matrix.GetXAxis() );
90 Vector3 yAxis( matrix.GetYAxis() );
91 Vector3 zAxis( matrix.GetZAxis() );
93 SetFromAxes( xAxis, yAxis, zAxis );
96 Quaternion::Quaternion( const Vector3& xAxis, const Vector3& yAxis, const Vector3& zAxis )
98 SetFromAxes( xAxis, yAxis, zAxis );
102 Quaternion Quaternion::FromAxisAngle(const Vector4 &axis, float angle)
104 return Quaternion(angle, axis);
107 Quaternion::~Quaternion()
111 bool Quaternion::ToAxisAngle(Vector3 &axis, float &angle) const
113 angle = acosf(mVector.w);
114 bool converted = false;
115 // pre-compute to save time
116 const float sine = sinf( angle );
118 // If sine(angle) is zero, conversion is not possible
120 if ( ! EqualsZero( sine ) )
122 MATH_INCREASE_BY(PerformanceMonitor::FLOAT_POINT_MULTIPLY,3);
124 float sinf_theta_inv = 1.0f / sine;
126 axis.x = mVector.x*sinf_theta_inv;
127 axis.y = mVector.y*sinf_theta_inv;
128 axis.z = mVector.z*sinf_theta_inv;
135 bool Quaternion::ToAxisAngle(Vector4 &axis, float &angle) const
138 bool converted = ToAxisAngle(axis3, angle);
149 const Vector4& Quaternion::AsVector() const
154 void Quaternion::SetEuler(float x, float y, float z)
156 MATH_INCREASE_BY(PerformanceMonitor::FLOAT_POINT_MULTIPLY,19);
158 const float halfX = 0.5f * x;
159 const float halfY = 0.5f * y;
160 const float halfZ = 0.5f * z;
162 float cosX2 = cosf(halfX);
163 float cosY2 = cosf(halfY);
164 float cosZ2 = cosf(halfZ);
166 float sinX2 = sinf(halfX);
167 float sinY2 = sinf(halfY);
168 float sinZ2 = sinf(halfZ);
170 mVector.w = cosZ2 * cosY2 * cosX2 + sinZ2 * sinY2 * sinX2;
171 mVector.x = cosZ2 * cosY2 * sinX2 - sinZ2 * sinY2 * cosX2;
172 mVector.y = cosZ2 * sinY2 * cosX2 + sinZ2 * cosY2 * sinX2;
173 mVector.z = sinZ2 * cosY2 * cosX2 - cosZ2 * sinY2 * sinX2;
176 Vector4 Quaternion::EulerAngles() const
178 MATH_INCREASE_BY(PerformanceMonitor::FLOAT_POINT_MULTIPLY,13);
180 float sqw = mVector.w*mVector.w;
181 float sqx = mVector.x*mVector.x;
182 float sqy = mVector.y*mVector.y;
183 float sqz = mVector.z*mVector.z;
186 euler.x = atan2f(2.0f * (mVector.y*mVector.z + mVector.x*mVector.w), -sqx - sqy + sqz + sqw);
187 euler.y = asinf(-2.0f * (mVector.x*mVector.z - mVector.y*mVector.w));
188 euler.z = atan2f(2.0f * (mVector.x*mVector.y + mVector.z*mVector.w), sqx - sqy - sqz + sqw);
192 const Quaternion Quaternion::operator +(const Quaternion &other) const
194 return Quaternion(mVector + other.mVector);
197 const Quaternion Quaternion::operator -(const Quaternion &other) const
199 return Quaternion(mVector - other.mVector);
202 const Quaternion Quaternion::operator *(const Quaternion &other) const
204 MATH_INCREASE_BY(PerformanceMonitor::FLOAT_POINT_MULTIPLY,12);
206 return Quaternion(mVector.w * other.mVector.w - mVector.Dot(other.mVector),
207 mVector.y * other.mVector.z - mVector.z * other.mVector.y + mVector.w * other.mVector.x + mVector.x * other.mVector.w,
208 mVector.z * other.mVector.x - mVector.x * other.mVector.z + mVector.w * other.mVector.y + mVector.y * other.mVector.w,
209 mVector.x * other.mVector.y - mVector.y * other.mVector.x + mVector.w * other.mVector.z + mVector.z * other.mVector.w);
212 Vector3 Quaternion::operator *(const Vector3& v) const
214 // nVidia SDK implementation
216 Vector3 qvec(mVector.x, mVector.y, mVector.z);
218 uuv = qvec.Cross(uv);
219 uv *= (2.0f * mVector.w);
225 const Quaternion Quaternion::operator /(const Quaternion &q) const
232 const Quaternion Quaternion::operator *(float scale) const
234 return Quaternion(mVector*scale);
237 const Quaternion Quaternion::operator /(float scale) const
239 return Quaternion(mVector/scale);
242 Quaternion Quaternion::operator -() const
244 return Quaternion(-mVector.w, -mVector.x, -mVector.y, -mVector.z);
247 const Quaternion& Quaternion::operator +=(const Quaternion &q)
249 mVector += q.mVector; return *this;
252 const Quaternion& Quaternion::operator -=(const Quaternion &q)
254 mVector -= q.mVector; return *this;
257 const Quaternion& Quaternion::operator *=(const Quaternion &q)
259 MATH_INCREASE_BY(PerformanceMonitor::FLOAT_POINT_MULTIPLY,12);
261 float x = mVector.x, y = mVector.y, z = mVector.z, w = mVector.w;
263 mVector.w = mVector.w * q.mVector.w - mVector.Dot(q.mVector);
264 mVector.x = y*q.mVector.z - z*q.mVector.y + w*q.mVector.x + x*q.mVector.w;
265 mVector.y = z*q.mVector.x - x*q.mVector.z + w*q.mVector.y + y*q.mVector.w;
266 mVector.z = x*q.mVector.y - y*q.mVector.x + w*q.mVector.z + z*q.mVector.w;
270 const Quaternion& Quaternion::operator *= (float scale)
272 mVector*=scale; return *this;
275 const Quaternion& Quaternion::operator /= (float scale)
277 mVector/=scale; return *this;
280 bool Quaternion::operator== (const Quaternion& rhs) const
282 return ( ( fabsf(mVector.x - rhs.mVector.x) < Math::MACHINE_EPSILON_1 &&
283 fabsf(mVector.y - rhs.mVector.y) < Math::MACHINE_EPSILON_1 &&
284 fabsf(mVector.z - rhs.mVector.z) < Math::MACHINE_EPSILON_1 &&
285 fabsf(mVector.w - rhs.mVector.w) < Math::MACHINE_EPSILON_1 ) ||
286 // Or equal to negation of rhs
287 ( fabsf(mVector.x + rhs.mVector.x) < Math::MACHINE_EPSILON_1 &&
288 fabsf(mVector.y + rhs.mVector.y) < Math::MACHINE_EPSILON_1 &&
289 fabsf(mVector.z + rhs.mVector.z) < Math::MACHINE_EPSILON_1 &&
290 fabsf(mVector.w + rhs.mVector.w) < Math::MACHINE_EPSILON_1 )
294 bool Quaternion::operator!= (const Quaternion& rhs) const
296 return !operator==(rhs);
299 float Quaternion::Length() const
301 return (float)sqrt(mVector.w * mVector.w + mVector.Dot(mVector));
304 float Quaternion::LengthSquared() const
306 return (float)(mVector.w * mVector.w + mVector.Dot(mVector));
309 void Quaternion::Normalize()
314 Quaternion Quaternion::Normalized() const
316 return *this/Length();
319 void Quaternion::Conjugate()
321 mVector.x = -mVector.x;
322 mVector.y = -mVector.y;
323 mVector.z = -mVector.z;
326 void Quaternion::Invert()
329 *this/=LengthSquared();
332 Quaternion Quaternion::Log() const
334 float a = acosf(mVector.w);
335 float sina = sinf(a);
339 if (fabsf(sina) >= Math::MACHINE_EPSILON_1)
341 MATH_INCREASE_BY(PerformanceMonitor::FLOAT_POINT_MULTIPLY,4);
343 float angleBySinAngle = a * (1.0f / sina);
344 ret.mVector.x = mVector.x * angleBySinAngle;
345 ret.mVector.y = mVector.y * angleBySinAngle;
346 ret.mVector.z = mVector.z * angleBySinAngle;
350 ret.mVector.x= ret.mVector.y= ret.mVector.z= 0;
355 Quaternion Quaternion::Exp() const
357 DALI_ASSERT_ALWAYS( EqualsZero( mVector.w ) && "Cannot perform Exponent" );
359 float a = mVector.Length();
360 float sina = sinf(a);
363 ret.mVector.w = cosf(a);
365 if (a >= Math::MACHINE_EPSILON_1)
367 MATH_INCREASE_BY(PerformanceMonitor::FLOAT_POINT_MULTIPLY,4);
369 float sinAOverA = sina * (1.0f / a);
370 ret.mVector.x = mVector.x * sinAOverA;
371 ret.mVector.y = mVector.y * sinAOverA;
372 ret.mVector.z = mVector.z * sinAOverA;
376 ret.mVector.x = ret.mVector.y = ret.mVector.z = 0.0f;
381 float Quaternion::Dot(const Quaternion &q1, const Quaternion &q2)
383 return q1.mVector.Dot4(q2.mVector);
386 Quaternion Quaternion::Lerp(const Quaternion &q1, const Quaternion &q2, float t)
388 return (q1*(1.0f-t) + q2*t).Normalized();
391 Quaternion Quaternion::Slerp(const Quaternion &q1, const Quaternion &q2, float progress)
394 float cosTheta = Quaternion::Dot(q1, q2);
397 * If cos(theta) < 0, q1 and q2 are more than 90 degrees apart,
398 * so invert one to reduce spinning.
402 cosTheta = -cosTheta;
410 if (fabsf(cosTheta) < 0.95f)
412 MATH_INCREASE_BY(PerformanceMonitor::FLOAT_POINT_MULTIPLY,5);
415 float sine = sqrtf(1.0f - cosTheta*cosTheta);
416 float angle = atan2f(sine, cosTheta);
417 float invSine = 1.0f / sine;
418 float coeff0 = sinf((1.0f - progress) * angle) * invSine;
419 float coeff1 = sinf(progress * angle) * invSine;
421 return q1*coeff0 + q3*coeff1;
425 // If the angle is small, use linear interpolation
426 Quaternion result = q1*(1.0f - progress) + q3*progress;
428 return result.Normalized();
432 Quaternion Quaternion::SlerpNoInvert(const Quaternion &q1, const Quaternion &q2, float t)
434 float cosTheta = Quaternion::Dot(q1, q2);
436 if (cosTheta > -0.95f && cosTheta < 0.95f)
438 MATH_INCREASE_BY(PerformanceMonitor::FLOAT_POINT_MULTIPLY,2);
440 float theta = acosf(cosTheta);
441 return (q1*sinf(theta*(1.0f-t)) + q2*sinf(theta*t))/sinf(theta);
445 return Lerp(q1, q2, t);
449 Quaternion Quaternion::Squad(
450 const Quaternion &q1, // start
451 const Quaternion &q2, // end
452 const Quaternion &a, // ctrl pt for q1
453 const Quaternion &b, // ctrl pt for q2
456 MATH_INCREASE_BY(PerformanceMonitor::FLOAT_POINT_MULTIPLY,2);
458 Quaternion c = SlerpNoInvert(q1, q2, t);
459 Quaternion d = SlerpNoInvert(a, b, t);
460 return SlerpNoInvert(c, d, 2*t*(1-t));
463 float Quaternion::AngleBetween(const Quaternion &q1, const Quaternion &q2)
471 //Formula for angle θ between two quaternion is:
472 //θ = cos^−1 (2⟨q1,q2⟩^2 − 1), Where (q1,q2) is inner product of the quaternions.
473 float X = from.mVector.Dot4(to.mVector);
474 float theta = acos( (2 * X * X) - 1);
479 Vector4 Quaternion::Rotate(const Vector4 &v) const
481 Quaternion V(0.0f, v.x, v.y, v.z);
482 Quaternion conjugate(*this);
483 conjugate.Conjugate();
484 return (*this * V * conjugate).mVector;
487 Vector3 Quaternion::Rotate(const Vector3 &v) const
489 Quaternion V(0.0f, v.x, v.y, v.z);
490 Quaternion conjugate(*this);
491 conjugate.Conjugate();
492 return Vector3((*this * V * conjugate).mVector);
495 void Quaternion::SetFromAxes( const Vector3& xAxis, const Vector3& yAxis, const Vector3& zAxis )
497 MATH_INCREASE_BY(PerformanceMonitor::FLOAT_POINT_MULTIPLY,4);
499 float t = xAxis.x + yAxis.y + zAxis.z;
500 if ( t > 0.0f ) // w is largest
502 float root = sqrtf( t + 1.0f );
503 float one_over_4w = 0.5f / root;
504 mVector.x = ( yAxis.z - zAxis.y ) * one_over_4w;
505 mVector.y = ( zAxis.x - xAxis.z ) * one_over_4w;
506 mVector.z = ( xAxis.y - yAxis.x ) * one_over_4w;
507 mVector.w = root * 0.5f;
509 else if( zAxis.z > xAxis.x && zAxis.z > yAxis.y ) // z is largest
511 float root = sqrtf( zAxis.z - xAxis.x - yAxis.y + 1.0f );
512 float one_over_4w = 0.5f / root;
513 mVector.x = ( xAxis.z + zAxis.x ) * one_over_4w;
514 mVector.y = ( yAxis.z + zAxis.y ) * one_over_4w;
515 mVector.z = root * 0.5f;
516 mVector.w = ( xAxis.y - yAxis.x ) * one_over_4w;
518 else if( yAxis.y > xAxis.x ) // y is largest
520 float root = sqrtf(yAxis.y - zAxis.z - xAxis.x + 1.0f );
521 float one_over_4w = 0.5f / root;
523 mVector.x = ( xAxis.y + yAxis.x ) * one_over_4w;
524 mVector.y = root * 0.5f;
525 mVector.z = ( zAxis.y + yAxis.z ) * one_over_4w;
526 mVector.w = ( zAxis.x - xAxis.z ) * one_over_4w;
530 float root = sqrtf( xAxis.x - yAxis.y - zAxis.z + 1.0f );
531 float one_over_4w = 0.5f / root;
532 mVector.x = root * 0.5f;
533 mVector.y = ( yAxis.x + xAxis.y ) * one_over_4w;
534 mVector.z = ( zAxis.x + xAxis.z ) * one_over_4w;
535 mVector.w = ( yAxis.z - zAxis.y ) * one_over_4w;
541 std::ostream& operator<< (std::ostream& o, const Quaternion& quaternion)
546 quaternion.ToAxisAngle( axis, angleRadians );
547 Degree degrees = Radian(angleRadians);
549 return o << "[ Axis: [" << axis.x << ", " << axis.y << ", " << axis.z << "], Angle: " << degrees << " degrees ]";