1// Copyright 2009-2021 Intel Corporation
2// SPDX-License-Identifier: Apache-2.0
3
4#pragma once
5
6#include "vec3.h"
7#include "vec4.h"
8
9#include "transcendental.h"
10
11namespace embree
12{
13 ////////////////////////////////////////////////////////////////
14 // Quaternion Struct
15 ////////////////////////////////////////////////////////////////
16
17 template<typename T>
18 struct QuaternionT
19 {
20 typedef Vec3<T> Vector;
21
22 ////////////////////////////////////////////////////////////////////////////////
23 /// Construction
24 ////////////////////////////////////////////////////////////////////////////////
25
26 __forceinline QuaternionT () { }
27 __forceinline QuaternionT ( const QuaternionT& other ) { r = other.r; i = other.i; j = other.j; k = other.k; }
28 __forceinline QuaternionT& operator=( const QuaternionT& other ) { r = other.r; i = other.i; j = other.j; k = other.k; return *this; }
29
30 __forceinline QuaternionT( const T& r ) : r(r), i(zero), j(zero), k(zero) {}
31 __forceinline explicit QuaternionT( const Vec3<T>& v ) : r(zero), i(v.x), j(v.y), k(v.z) {}
32 __forceinline explicit QuaternionT( const Vec4<T>& v ) : r(v.x), i(v.y), j(v.z), k(v.w) {}
33 __forceinline QuaternionT( const T& r, const T& i, const T& j, const T& k ) : r(r), i(i), j(j), k(k) {}
34 __forceinline QuaternionT( const T& r, const Vec3<T>& v ) : r(r), i(v.x), j(v.y), k(v.z) {}
35
36 __inline QuaternionT( const Vec3<T>& vx, const Vec3<T>& vy, const Vec3<T>& vz );
37 __inline QuaternionT( const T& yaw, const T& pitch, const T& roll );
38
39 ////////////////////////////////////////////////////////////////////////////////
40 /// Constants
41 ////////////////////////////////////////////////////////////////////////////////
42
43 __forceinline QuaternionT( ZeroTy ) : r(zero), i(zero), j(zero), k(zero) {}
44 __forceinline QuaternionT( OneTy ) : r( one), i(zero), j(zero), k(zero) {}
45
46 /*! return quaternion for rotation around arbitrary axis */
47 static __forceinline QuaternionT rotate(const Vec3<T>& u, const T& r) {
48 return QuaternionT<T>(cos(T(0.5)*r),sin(T(0.5)*r)*normalize(u));
49 }
50
51 /*! returns the rotation axis of the quaternion as a vector */
52 __forceinline Vec3<T> v( ) const { return Vec3<T>(i, j, k); }
53
54 public:
55 T r, i, j, k;
56 };
57
58 template<typename T> __forceinline QuaternionT<T> operator *( const T & a, const QuaternionT<T>& b ) { return QuaternionT<T>(a * b.r, a * b.i, a * b.j, a * b.k); }
59 template<typename T> __forceinline QuaternionT<T> operator *( const QuaternionT<T>& a, const T & b ) { return QuaternionT<T>(a.r * b, a.i * b, a.j * b, a.k * b); }
60
61 ////////////////////////////////////////////////////////////////
62 // Unary Operators
63 ////////////////////////////////////////////////////////////////
64
65 template<typename T> __forceinline QuaternionT<T> operator +( const QuaternionT<T>& a ) { return QuaternionT<T>(+a.r, +a.i, +a.j, +a.k); }
66 template<typename T> __forceinline QuaternionT<T> operator -( const QuaternionT<T>& a ) { return QuaternionT<T>(-a.r, -a.i, -a.j, -a.k); }
67 template<typename T> __forceinline QuaternionT<T> conj ( const QuaternionT<T>& a ) { return QuaternionT<T>(a.r, -a.i, -a.j, -a.k); }
68 template<typename T> __forceinline T abs ( const QuaternionT<T>& a ) { return sqrt(a.r*a.r + a.i*a.i + a.j*a.j + a.k*a.k); }
69 template<typename T> __forceinline QuaternionT<T> rcp ( const QuaternionT<T>& a ) { return conj(a)*rcp(a.r*a.r + a.i*a.i + a.j*a.j + a.k*a.k); }
70 template<typename T> __forceinline QuaternionT<T> normalize ( const QuaternionT<T>& a ) { return a*rsqrt(a.r*a.r + a.i*a.i + a.j*a.j + a.k*a.k); }
71
72 // evaluates a*q-r
73 template<typename T> __forceinline QuaternionT<T>
74 msub(const T& a, const QuaternionT<T>& q, const QuaternionT<T>& p)
75 {
76 return QuaternionT<T>(msub(a, q.r, p.r),
77 msub(a, q.i, p.i),
78 msub(a, q.j, p.j),
79 msub(a, q.k, p.k));
80 }
81 // evaluates a*q-r
82 template<typename T> __forceinline QuaternionT<T>
83 madd (const T& a, const QuaternionT<T>& q, const QuaternionT<T>& p)
84 {
85 return QuaternionT<T>(madd(a, q.r, p.r),
86 madd(a, q.i, p.i),
87 madd(a, q.j, p.j),
88 madd(a, q.k, p.k));
89 }
90
91 ////////////////////////////////////////////////////////////////
92 // Binary Operators
93 ////////////////////////////////////////////////////////////////
94
95 template<typename T> __forceinline QuaternionT<T> operator +( const T & a, const QuaternionT<T>& b ) { return QuaternionT<T>(a + b.r, b.i, b.j, b.k); }
96 template<typename T> __forceinline QuaternionT<T> operator +( const QuaternionT<T>& a, const T & b ) { return QuaternionT<T>(a.r + b, a.i, a.j, a.k); }
97 template<typename T> __forceinline QuaternionT<T> operator +( const QuaternionT<T>& a, const QuaternionT<T>& b ) { return QuaternionT<T>(a.r + b.r, a.i + b.i, a.j + b.j, a.k + b.k); }
98 template<typename T> __forceinline QuaternionT<T> operator -( const T & a, const QuaternionT<T>& b ) { return QuaternionT<T>(a - b.r, -b.i, -b.j, -b.k); }
99 template<typename T> __forceinline QuaternionT<T> operator -( const QuaternionT<T>& a, const T & b ) { return QuaternionT<T>(a.r - b, a.i, a.j, a.k); }
100 template<typename T> __forceinline QuaternionT<T> operator -( const QuaternionT<T>& a, const QuaternionT<T>& b ) { return QuaternionT<T>(a.r - b.r, a.i - b.i, a.j - b.j, a.k - b.k); }
101
102 template<typename T> __forceinline Vec3<T> operator *( const QuaternionT<T>& a, const Vec3<T> & b ) { return (a*QuaternionT<T>(b)*conj(a)).v(); }
103 template<typename T> __forceinline QuaternionT<T> operator *( const QuaternionT<T>& a, const QuaternionT<T>& b ) {
104 return QuaternionT<T>(a.r*b.r - a.i*b.i - a.j*b.j - a.k*b.k,
105 a.r*b.i + a.i*b.r + a.j*b.k - a.k*b.j,
106 a.r*b.j - a.i*b.k + a.j*b.r + a.k*b.i,
107 a.r*b.k + a.i*b.j - a.j*b.i + a.k*b.r);
108 }
109 template<typename T> __forceinline QuaternionT<T> operator /( const T & a, const QuaternionT<T>& b ) { return a*rcp(b); }
110 template<typename T> __forceinline QuaternionT<T> operator /( const QuaternionT<T>& a, const T & b ) { return a*rcp(b); }
111 template<typename T> __forceinline QuaternionT<T> operator /( const QuaternionT<T>& a, const QuaternionT<T>& b ) { return a*rcp(b); }
112
113 template<typename T> __forceinline QuaternionT<T>& operator +=( QuaternionT<T>& a, const T & b ) { return a = a+b; }
114 template<typename T> __forceinline QuaternionT<T>& operator +=( QuaternionT<T>& a, const QuaternionT<T>& b ) { return a = a+b; }
115 template<typename T> __forceinline QuaternionT<T>& operator -=( QuaternionT<T>& a, const T & b ) { return a = a-b; }
116 template<typename T> __forceinline QuaternionT<T>& operator -=( QuaternionT<T>& a, const QuaternionT<T>& b ) { return a = a-b; }
117 template<typename T> __forceinline QuaternionT<T>& operator *=( QuaternionT<T>& a, const T & b ) { return a = a*b; }
118 template<typename T> __forceinline QuaternionT<T>& operator *=( QuaternionT<T>& a, const QuaternionT<T>& b ) { return a = a*b; }
119 template<typename T> __forceinline QuaternionT<T>& operator /=( QuaternionT<T>& a, const T & b ) { return a = a*rcp(b); }
120 template<typename T> __forceinline QuaternionT<T>& operator /=( QuaternionT<T>& a, const QuaternionT<T>& b ) { return a = a*rcp(b); }
121
122 template<typename T, typename M> __forceinline QuaternionT<T>
123 select(const M& m, const QuaternionT<T>& q, const QuaternionT<T>& p)
124 {
125 return QuaternionT<T>(select(m, q.r, p.r),
126 select(m, q.i, p.i),
127 select(m, q.j, p.j),
128 select(m, q.k, p.k));
129 }
130
131
132 template<typename T> __forceinline Vec3<T> xfmPoint ( const QuaternionT<T>& a, const Vec3<T>& b ) { return (a*QuaternionT<T>(b)*conj(a)).v(); }
133 template<typename T> __forceinline Vec3<T> xfmVector( const QuaternionT<T>& a, const Vec3<T>& b ) { return (a*QuaternionT<T>(b)*conj(a)).v(); }
134 template<typename T> __forceinline Vec3<T> xfmNormal( const QuaternionT<T>& a, const Vec3<T>& b ) { return (a*QuaternionT<T>(b)*conj(a)).v(); }
135
136 template<typename T> __forceinline T dot(const QuaternionT<T>& a, const QuaternionT<T>& b) { return a.r*b.r + a.i*b.i + a.j*b.j + a.k*b.k; }
137
138 ////////////////////////////////////////////////////////////////////////////////
139 /// Comparison Operators
140 ////////////////////////////////////////////////////////////////////////////////
141
142 template<typename T> __forceinline bool operator ==( const QuaternionT<T>& a, const QuaternionT<T>& b ) { return a.r == b.r && a.i == b.i && a.j == b.j && a.k == b.k; }
143 template<typename T> __forceinline bool operator !=( const QuaternionT<T>& a, const QuaternionT<T>& b ) { return a.r != b.r || a.i != b.i || a.j != b.j || a.k != b.k; }
144
145
146 ////////////////////////////////////////////////////////////////////////////////
147 /// Orientation Functions
148 ////////////////////////////////////////////////////////////////////////////////
149
150 template<typename T> QuaternionT<T>::QuaternionT( const Vec3<T>& vx, const Vec3<T>& vy, const Vec3<T>& vz )
151 {
152 if ( vx.x + vy.y + vz.z >= T(zero) )
153 {
154 const T t = T(one) + (vx.x + vy.y + vz.z);
155 const T s = rsqrt(t)*T(0.5f);
156 r = t*s;
157 i = (vy.z - vz.y)*s;
158 j = (vz.x - vx.z)*s;
159 k = (vx.y - vy.x)*s;
160 }
161 else if ( vx.x >= max(vy.y, vz.z) )
162 {
163 const T t = (T(one) + vx.x) - (vy.y + vz.z);
164 const T s = rsqrt(t)*T(0.5f);
165 r = (vy.z - vz.y)*s;
166 i = t*s;
167 j = (vx.y + vy.x)*s;
168 k = (vz.x + vx.z)*s;
169 }
170 else if ( vy.y >= vz.z ) // if ( vy.y >= max(vz.z, vx.x) )
171 {
172 const T t = (T(one) + vy.y) - (vz.z + vx.x);
173 const T s = rsqrt(t)*T(0.5f);
174 r = (vz.x - vx.z)*s;
175 i = (vx.y + vy.x)*s;
176 j = t*s;
177 k = (vy.z + vz.y)*s;
178 }
179 else //if ( vz.z >= max(vy.y, vx.x) )
180 {
181 const T t = (T(one) + vz.z) - (vx.x + vy.y);
182 const T s = rsqrt(t)*T(0.5f);
183 r = (vx.y - vy.x)*s;
184 i = (vz.x + vx.z)*s;
185 j = (vy.z + vz.y)*s;
186 k = t*s;
187 }
188 }
189
190 template<typename T> QuaternionT<T>::QuaternionT( const T& yaw, const T& pitch, const T& roll )
191 {
192 const T cya = cos(yaw *T(0.5f));
193 const T cpi = cos(pitch*T(0.5f));
194 const T cro = cos(roll *T(0.5f));
195 const T sya = sin(yaw *T(0.5f));
196 const T spi = sin(pitch*T(0.5f));
197 const T sro = sin(roll *T(0.5f));
198 r = cro*cya*cpi + sro*sya*spi;
199 i = cro*cya*spi + sro*sya*cpi;
200 j = cro*sya*cpi - sro*cya*spi;
201 k = sro*cya*cpi - cro*sya*spi;
202 }
203
204 //////////////////////////////////////////////////////////////////////////////
205 /// Output Operators
206 //////////////////////////////////////////////////////////////////////////////
207
208 template<typename T> static embree_ostream operator<<(embree_ostream cout, const QuaternionT<T>& q) {
209 return cout << "{ r = " << q.r << ", i = " << q.i << ", j = " << q.j << ", k = " << q.k << " }";
210 }
211
212 /*! default template instantiations */
213 typedef QuaternionT<float> Quaternion3f;
214 typedef QuaternionT<double> Quaternion3d;
215
216 template<int N> using Quaternion3vf = QuaternionT<vfloat<N>>;
217 typedef QuaternionT<vfloat<4>> Quaternion3vf4;
218 typedef QuaternionT<vfloat<8>> Quaternion3vf8;
219 typedef QuaternionT<vfloat<16>> Quaternion3vf16;
220
221 //////////////////////////////////////////////////////////////////////////////
222 /// Interpolation
223 //////////////////////////////////////////////////////////////////////////////
224 template<typename T>
225 __forceinline QuaternionT<T>lerp(const QuaternionT<T>& q0,
226 const QuaternionT<T>& q1,
227 const T& factor)
228 {
229 QuaternionT<T> q;
230 q.r = lerp(q0.r, q1.r, factor);
231 q.i = lerp(q0.i, q1.i, factor);
232 q.j = lerp(q0.j, q1.j, factor);
233 q.k = lerp(q0.k, q1.k, factor);
234 return q;
235 }
236
237 template<typename T>
238 __forceinline QuaternionT<T> slerp(const QuaternionT<T>& q0,
239 const QuaternionT<T>& q1_,
240 const T& t)
241 {
242 T cosTheta = dot(q0, q1_);
243 QuaternionT<T> q1 = select(cosTheta < 0.f, -q1_, q1_);
244 cosTheta = select(cosTheta < 0.f, -cosTheta, cosTheta);
245
246 // spherical linear interpolation
247 const T phi = t * fastapprox::acos(cosTheta);
248 T sinPhi, cosPhi;
249 fastapprox::sincos(phi, sinPhi, cosPhi);
250 QuaternionT<T> qperp = sinPhi * normalize(msub(cosTheta, q0, q1));
251 QuaternionT<T> qslerp = msub(cosPhi, q0, qperp);
252
253 // regular linear interpolation as fallback
254 QuaternionT<T> qlerp = normalize(lerp(q0, q1, t));
255
256 return select(cosTheta > 0.9995f, qlerp, qslerp);
257 }
258}
259

source code of qtquick3d/src/3rdparty/embree/common/math/quaternion.h