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