1// Copyright 2009-2021 Intel Corporation
2// SPDX-License-Identifier: Apache-2.0
3
4#pragma once
5
6#include "../common/default.h"
7//#include "../common/scene_curves.h"
8#include "../common/context.h"
9
10namespace embree
11{
12 class BezierBasis
13 {
14 public:
15
16 template<typename T>
17 static __forceinline Vec4<T> eval(const T& u)
18 {
19 const T t1 = u;
20 const T t0 = 1.0f-t1;
21 const T B0 = t0 * t0 * t0;
22 const T B1 = 3.0f * t1 * (t0 * t0);
23 const T B2 = 3.0f * (t1 * t1) * t0;
24 const T B3 = t1 * t1 * t1;
25 return Vec4<T>(B0,B1,B2,B3);
26 }
27
28 template<typename T>
29 static __forceinline Vec4<T> derivative(const T& u)
30 {
31 const T t1 = u;
32 const T t0 = 1.0f-t1;
33 const T B0 = -(t0*t0);
34 const T B1 = madd(-2.0f,t0*t1,t0*t0);
35 const T B2 = msub(+2.0f,t0*t1,t1*t1);
36 const T B3 = +(t1*t1);
37 return T(3.0f)*Vec4<T>(B0,B1,B2,B3);
38 }
39
40 template<typename T>
41 static __forceinline Vec4<T> derivative2(const T& u)
42 {
43 const T t1 = u;
44 const T t0 = 1.0f-t1;
45 const T B0 = t0;
46 const T B1 = madd(-2.0f,t0,t1);
47 const T B2 = madd(-2.0f,t1,t0);
48 const T B3 = t1;
49 return T(6.0f)*Vec4<T>(B0,B1,B2,B3);
50 }
51 };
52
53 struct PrecomputedBezierBasis
54 {
55 enum { N = 16 };
56 public:
57 PrecomputedBezierBasis() {}
58 PrecomputedBezierBasis(int shift);
59
60 /* basis for bezier evaluation */
61 public:
62 float c0[N+1][N+1];
63 float c1[N+1][N+1];
64 float c2[N+1][N+1];
65 float c3[N+1][N+1];
66
67 /* basis for bezier derivative evaluation */
68 public:
69 float d0[N+1][N+1];
70 float d1[N+1][N+1];
71 float d2[N+1][N+1];
72 float d3[N+1][N+1];
73 };
74 extern PrecomputedBezierBasis bezier_basis0;
75 extern PrecomputedBezierBasis bezier_basis1;
76
77
78 template<typename V>
79 struct LinearBezierCurve
80 {
81 V v0,v1;
82
83 __forceinline LinearBezierCurve () {}
84
85 __forceinline LinearBezierCurve (const LinearBezierCurve& other)
86 : v0(other.v0), v1(other.v1) {}
87
88 __forceinline LinearBezierCurve& operator= (const LinearBezierCurve& other) {
89 v0 = other.v0; v1 = other.v1; return *this;
90 }
91
92 __forceinline LinearBezierCurve (const V& v0, const V& v1)
93 : v0(v0), v1(v1) {}
94
95 __forceinline V begin() const { return v0; }
96 __forceinline V end () const { return v1; }
97
98 bool hasRoot() const;
99
100 friend embree_ostream operator<<(embree_ostream cout, const LinearBezierCurve& a) {
101 return cout << "LinearBezierCurve (" << a.v0 << ", " << a.v1 << ")";
102 }
103 };
104
105 template<> __forceinline bool LinearBezierCurve<Interval1f>::hasRoot() const {
106 return numRoots(p0: v0,p1: v1);
107 }
108
109 template<typename V>
110 struct QuadraticBezierCurve
111 {
112 V v0,v1,v2;
113
114 __forceinline QuadraticBezierCurve () {}
115
116 __forceinline QuadraticBezierCurve (const QuadraticBezierCurve& other)
117 : v0(other.v0), v1(other.v1), v2(other.v2) {}
118
119 __forceinline QuadraticBezierCurve& operator= (const QuadraticBezierCurve& other) {
120 v0 = other.v0; v1 = other.v1; v2 = other.v2; return *this;
121 }
122
123 __forceinline QuadraticBezierCurve (const V& v0, const V& v1, const V& v2)
124 : v0(v0), v1(v1), v2(v2) {}
125
126 __forceinline V begin() const { return v0; }
127 __forceinline V end () const { return v2; }
128
129 __forceinline V interval() const {
130 return merge(v0,v1,v2);
131 }
132
133 __forceinline BBox<V> bounds() const {
134 return merge(BBox<V>(v0),BBox<V>(v1),BBox<V>(v2));
135 }
136
137 friend embree_ostream operator<<(embree_ostream cout, const QuadraticBezierCurve& a) {
138 return cout << "QuadraticBezierCurve ( (" << a.u.lower << ", " << a.u.upper << "), " << a.v0 << ", " << a.v1 << ", " << a.v2 << ")";
139 }
140 };
141
142
143 typedef QuadraticBezierCurve<float> QuadraticBezierCurve1f;
144 typedef QuadraticBezierCurve<Vec2fa> QuadraticBezierCurve2fa;
145 typedef QuadraticBezierCurve<Vec3fa> QuadraticBezierCurve3fa;
146
147 template<typename Vertex>
148 struct CubicBezierCurve
149 {
150 Vertex v0,v1,v2,v3;
151
152 __forceinline CubicBezierCurve() {}
153
154 template<typename T1>
155 __forceinline CubicBezierCurve (const CubicBezierCurve<T1>& other)
156 : v0(other.v0), v1(other.v1), v2(other.v2), v3(other.v3) {}
157
158 __forceinline CubicBezierCurve& operator= (const CubicBezierCurve& other) {
159 v0 = other.v0; v1 = other.v1; v2 = other.v2; v3 = other.v3; return *this;
160 }
161
162 __forceinline CubicBezierCurve(const Vertex& v0, const Vertex& v1, const Vertex& v2, const Vertex& v3)
163 : v0(v0), v1(v1), v2(v2), v3(v3) {}
164
165 __forceinline Vertex begin() const {
166 return v0;
167 }
168
169 __forceinline Vertex end() const {
170 return v3;
171 }
172
173 __forceinline Vertex center() const {
174 return 0.25f*(v0+v1+v2+v3);
175 }
176
177 __forceinline Vertex begin_direction() const {
178 return v1-v0;
179 }
180
181 __forceinline Vertex end_direction() const {
182 return v3-v2;
183 }
184
185 __forceinline CubicBezierCurve<float> xfm(const Vertex& dx) const {
186 return CubicBezierCurve<float>(dot(v0,dx),dot(v1,dx),dot(v2,dx),dot(v3,dx));
187 }
188
189 __forceinline CubicBezierCurve<vfloatx> vxfm(const Vertex& dx) const {
190 return CubicBezierCurve<vfloatx>(dot(v0,dx),dot(v1,dx),dot(v2,dx),dot(v3,dx));
191 }
192
193 __forceinline CubicBezierCurve<float> xfm(const Vertex& dx, const Vertex& p) const {
194 return CubicBezierCurve<float>(dot(v0-p,dx),dot(v1-p,dx),dot(v2-p,dx),dot(v3-p,dx));
195 }
196
197 __forceinline CubicBezierCurve<Vec3fa> xfm(const LinearSpace3fa& space) const
198 {
199 const Vec3fa q0 = xfmVector(space,v0);
200 const Vec3fa q1 = xfmVector(space,v1);
201 const Vec3fa q2 = xfmVector(space,v2);
202 const Vec3fa q3 = xfmVector(space,v3);
203 return CubicBezierCurve<Vec3fa>(q0,q1,q2,q3);
204 }
205
206 __forceinline CubicBezierCurve<Vec3fa> xfm(const LinearSpace3fa& space, const Vec3fa& p) const
207 {
208 const Vec3fa q0 = xfmVector(space,v0-p);
209 const Vec3fa q1 = xfmVector(space,v1-p);
210 const Vec3fa q2 = xfmVector(space,v2-p);
211 const Vec3fa q3 = xfmVector(space,v3-p);
212 return CubicBezierCurve<Vec3fa>(q0,q1,q2,q3);
213 }
214
215 __forceinline CubicBezierCurve<Vec3ff> xfm_pr(const LinearSpace3fa& space, const Vec3fa& p) const
216 {
217 const Vec3ff q0(xfmVector(s: space,a: (Vec3fa)v0-p), v0.w);
218 const Vec3ff q1(xfmVector(s: space,a: (Vec3fa)v1-p), v1.w);
219 const Vec3ff q2(xfmVector(s: space,a: (Vec3fa)v2-p), v2.w);
220 const Vec3ff q3(xfmVector(s: space,a: (Vec3fa)v3-p), v3.w);
221 return CubicBezierCurve<Vec3ff>(q0,q1,q2,q3);
222 }
223
224 __forceinline CubicBezierCurve<Vec3fa> xfm(const LinearSpace3fa& space, const Vec3fa& p, const float s) const
225 {
226 const Vec3fa q0 = xfmVector(space,s*(v0-p));
227 const Vec3fa q1 = xfmVector(space,s*(v1-p));
228 const Vec3fa q2 = xfmVector(space,s*(v2-p));
229 const Vec3fa q3 = xfmVector(space,s*(v3-p));
230 return CubicBezierCurve<Vec3fa>(q0,q1,q2,q3);
231 }
232
233 __forceinline int maxRoots() const;
234
235 __forceinline BBox<Vertex> bounds() const {
236 return merge(BBox<Vertex>(v0),BBox<Vertex>(v1),BBox<Vertex>(v2),BBox<Vertex>(v3));
237 }
238
239 __forceinline friend CubicBezierCurve operator +( const CubicBezierCurve& a, const CubicBezierCurve& b ) {
240 return CubicBezierCurve(a.v0+b.v0,a.v1+b.v1,a.v2+b.v2,a.v3+b.v3);
241 }
242
243 __forceinline friend CubicBezierCurve operator -( const CubicBezierCurve& a, const CubicBezierCurve& b ) {
244 return CubicBezierCurve(a.v0-b.v0,a.v1-b.v1,a.v2-b.v2,a.v3-b.v3);
245 }
246
247 __forceinline friend CubicBezierCurve operator -( const CubicBezierCurve& a, const Vertex& b ) {
248 return CubicBezierCurve(a.v0-b,a.v1-b,a.v2-b,a.v3-b);
249 }
250
251 __forceinline friend CubicBezierCurve operator *( const Vertex& a, const CubicBezierCurve& b ) {
252 return CubicBezierCurve(a*b.v0,a*b.v1,a*b.v2,a*b.v3);
253 }
254
255 __forceinline friend CubicBezierCurve cmadd( const Vertex& a, const CubicBezierCurve& b, const CubicBezierCurve& c) {
256 return CubicBezierCurve(madd(a,b.v0,c.v0),madd(a,b.v1,c.v1),madd(a,b.v2,c.v2),madd(a,b.v3,c.v3));
257 }
258
259 __forceinline friend CubicBezierCurve clerp ( const CubicBezierCurve& a, const CubicBezierCurve& b, const Vertex& t ) {
260 return cmadd((Vertex(1.0f)-t),a,t*b);
261 }
262
263 __forceinline friend CubicBezierCurve merge ( const CubicBezierCurve& a, const CubicBezierCurve& b ) {
264 return CubicBezierCurve(merge(a.v0,b.v0),merge(a.v1,b.v1),merge(a.v2,b.v2),merge(a.v3,b.v3));
265 }
266
267 __forceinline void split(CubicBezierCurve& left, CubicBezierCurve& right, const float t = 0.5f) const
268 {
269 const Vertex p00 = v0;
270 const Vertex p01 = v1;
271 const Vertex p02 = v2;
272 const Vertex p03 = v3;
273
274 const Vertex p10 = lerp(p00,p01,t);
275 const Vertex p11 = lerp(p01,p02,t);
276 const Vertex p12 = lerp(p02,p03,t);
277 const Vertex p20 = lerp(p10,p11,t);
278 const Vertex p21 = lerp(p11,p12,t);
279 const Vertex p30 = lerp(p20,p21,t);
280
281 new (&left ) CubicBezierCurve(p00,p10,p20,p30);
282 new (&right) CubicBezierCurve(p30,p21,p12,p03);
283 }
284
285 __forceinline CubicBezierCurve<Vec2vfx> split() const
286 {
287 const float u0 = 0.0f, u1 = 1.0f;
288 const float dscale = (u1-u0)*(1.0f/(3.0f*(VSIZEX-1)));
289 const vfloatx vu0 = lerp(a: u0,b: u1,t: vfloatx(step)*(1.0f/(VSIZEX-1)));
290 Vec2vfx P0, dP0du; evalN(t: vu0,p&: P0,dp&: dP0du); dP0du = dP0du * Vec2vfx(dscale);
291 const Vec2vfx P3 = shift_right_1(a: P0);
292 const Vec2vfx dP3du = shift_right_1(a: dP0du);
293 const Vec2vfx P1 = P0 + dP0du;
294 const Vec2vfx P2 = P3 - dP3du;
295 return CubicBezierCurve<Vec2vfx>(P0,P1,P2,P3);
296 }
297
298 __forceinline CubicBezierCurve<Vec2vfx> split(const BBox1f& u) const
299 {
300 const float u0 = u.lower, u1 = u.upper;
301 const float dscale = (u1-u0)*(1.0f/(3.0f*(VSIZEX-1)));
302 const vfloatx vu0 = lerp(a: u0,b: u1,t: vfloatx(step)*(1.0f/(VSIZEX-1)));
303 Vec2vfx P0, dP0du; evalN(t: vu0,p&: P0,dp&: dP0du); dP0du = dP0du * Vec2vfx(dscale);
304 const Vec2vfx P3 = shift_right_1(a: P0);
305 const Vec2vfx dP3du = shift_right_1(a: dP0du);
306 const Vec2vfx P1 = P0 + dP0du;
307 const Vec2vfx P2 = P3 - dP3du;
308 return CubicBezierCurve<Vec2vfx>(P0,P1,P2,P3);
309 }
310
311 __forceinline void eval(float t, Vertex& p, Vertex& dp) const
312 {
313 const Vertex p00 = v0;
314 const Vertex p01 = v1;
315 const Vertex p02 = v2;
316 const Vertex p03 = v3;
317
318 const Vertex p10 = lerp(p00,p01,t);
319 const Vertex p11 = lerp(p01,p02,t);
320 const Vertex p12 = lerp(p02,p03,t);
321 const Vertex p20 = lerp(p10,p11,t);
322 const Vertex p21 = lerp(p11,p12,t);
323 const Vertex p30 = lerp(p20,p21,t);
324
325 p = p30;
326 dp = Vertex(3.0f)*(p21-p20);
327 }
328
329#if 0
330 __forceinline Vertex eval(float t) const
331 {
332 const Vertex p00 = v0;
333 const Vertex p01 = v1;
334 const Vertex p02 = v2;
335 const Vertex p03 = v3;
336
337 const Vertex p10 = lerp(p00,p01,t);
338 const Vertex p11 = lerp(p01,p02,t);
339 const Vertex p12 = lerp(p02,p03,t);
340 const Vertex p20 = lerp(p10,p11,t);
341 const Vertex p21 = lerp(p11,p12,t);
342 const Vertex p30 = lerp(p20,p21,t);
343
344 return p30;
345 }
346#else
347 __forceinline Vertex eval(const float t) const
348 {
349 const Vec4<float> b = BezierBasis::eval(u: t);
350 return madd(b.x,v0,madd(b.y,v1,madd(b.z,v2,b.w*v3)));
351 }
352#endif
353
354 __forceinline Vertex eval_dt(float t) const
355 {
356 const Vertex p00 = v1-v0;
357 const Vertex p01 = v2-v1;
358 const Vertex p02 = v3-v2;
359 const Vertex p10 = lerp(p00,p01,t);
360 const Vertex p11 = lerp(p01,p02,t);
361 const Vertex p20 = lerp(p10,p11,t);
362 return Vertex(3.0f)*p20;
363 }
364
365 __forceinline Vertex eval_du(const float t) const
366 {
367 const Vec4<float> b = BezierBasis::derivative(u: t);
368 return madd(b.x,v0,madd(b.y,v1,madd(b.z,v2,b.w*v3)));
369 }
370
371 __forceinline Vertex eval_dudu(const float t) const
372 {
373 const Vec4<float> b = BezierBasis::derivative2(u: t);
374 return madd(b.x,v0,madd(b.y,v1,madd(b.z,v2,b.w*v3)));
375 }
376
377 __forceinline void evalN(const vfloatx& t, Vec2vfx& p, Vec2vfx& dp) const
378 {
379 const Vec2vfx p00 = v0;
380 const Vec2vfx p01 = v1;
381 const Vec2vfx p02 = v2;
382 const Vec2vfx p03 = v3;
383
384 const Vec2vfx p10 = lerp(v0: p00,v1: p01,t);
385 const Vec2vfx p11 = lerp(v0: p01,v1: p02,t);
386 const Vec2vfx p12 = lerp(v0: p02,v1: p03,t);
387
388 const Vec2vfx p20 = lerp(v0: p10,v1: p11,t);
389 const Vec2vfx p21 = lerp(v0: p11,v1: p12,t);
390
391 const Vec2vfx p30 = lerp(v0: p20,v1: p21,t);
392
393 p = p30;
394 dp = vfloatx(3.0f)*(p21-p20);
395 }
396
397 __forceinline void eval(const float t, Vertex& p, Vertex& dp, Vertex& ddp) const
398 {
399 const Vertex p00 = v0;
400 const Vertex p01 = v1;
401 const Vertex p02 = v2;
402 const Vertex p03 = v3;
403 const Vertex p10 = lerp(p00,p01,t);
404 const Vertex p11 = lerp(p01,p02,t);
405 const Vertex p12 = lerp(p02,p03,t);
406 const Vertex p20 = lerp(p10,p11,t);
407 const Vertex p21 = lerp(p11,p12,t);
408 const Vertex p30 = lerp(p20,p21,t);
409 p = p30;
410 dp = 3.0f*(p21-p20);
411 ddp = eval_dudu(t);
412 }
413
414 __forceinline CubicBezierCurve clip(const Interval1f& u1) const
415 {
416 Vertex f0,df0; eval(u1.lower,f0,df0);
417 Vertex f1,df1; eval(u1.upper,f1,df1);
418 float s = u1.upper-u1.lower;
419 return CubicBezierCurve(f0,f0+s*(1.0f/3.0f)*df0,f1-s*(1.0f/3.0f)*df1,f1);
420 }
421
422 __forceinline QuadraticBezierCurve<Vertex> derivative() const
423 {
424 const Vertex q0 = 3.0f*(v1-v0);
425 const Vertex q1 = 3.0f*(v2-v1);
426 const Vertex q2 = 3.0f*(v3-v2);
427 return QuadraticBezierCurve<Vertex>(q0,q1,q2);
428 }
429
430 __forceinline BBox<Vertex> derivative_bounds(const Interval1f& u1) const
431 {
432 Vertex f0,df0; eval(u1.lower,f0,df0);
433 Vertex f3,df3; eval(u1.upper,f3,df3);
434 const float s = u1.upper-u1.lower;
435 const Vertex f1 = f0+s*(1.0f/3.0f)*df0;
436 const Vertex f2 = f3-s*(1.0f/3.0f)*df3;
437 const Vertex q0 = s*df0;
438 const Vertex q1 = 3.0f*(f2-f1);
439 const Vertex q2 = s*df3;
440 return merge(BBox<Vertex>(q0),BBox<Vertex>(q1),BBox<Vertex>(q2));
441 }
442
443 template<int M>
444 __forceinline Vec4vf<M> veval(const vfloat<M>& t) const
445 {
446 const Vec4vf<M> b = BezierBasis::eval(t);
447 return madd(b.x, Vec4vf<M>(v0), madd(b.y, Vec4vf<M>(v1), madd(b.z, Vec4vf<M>(v2), b.w * Vec4vf<M>(v3))));
448 }
449
450 template<int M>
451 __forceinline Vec4vf<M> veval_du(const vfloat<M>& t) const
452 {
453 const Vec4vf<M> b = BezierBasis::derivative(t);
454 return madd(b.x, Vec4vf<M>(v0), madd(b.y, Vec4vf<M>(v1), madd(b.z, Vec4vf<M>(v2), b.w * Vec4vf<M>(v3))));
455 }
456
457 template<int M>
458 __forceinline Vec4vf<M> veval_dudu(const vfloat<M>& t) const
459 {
460 const Vec4vf<M> b = BezierBasis::derivative2(t);
461 return madd(b.x, Vec4vf<M>(v0), madd(b.y, Vec4vf<M>(v1), madd(b.z, Vec4vf<M>(v2), b.w * Vec4vf<M>(v3))));
462 }
463
464 template<int M>
465 __forceinline void veval(const vfloat<M>& t, Vec4vf<M>& p, Vec4vf<M>& dp) const
466 {
467 const Vec4vf<M> p00 = v0;
468 const Vec4vf<M> p01 = v1;
469 const Vec4vf<M> p02 = v2;
470 const Vec4vf<M> p03 = v3;
471
472 const Vec4vf<M> p10 = lerp(p00,p01,t);
473 const Vec4vf<M> p11 = lerp(p01,p02,t);
474 const Vec4vf<M> p12 = lerp(p02,p03,t);
475 const Vec4vf<M> p20 = lerp(p10,p11,t);
476 const Vec4vf<M> p21 = lerp(p11,p12,t);
477 const Vec4vf<M> p30 = lerp(p20,p21,t);
478
479 p = p30;
480 dp = vfloat<M>(3.0f)*(p21-p20);
481 }
482
483 template<int M, typename Vec = Vec4vf<M>>
484 __forceinline Vec eval0(const int ofs, const int size) const
485 {
486 assert(size <= PrecomputedBezierBasis::N);
487 assert(ofs <= size);
488 return madd(vfloat<M>::loadu(&bezier_basis0.c0[size][ofs]), Vec(v0),
489 madd(vfloat<M>::loadu(&bezier_basis0.c1[size][ofs]), Vec(v1),
490 madd(vfloat<M>::loadu(&bezier_basis0.c2[size][ofs]), Vec(v2),
491 vfloat<M>::loadu(&bezier_basis0.c3[size][ofs]) * Vec(v3))));
492 }
493
494 template<int M, typename Vec = Vec4vf<M>>
495 __forceinline Vec eval1(const int ofs, const int size) const
496 {
497 assert(size <= PrecomputedBezierBasis::N);
498 assert(ofs <= size);
499 return madd(vfloat<M>::loadu(&bezier_basis1.c0[size][ofs]), Vec(v0),
500 madd(vfloat<M>::loadu(&bezier_basis1.c1[size][ofs]), Vec(v1),
501 madd(vfloat<M>::loadu(&bezier_basis1.c2[size][ofs]), Vec(v2),
502 vfloat<M>::loadu(&bezier_basis1.c3[size][ofs]) * Vec(v3))));
503 }
504
505 template<int M, typename Vec = Vec4vf<M>>
506 __forceinline Vec derivative0(const int ofs, const int size) const
507 {
508 assert(size <= PrecomputedBezierBasis::N);
509 assert(ofs <= size);
510 return madd(vfloat<M>::loadu(&bezier_basis0.d0[size][ofs]), Vec(v0),
511 madd(vfloat<M>::loadu(&bezier_basis0.d1[size][ofs]), Vec(v1),
512 madd(vfloat<M>::loadu(&bezier_basis0.d2[size][ofs]), Vec(v2),
513 vfloat<M>::loadu(&bezier_basis0.d3[size][ofs]) * Vec(v3))));
514 }
515
516 template<int M, typename Vec = Vec4vf<M>>
517 __forceinline Vec derivative1(const int ofs, const int size) const
518 {
519 assert(size <= PrecomputedBezierBasis::N);
520 assert(ofs <= size);
521 return madd(vfloat<M>::loadu(&bezier_basis1.d0[size][ofs]), Vec(v0),
522 madd(vfloat<M>::loadu(&bezier_basis1.d1[size][ofs]), Vec(v1),
523 madd(vfloat<M>::loadu(&bezier_basis1.d2[size][ofs]), Vec(v2),
524 vfloat<M>::loadu(&bezier_basis1.d3[size][ofs]) * Vec(v3))));
525 }
526
527 /* calculates bounds of bezier curve geometry */
528 __forceinline BBox3fa accurateBounds() const
529 {
530 const int N = 7;
531 const float scale = 1.0f/(3.0f*(N-1));
532 Vec3vfx pl(pos_inf), pu(neg_inf);
533 for (int i=0; i<=N; i+=VSIZEX)
534 {
535 vintx vi = vintx(i)+vintx(step);
536 vboolx valid = vi <= vintx(N);
537 const Vec3vfx p = eval0<VSIZEX,Vec3vf<VSIZEX>>(i,N);
538 const Vec3vfx dp = derivative0<VSIZEX,Vec3vf<VSIZEX>>(i,N);
539 const Vec3vfx pm = p-Vec3vfx(scale)*select(s: vi!=vintx(0),t: dp,f: Vec3vfx(zero));
540 const Vec3vfx pp = p+Vec3vfx(scale)*select(s: vi!=vintx(N),t: dp,f: Vec3vfx(zero));
541 pl = select(s: valid,t: min(a: pl,b: p,c: pm,d: pp),f: pl); // FIXME: use masked min
542 pu = select(s: valid,t: max(a: pu,b: p,c: pm,d: pp),f: pu); // FIXME: use masked min
543 }
544 const Vec3fa lower(reduce_min(v: pl.x),reduce_min(v: pl.y),reduce_min(v: pl.z));
545 const Vec3fa upper(reduce_max(v: pu.x),reduce_max(v: pu.y),reduce_max(v: pu.z));
546 return BBox3fa(lower,upper);
547 }
548
549 /* calculates bounds of bezier curve geometry */
550 __forceinline BBox3fa accurateRoundBounds() const
551 {
552 const int N = 7;
553 const float scale = 1.0f/(3.0f*(N-1));
554 Vec4vfx pl(pos_inf), pu(neg_inf);
555 for (int i=0; i<=N; i+=VSIZEX)
556 {
557 vintx vi = vintx(i)+vintx(step);
558 vboolx valid = vi <= vintx(N);
559 const Vec4vfx p = eval0<VSIZEX>(i,N);
560 const Vec4vfx dp = derivative0<VSIZEX>(i,N);
561 const Vec4vfx pm = p-Vec4vfx(scale)*select(s: vi!=vintx(0),t: dp,f: Vec4vfx(zero));
562 const Vec4vfx pp = p+Vec4vfx(scale)*select(s: vi!=vintx(N),t: dp,f: Vec4vfx(zero));
563 pl = select(s: valid,t: min(a: pl,b: p,c: pm,d: pp),f: pl); // FIXME: use masked min
564 pu = select(s: valid,t: max(a: pu,b: p,c: pm,d: pp),f: pu); // FIXME: use masked min
565 }
566 const Vec3fa lower(reduce_min(v: pl.x),reduce_min(v: pl.y),reduce_min(v: pl.z));
567 const Vec3fa upper(reduce_max(v: pu.x),reduce_max(v: pu.y),reduce_max(v: pu.z));
568 const float r_min = reduce_min(v: pl.w);
569 const float r_max = reduce_max(v: pu.w);
570 const Vec3fa upper_r = Vec3fa(max(a: abs(x: r_min),b: abs(x: r_max)));
571 return enlarge(a: BBox3fa(lower,upper),b: upper_r);
572 }
573
574 /* calculates bounds when tessellated into N line segments */
575 __forceinline BBox3fa accurateFlatBounds(int N) const
576 {
577 if (likely(N == 4))
578 {
579 const Vec4vf4 pi = eval0<4>(0,4);
580 const Vec3fa lower(reduce_min(v: pi.x),reduce_min(v: pi.y),reduce_min(v: pi.z));
581 const Vec3fa upper(reduce_max(v: pi.x),reduce_max(v: pi.y),reduce_max(v: pi.z));
582 const Vec3fa upper_r = Vec3fa(reduce_max(v: abs(a: pi.w)));
583 return enlarge(a: BBox3fa(min(lower,v3),max(upper,v3)),b: max(a: upper_r,b: Vec3fa(abs(v3.w))));
584 }
585 else
586 {
587 Vec3vfx pl(pos_inf), pu(neg_inf); vfloatx ru(0.0f);
588 for (int i=0; i<N; i+=VSIZEX)
589 {
590 vboolx valid = vintx(i)+vintx(step) < vintx(N);
591 const Vec4vfx pi = eval0<VSIZEX>(i,N);
592
593 pl.x = select(m: valid,t: min(a: pl.x,b: pi.x),f: pl.x); // FIXME: use masked min
594 pl.y = select(m: valid,t: min(a: pl.y,b: pi.y),f: pl.y);
595 pl.z = select(m: valid,t: min(a: pl.z,b: pi.z),f: pl.z);
596
597 pu.x = select(m: valid,t: max(a: pu.x,b: pi.x),f: pu.x); // FIXME: use masked min
598 pu.y = select(m: valid,t: max(a: pu.y,b: pi.y),f: pu.y);
599 pu.z = select(m: valid,t: max(a: pu.z,b: pi.z),f: pu.z);
600
601 ru = select(m: valid,t: max(a: ru,b: abs(a: pi.w)),f: ru);
602 }
603 const Vec3fa lower(reduce_min(v: pl.x),reduce_min(v: pl.y),reduce_min(v: pl.z));
604 const Vec3fa upper(reduce_max(v: pu.x),reduce_max(v: pu.y),reduce_max(v: pu.z));
605 const Vec3fa upper_r(reduce_max(v: ru));
606 return enlarge(a: BBox3fa(min(lower,v3),max(upper,v3)),b: max(a: upper_r,b: Vec3fa(abs(v3.w))));
607 }
608 }
609
610 friend __forceinline embree_ostream operator<<(embree_ostream cout, const CubicBezierCurve& curve) {
611 return cout << "CubicBezierCurve { v0 = " << curve.v0 << ", v1 = " << curve.v1 << ", v2 = " << curve.v2 << ", v3 = " << curve.v3 << " }";
612 }
613 };
614
615#if defined(__AVX__)
616 template<>
617 __forceinline CubicBezierCurve<vfloat4> CubicBezierCurve<vfloat4>::clip(const Interval1f& u1) const
618 {
619 const vfloat8 p00 = vfloat8(v0);
620 const vfloat8 p01 = vfloat8(v1);
621 const vfloat8 p02 = vfloat8(v2);
622 const vfloat8 p03 = vfloat8(v3);
623
624 const vfloat8 t(vfloat4(u1.lower),vfloat4(u1.upper));
625 const vfloat8 p10 = lerp(p00,p01,t);
626 const vfloat8 p11 = lerp(p01,p02,t);
627 const vfloat8 p12 = lerp(p02,p03,t);
628 const vfloat8 p20 = lerp(p10,p11,t);
629 const vfloat8 p21 = lerp(p11,p12,t);
630 const vfloat8 p30 = lerp(p20,p21,t);
631
632 const vfloat8 f01 = p30;
633 const vfloat8 df01 = vfloat8(3.0f)*(p21-p20);
634
635 const vfloat4 f0 = extract4<0>(f01), f1 = extract4<1>(f01);
636 const vfloat4 df0 = extract4<0>(df01), df1 = extract4<1>(df01);
637 const float s = u1.upper-u1.lower;
638 return CubicBezierCurve(f0,f0+s*(1.0f/3.0f)*df0,f1-s*(1.0f/3.0f)*df1,f1);
639 }
640#endif
641
642 template<typename Vertex> using BezierCurveT = CubicBezierCurve<Vertex>;
643
644 typedef CubicBezierCurve<float> CubicBezierCurve1f;
645 typedef CubicBezierCurve<Vec2fa> CubicBezierCurve2fa;
646 typedef CubicBezierCurve<Vec3fa> CubicBezierCurve3fa;
647 typedef CubicBezierCurve<Vec3fa> BezierCurve3fa;
648
649 template<> __forceinline int CubicBezierCurve<float>::maxRoots() const
650 {
651 float eps = 1E-4f;
652 bool neg0 = v0 <= 0.0f; bool zero0 = fabs(x: v0) < eps;
653 bool neg1 = v1 <= 0.0f; bool zero1 = fabs(x: v1) < eps;
654 bool neg2 = v2 <= 0.0f; bool zero2 = fabs(x: v2) < eps;
655 bool neg3 = v3 <= 0.0f; bool zero3 = fabs(x: v3) < eps;
656 return (neg0 != neg1 || zero0) + (neg1 != neg2 || zero1) + (neg2 != neg3 || zero2 || zero3);
657 }
658
659 template<> __forceinline int CubicBezierCurve<Interval1f>::maxRoots() const {
660 return numRoots(p0: v0,p1: v1) + numRoots(p0: v1,p1: v2) + numRoots(p0: v2,p1: v3);
661 }
662
663 template<typename CurveGeometry>
664 __forceinline CubicBezierCurve<Vec3ff> enlargeRadiusToMinWidth(const IntersectContext* context, const CurveGeometry* geom, const Vec3fa& ray_org, const CubicBezierCurve<Vec3ff>& curve)
665 {
666 return CubicBezierCurve<Vec3ff>(enlargeRadiusToMinWidth(context,geom,ray_org,curve.v0),
667 enlargeRadiusToMinWidth(context,geom,ray_org,curve.v1),
668 enlargeRadiusToMinWidth(context,geom,ray_org,curve.v2),
669 enlargeRadiusToMinWidth(context,geom,ray_org,curve.v3));
670 }
671}
672

source code of qtquick3d/src/3rdparty/embree/kernels/subdiv/bezier_curve.h