SpotShadow.cpp revision 28c3ea018771562a9150f30c6a088e5bf7502972
1/* 2 * Copyright (C) 2014 The Android Open Source Project 3 * 4 * Licensed under the Apache License, Version 2.0 (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 7 * 8 * http://www.apache.org/licenses/LICENSE-2.0 9 * 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. 15 */ 16 17#define LOG_TAG "OpenGLRenderer" 18 19#define SHADOW_SHRINK_SCALE 0.1f 20 21#include <math.h> 22#include <stdlib.h> 23#include <utils/Log.h> 24 25#include "ShadowTessellator.h" 26#include "SpotShadow.h" 27#include "Vertex.h" 28 29namespace android { 30namespace uirenderer { 31 32static const double EPSILON = 1e-7; 33 34/** 35 * Calculate the angle between and x and a y coordinate. 36 * The atan2 range from -PI to PI. 37 */ 38static float angle(const Vector2& point, const Vector2& center) { 39 return atan2(point.y - center.y, point.x - center.x); 40} 41 42/** 43 * Calculate the intersection of a ray with the line segment defined by two points. 44 * 45 * Returns a negative value in error conditions. 46 47 * @param rayOrigin The start of the ray 48 * @param dx The x vector of the ray 49 * @param dy The y vector of the ray 50 * @param p1 The first point defining the line segment 51 * @param p2 The second point defining the line segment 52 * @return The distance along the ray if it intersects with the line segment, negative if otherwise 53 */ 54static float rayIntersectPoints(const Vector2& rayOrigin, float dx, float dy, 55 const Vector2& p1, const Vector2& p2) { 56 // The math below is derived from solving this formula, basically the 57 // intersection point should stay on both the ray and the edge of (p1, p2). 58 // solve([p1x+t*(p2x-p1x)=dx*t2+px,p1y+t*(p2y-p1y)=dy*t2+py],[t,t2]); 59 60 double divisor = (dx * (p1.y - p2.y) + dy * p2.x - dy * p1.x); 61 if (divisor == 0) return -1.0f; // error, invalid divisor 62 63#if DEBUG_SHADOW 64 double interpVal = (dx * (p1.y - rayOrigin.y) + dy * rayOrigin.x - dy * p1.x) / divisor; 65 if (interpVal < 0 || interpVal > 1) { 66 ALOGW("rayIntersectPoints is hitting outside the segment %f", interpVal); 67 } 68#endif 69 70 double distance = (p1.x * (rayOrigin.y - p2.y) + p2.x * (p1.y - rayOrigin.y) + 71 rayOrigin.x * (p2.y - p1.y)) / divisor; 72 73 return distance; // may be negative in error cases 74} 75 76/** 77 * Sort points by their X coordinates 78 * 79 * @param points the points as a Vector2 array. 80 * @param pointsLength the number of vertices of the polygon. 81 */ 82void SpotShadow::xsort(Vector2* points, int pointsLength) { 83 quicksortX(points, 0, pointsLength - 1); 84} 85 86/** 87 * compute the convex hull of a collection of Points 88 * 89 * @param points the points as a Vector2 array. 90 * @param pointsLength the number of vertices of the polygon. 91 * @param retPoly pre allocated array of floats to put the vertices 92 * @return the number of points in the polygon 0 if no intersection 93 */ 94int SpotShadow::hull(Vector2* points, int pointsLength, Vector2* retPoly) { 95 xsort(points, pointsLength); 96 int n = pointsLength; 97 Vector2 lUpper[n]; 98 lUpper[0] = points[0]; 99 lUpper[1] = points[1]; 100 101 int lUpperSize = 2; 102 103 for (int i = 2; i < n; i++) { 104 lUpper[lUpperSize] = points[i]; 105 lUpperSize++; 106 107 while (lUpperSize > 2 && !ccw( 108 lUpper[lUpperSize - 3].x, lUpper[lUpperSize - 3].y, 109 lUpper[lUpperSize - 2].x, lUpper[lUpperSize - 2].y, 110 lUpper[lUpperSize - 1].x, lUpper[lUpperSize - 1].y)) { 111 // Remove the middle point of the three last 112 lUpper[lUpperSize - 2].x = lUpper[lUpperSize - 1].x; 113 lUpper[lUpperSize - 2].y = lUpper[lUpperSize - 1].y; 114 lUpperSize--; 115 } 116 } 117 118 Vector2 lLower[n]; 119 lLower[0] = points[n - 1]; 120 lLower[1] = points[n - 2]; 121 122 int lLowerSize = 2; 123 124 for (int i = n - 3; i >= 0; i--) { 125 lLower[lLowerSize] = points[i]; 126 lLowerSize++; 127 128 while (lLowerSize > 2 && !ccw( 129 lLower[lLowerSize - 3].x, lLower[lLowerSize - 3].y, 130 lLower[lLowerSize - 2].x, lLower[lLowerSize - 2].y, 131 lLower[lLowerSize - 1].x, lLower[lLowerSize - 1].y)) { 132 // Remove the middle point of the three last 133 lLower[lLowerSize - 2] = lLower[lLowerSize - 1]; 134 lLowerSize--; 135 } 136 } 137 138 // output points in CW ordering 139 const int total = lUpperSize + lLowerSize - 2; 140 int outIndex = total - 1; 141 for (int i = 0; i < lUpperSize; i++) { 142 retPoly[outIndex] = lUpper[i]; 143 outIndex--; 144 } 145 146 for (int i = 1; i < lLowerSize - 1; i++) { 147 retPoly[outIndex] = lLower[i]; 148 outIndex--; 149 } 150 // TODO: Add test harness which verify that all the points are inside the hull. 151 return total; 152} 153 154/** 155 * Test whether the 3 points form a counter clockwise turn. 156 * 157 * @return true if a right hand turn 158 */ 159bool SpotShadow::ccw(double ax, double ay, double bx, double by, 160 double cx, double cy) { 161 return (bx - ax) * (cy - ay) - (by - ay) * (cx - ax) > EPSILON; 162} 163 164/** 165 * Calculates the intersection of poly1 with poly2 and put in poly2. 166 * Note that both poly1 and poly2 must be in CW order already! 167 * 168 * @param poly1 The 1st polygon, as a Vector2 array. 169 * @param poly1Length The number of vertices of 1st polygon. 170 * @param poly2 The 2nd and output polygon, as a Vector2 array. 171 * @param poly2Length The number of vertices of 2nd polygon. 172 * @return number of vertices in output polygon as poly2. 173 */ 174int SpotShadow::intersection(const Vector2* poly1, int poly1Length, 175 Vector2* poly2, int poly2Length) { 176#if DEBUG_SHADOW 177 if (!isClockwise(poly1, poly1Length)) { 178 ALOGW("Poly1 is not clockwise! Intersection is wrong!"); 179 } 180 if (!isClockwise(poly2, poly2Length)) { 181 ALOGW("Poly2 is not clockwise! Intersection is wrong!"); 182 } 183#endif 184 Vector2 poly[poly1Length * poly2Length + 2]; 185 int count = 0; 186 int pcount = 0; 187 188 // If one vertex from one polygon sits inside another polygon, add it and 189 // count them. 190 for (int i = 0; i < poly1Length; i++) { 191 if (testPointInsidePolygon(poly1[i], poly2, poly2Length)) { 192 poly[count] = poly1[i]; 193 count++; 194 pcount++; 195 196 } 197 } 198 199 int insidePoly2 = pcount; 200 for (int i = 0; i < poly2Length; i++) { 201 if (testPointInsidePolygon(poly2[i], poly1, poly1Length)) { 202 poly[count] = poly2[i]; 203 count++; 204 } 205 } 206 207 int insidePoly1 = count - insidePoly2; 208 // If all vertices from poly1 are inside poly2, then just return poly1. 209 if (insidePoly2 == poly1Length) { 210 memcpy(poly2, poly1, poly1Length * sizeof(Vector2)); 211 return poly1Length; 212 } 213 214 // If all vertices from poly2 are inside poly1, then just return poly2. 215 if (insidePoly1 == poly2Length) { 216 return poly2Length; 217 } 218 219 // Since neither polygon fully contain the other one, we need to add all the 220 // intersection points. 221 Vector2 intersection; 222 for (int i = 0; i < poly2Length; i++) { 223 for (int j = 0; j < poly1Length; j++) { 224 int poly2LineStart = i; 225 int poly2LineEnd = ((i + 1) % poly2Length); 226 int poly1LineStart = j; 227 int poly1LineEnd = ((j + 1) % poly1Length); 228 bool found = lineIntersection( 229 poly2[poly2LineStart].x, poly2[poly2LineStart].y, 230 poly2[poly2LineEnd].x, poly2[poly2LineEnd].y, 231 poly1[poly1LineStart].x, poly1[poly1LineStart].y, 232 poly1[poly1LineEnd].x, poly1[poly1LineEnd].y, 233 intersection); 234 if (found) { 235 poly[count].x = intersection.x; 236 poly[count].y = intersection.y; 237 count++; 238 } else { 239 Vector2 delta = poly2[i] - poly1[j]; 240 if (delta.lengthSquared() < EPSILON) { 241 poly[count] = poly2[i]; 242 count++; 243 } 244 } 245 } 246 } 247 248 if (count == 0) { 249 return 0; 250 } 251 252 // Sort the result polygon around the center. 253 Vector2 center(0.0f, 0.0f); 254 for (int i = 0; i < count; i++) { 255 center += poly[i]; 256 } 257 center /= count; 258 sort(poly, count, center); 259 260#if DEBUG_SHADOW 261 // Since poly2 is overwritten as the result, we need to save a copy to do 262 // our verification. 263 Vector2 oldPoly2[poly2Length]; 264 int oldPoly2Length = poly2Length; 265 memcpy(oldPoly2, poly2, sizeof(Vector2) * poly2Length); 266#endif 267 268 // Filter the result out from poly and put it into poly2. 269 poly2[0] = poly[0]; 270 int lastOutputIndex = 0; 271 for (int i = 1; i < count; i++) { 272 Vector2 delta = poly[i] - poly2[lastOutputIndex]; 273 if (delta.lengthSquared() >= EPSILON) { 274 poly2[++lastOutputIndex] = poly[i]; 275 } else { 276 // If the vertices are too close, pick the inner one, because the 277 // inner one is more likely to be an intersection point. 278 Vector2 delta1 = poly[i] - center; 279 Vector2 delta2 = poly2[lastOutputIndex] - center; 280 if (delta1.lengthSquared() < delta2.lengthSquared()) { 281 poly2[lastOutputIndex] = poly[i]; 282 } 283 } 284 } 285 int resultLength = lastOutputIndex + 1; 286 287#if DEBUG_SHADOW 288 testConvex(poly2, resultLength, "intersection"); 289 testConvex(poly1, poly1Length, "input poly1"); 290 testConvex(oldPoly2, oldPoly2Length, "input poly2"); 291 292 testIntersection(poly1, poly1Length, oldPoly2, oldPoly2Length, poly2, resultLength); 293#endif 294 295 return resultLength; 296} 297 298/** 299 * Sort points about a center point 300 * 301 * @param poly The in and out polyogon as a Vector2 array. 302 * @param polyLength The number of vertices of the polygon. 303 * @param center the center ctr[0] = x , ctr[1] = y to sort around. 304 */ 305void SpotShadow::sort(Vector2* poly, int polyLength, const Vector2& center) { 306 quicksortCirc(poly, 0, polyLength - 1, center); 307} 308 309/** 310 * Swap points pointed to by i and j 311 */ 312void SpotShadow::swap(Vector2* points, int i, int j) { 313 Vector2 temp = points[i]; 314 points[i] = points[j]; 315 points[j] = temp; 316} 317 318/** 319 * quick sort implementation about the center. 320 */ 321void SpotShadow::quicksortCirc(Vector2* points, int low, int high, 322 const Vector2& center) { 323 int i = low, j = high; 324 int p = low + (high - low) / 2; 325 float pivot = angle(points[p], center); 326 while (i <= j) { 327 while (angle(points[i], center) > pivot) { 328 i++; 329 } 330 while (angle(points[j], center) < pivot) { 331 j--; 332 } 333 334 if (i <= j) { 335 swap(points, i, j); 336 i++; 337 j--; 338 } 339 } 340 if (low < j) quicksortCirc(points, low, j, center); 341 if (i < high) quicksortCirc(points, i, high, center); 342} 343 344/** 345 * Sort points by x axis 346 * 347 * @param points points to sort 348 * @param low start index 349 * @param high end index 350 */ 351void SpotShadow::quicksortX(Vector2* points, int low, int high) { 352 int i = low, j = high; 353 int p = low + (high - low) / 2; 354 float pivot = points[p].x; 355 while (i <= j) { 356 while (points[i].x < pivot) { 357 i++; 358 } 359 while (points[j].x > pivot) { 360 j--; 361 } 362 363 if (i <= j) { 364 swap(points, i, j); 365 i++; 366 j--; 367 } 368 } 369 if (low < j) quicksortX(points, low, j); 370 if (i < high) quicksortX(points, i, high); 371} 372 373/** 374 * Test whether a point is inside the polygon. 375 * 376 * @param testPoint the point to test 377 * @param poly the polygon 378 * @return true if the testPoint is inside the poly. 379 */ 380bool SpotShadow::testPointInsidePolygon(const Vector2 testPoint, 381 const Vector2* poly, int len) { 382 bool c = false; 383 double testx = testPoint.x; 384 double testy = testPoint.y; 385 for (int i = 0, j = len - 1; i < len; j = i++) { 386 double startX = poly[j].x; 387 double startY = poly[j].y; 388 double endX = poly[i].x; 389 double endY = poly[i].y; 390 391 if (((endY > testy) != (startY > testy)) && 392 (testx < (startX - endX) * (testy - endY) 393 / (startY - endY) + endX)) { 394 c = !c; 395 } 396 } 397 return c; 398} 399 400/** 401 * Make the polygon turn clockwise. 402 * 403 * @param polygon the polygon as a Vector2 array. 404 * @param len the number of points of the polygon 405 */ 406void SpotShadow::makeClockwise(Vector2* polygon, int len) { 407 if (polygon == 0 || len == 0) { 408 return; 409 } 410 if (!isClockwise(polygon, len)) { 411 reverse(polygon, len); 412 } 413} 414 415/** 416 * Test whether the polygon is order in clockwise. 417 * 418 * @param polygon the polygon as a Vector2 array 419 * @param len the number of points of the polygon 420 */ 421bool SpotShadow::isClockwise(const Vector2* polygon, int len) { 422 double sum = 0; 423 double p1x = polygon[len - 1].x; 424 double p1y = polygon[len - 1].y; 425 for (int i = 0; i < len; i++) { 426 427 double p2x = polygon[i].x; 428 double p2y = polygon[i].y; 429 sum += p1x * p2y - p2x * p1y; 430 p1x = p2x; 431 p1y = p2y; 432 } 433 return sum < 0; 434} 435 436/** 437 * Reverse the polygon 438 * 439 * @param polygon the polygon as a Vector2 array 440 * @param len the number of points of the polygon 441 */ 442void SpotShadow::reverse(Vector2* polygon, int len) { 443 int n = len / 2; 444 for (int i = 0; i < n; i++) { 445 Vector2 tmp = polygon[i]; 446 int k = len - 1 - i; 447 polygon[i] = polygon[k]; 448 polygon[k] = tmp; 449 } 450} 451 452/** 453 * Intersects two lines in parametric form. This function is called in a tight 454 * loop, and we need double precision to get things right. 455 * 456 * @param x1 the x coordinate point 1 of line 1 457 * @param y1 the y coordinate point 1 of line 1 458 * @param x2 the x coordinate point 2 of line 1 459 * @param y2 the y coordinate point 2 of line 1 460 * @param x3 the x coordinate point 1 of line 2 461 * @param y3 the y coordinate point 1 of line 2 462 * @param x4 the x coordinate point 2 of line 2 463 * @param y4 the y coordinate point 2 of line 2 464 * @param ret the x,y location of the intersection 465 * @return true if it found an intersection 466 */ 467inline bool SpotShadow::lineIntersection(double x1, double y1, double x2, double y2, 468 double x3, double y3, double x4, double y4, Vector2& ret) { 469 double d = (x1 - x2) * (y3 - y4) - (y1 - y2) * (x3 - x4); 470 if (d == 0.0) return false; 471 472 double dx = (x1 * y2 - y1 * x2); 473 double dy = (x3 * y4 - y3 * x4); 474 double x = (dx * (x3 - x4) - (x1 - x2) * dy) / d; 475 double y = (dx * (y3 - y4) - (y1 - y2) * dy) / d; 476 477 // The intersection should be in the middle of the point 1 and point 2, 478 // likewise point 3 and point 4. 479 if (((x - x1) * (x - x2) > EPSILON) 480 || ((x - x3) * (x - x4) > EPSILON) 481 || ((y - y1) * (y - y2) > EPSILON) 482 || ((y - y3) * (y - y4) > EPSILON)) { 483 // Not interesected 484 return false; 485 } 486 ret.x = x; 487 ret.y = y; 488 return true; 489 490} 491 492/** 493 * Compute a horizontal circular polygon about point (x , y , height) of radius 494 * (size) 495 * 496 * @param points number of the points of the output polygon. 497 * @param lightCenter the center of the light. 498 * @param size the light size. 499 * @param ret result polygon. 500 */ 501void SpotShadow::computeLightPolygon(int points, const Vector3& lightCenter, 502 float size, Vector3* ret) { 503 // TODO: Caching all the sin / cos values and store them in a look up table. 504 for (int i = 0; i < points; i++) { 505 double angle = 2 * i * M_PI / points; 506 ret[i].x = cosf(angle) * size + lightCenter.x; 507 ret[i].y = sinf(angle) * size + lightCenter.y; 508 ret[i].z = lightCenter.z; 509 } 510} 511 512/** 513* Generate the shadow from a spot light. 514* 515* @param poly x,y,z vertexes of a convex polygon that occludes the light source 516* @param polyLength number of vertexes of the occluding polygon 517* @param lightCenter the center of the light 518* @param lightSize the radius of the light source 519* @param lightVertexCount the vertex counter for the light polygon 520* @param shadowTriangleStrip return an (x,y,alpha) triangle strip representing the shadow. Return 521* empty strip if error. 522* 523*/ 524VertexBufferMode SpotShadow::createSpotShadow(bool isCasterOpaque, const Vector3* poly, 525 int polyLength, const Vector3& lightCenter, float lightSize, 526 int lightVertexCount, VertexBuffer& retStrips) { 527 Vector3 light[lightVertexCount * 3]; 528 computeLightPolygon(lightVertexCount, lightCenter, lightSize, light); 529 computeSpotShadow(isCasterOpaque, light, lightVertexCount, lightCenter, poly, 530 polyLength, retStrips); 531 return kVertexBufferMode_TwoPolyRingShadow; 532} 533 534/** 535 * Generate the shadow spot light of shape lightPoly and a object poly 536 * 537 * @param lightPoly x,y,z vertex of a convex polygon that is the light source 538 * @param lightPolyLength number of vertexes of the light source polygon 539 * @param poly x,y,z vertexes of a convex polygon that occludes the light source 540 * @param polyLength number of vertexes of the occluding polygon 541 * @param shadowTriangleStrip return an (x,y,alpha) triangle strip representing the shadow. Return 542 * empty strip if error. 543 */ 544void SpotShadow::computeSpotShadow(bool isCasterOpaque, const Vector3* lightPoly, 545 int lightPolyLength, const Vector3& lightCenter, const Vector3* poly, 546 int polyLength, VertexBuffer& shadowTriangleStrip) { 547 // Point clouds for all the shadowed vertices 548 Vector2 shadowRegion[lightPolyLength * polyLength]; 549 // Shadow polygon from one point light. 550 Vector2 outline[polyLength]; 551 Vector2 umbraMem[polyLength * lightPolyLength]; 552 Vector2* umbra = umbraMem; 553 554 int umbraLength = 0; 555 556 // Validate input, receiver is always at z = 0 plane. 557 bool inputPolyPositionValid = true; 558 for (int i = 0; i < polyLength; i++) { 559 if (poly[i].z >= lightPoly[0].z) { 560 inputPolyPositionValid = false; 561 ALOGW("polygon above the light"); 562 break; 563 } 564 } 565 566 // If the caster's position is invalid, don't draw anything. 567 if (!inputPolyPositionValid) { 568 return; 569 } 570 571 // Calculate the umbra polygon based on intersections of all outlines 572 int k = 0; 573 for (int j = 0; j < lightPolyLength; j++) { 574 int m = 0; 575 for (int i = 0; i < polyLength; i++) { 576 // After validating the input, deltaZ is guaranteed to be positive. 577 float deltaZ = lightPoly[j].z - poly[i].z; 578 float ratioZ = lightPoly[j].z / deltaZ; 579 float x = lightPoly[j].x - ratioZ * (lightPoly[j].x - poly[i].x); 580 float y = lightPoly[j].y - ratioZ * (lightPoly[j].y - poly[i].y); 581 582 Vector2 newPoint = Vector2(x, y); 583 shadowRegion[k] = newPoint; 584 outline[m] = newPoint; 585 586 k++; 587 m++; 588 } 589 590 // For the first light polygon's vertex, use the outline as the umbra. 591 // Later on, use the intersection of the outline and existing umbra. 592 if (umbraLength == 0) { 593 for (int i = 0; i < polyLength; i++) { 594 umbra[i] = outline[i]; 595 } 596 umbraLength = polyLength; 597 } else { 598 int col = ((j * 255) / lightPolyLength); 599 umbraLength = intersection(outline, polyLength, umbra, umbraLength); 600 if (umbraLength == 0) { 601 break; 602 } 603 } 604 } 605 606 // Generate the penumbra area using the hull of all shadow regions. 607 int shadowRegionLength = k; 608 Vector2 penumbra[k]; 609 int penumbraLength = hull(shadowRegion, shadowRegionLength, penumbra); 610 611 Vector2 fakeUmbra[polyLength]; 612 if (umbraLength < 3) { 613 // If there is no real umbra, make a fake one. 614 for (int i = 0; i < polyLength; i++) { 615 float deltaZ = lightCenter.z - poly[i].z; 616 float ratioZ = lightCenter.z / deltaZ; 617 float x = lightCenter.x - ratioZ * (lightCenter.x - poly[i].x); 618 float y = lightCenter.y - ratioZ * (lightCenter.y - poly[i].y); 619 620 fakeUmbra[i].x = x; 621 fakeUmbra[i].y = y; 622 } 623 624 // Shrink the centroid's shadow by 10%. 625 // TODO: Study the magic number of 10%. 626 Vector2 shadowCentroid = 627 ShadowTessellator::centroid2d(fakeUmbra, polyLength); 628 for (int i = 0; i < polyLength; i++) { 629 fakeUmbra[i] = shadowCentroid * (1.0f - SHADOW_SHRINK_SCALE) + 630 fakeUmbra[i] * SHADOW_SHRINK_SCALE; 631 } 632#if DEBUG_SHADOW 633 ALOGD("No real umbra make a fake one, centroid2d = %f , %f", 634 shadowCentroid.x, shadowCentroid.y); 635#endif 636 // Set the fake umbra, whose size is the same as the original polygon. 637 umbra = fakeUmbra; 638 umbraLength = polyLength; 639 } 640 641 generateTriangleStrip(isCasterOpaque, penumbra, penumbraLength, umbra, 642 umbraLength, poly, polyLength, shadowTriangleStrip); 643} 644 645/** 646 * Converts a polygon specified with CW vertices into an array of distance-from-centroid values. 647 * 648 * Returns false in error conditions 649 * 650 * @param poly Array of vertices. Note that these *must* be CW. 651 * @param polyLength The number of vertices in the polygon. 652 * @param polyCentroid The centroid of the polygon, from which rays will be cast 653 * @param rayDist The output array for the calculated distances, must be SHADOW_RAY_COUNT in size 654 */ 655bool convertPolyToRayDist(const Vector2* poly, int polyLength, const Vector2& polyCentroid, 656 float* rayDist) { 657 const int rays = SHADOW_RAY_COUNT; 658 const float step = M_PI * 2 / rays; 659 660 const Vector2* lastVertex = &(poly[polyLength - 1]); 661 float startAngle = angle(*lastVertex, polyCentroid); 662 663 // Start with the ray that's closest to and less than startAngle 664 int rayIndex = floor((startAngle - EPSILON) / step); 665 rayIndex = (rayIndex + rays) % rays; // ensure positive 666 667 for (int polyIndex = 0; polyIndex < polyLength; polyIndex++) { 668 /* 669 * For a given pair of vertices on the polygon, poly[i-1] and poly[i], the rays that 670 * intersect these will be those that are between the two angles from the centroid that the 671 * vertices define. 672 * 673 * Because the polygon vertices are stored clockwise, the closest ray with an angle 674 * *smaller* than that defined by angle(poly[i], centroid) will be the first ray that does 675 * not intersect with poly[i-1], poly[i]. 676 */ 677 float currentAngle = angle(poly[polyIndex], polyCentroid); 678 679 // find first ray that will not intersect the line segment poly[i-1] & poly[i] 680 int firstRayIndexOnNextSegment = floor((currentAngle - EPSILON) / step); 681 firstRayIndexOnNextSegment = (firstRayIndexOnNextSegment + rays) % rays; // ensure positive 682 683 // Iterate through all rays that intersect with poly[i-1], poly[i] line segment. 684 // This may be 0 rays. 685 while (rayIndex != firstRayIndexOnNextSegment) { 686 float distanceToIntersect = rayIntersectPoints(polyCentroid, 687 cos(rayIndex * step), 688 sin(rayIndex * step), 689 *lastVertex, poly[polyIndex]); 690 if (distanceToIntersect < 0) { 691#if DEBUG_SHADOW 692 ALOGW("ERROR: convertPolyToRayDist failed"); 693#endif 694 return false; // error case, abort 695 } 696 697 rayDist[rayIndex] = distanceToIntersect; 698 699 rayIndex = (rayIndex - 1 + rays) % rays; 700 } 701 lastVertex = &poly[polyIndex]; 702 } 703 704 return true; 705} 706 707int SpotShadow::calculateOccludedUmbra(const Vector2* umbra, int umbraLength, 708 const Vector3* poly, int polyLength, Vector2* occludedUmbra) { 709 // Occluded umbra area is computed as the intersection of the projected 2D 710 // poly and umbra. 711 for (int i = 0; i < polyLength; i++) { 712 occludedUmbra[i].x = poly[i].x; 713 occludedUmbra[i].y = poly[i].y; 714 } 715 716 // Both umbra and incoming polygon are guaranteed to be CW, so we can call 717 // intersection() directly. 718 return intersection(umbra, umbraLength, 719 occludedUmbra, polyLength); 720} 721 722#define OCLLUDED_UMBRA_SHRINK_FACTOR 0.95f 723/** 724 * Generate a triangle strip given two convex polygons 725 * 726 * @param penumbra The outer polygon x,y vertexes 727 * @param penumbraLength The number of vertexes in the outer polygon 728 * @param umbra The inner outer polygon x,y vertexes 729 * @param umbraLength The number of vertexes in the inner polygon 730 * @param shadowTriangleStrip return an (x,y,alpha) triangle strip representing the shadow. Return 731 * empty strip if error. 732**/ 733void SpotShadow::generateTriangleStrip(bool isCasterOpaque, const Vector2* penumbra, 734 int penumbraLength, const Vector2* umbra, int umbraLength, 735 const Vector3* poly, int polyLength, VertexBuffer& shadowTriangleStrip) { 736 const int rays = SHADOW_RAY_COUNT; 737 const int size = 2 * rays; 738 const float step = M_PI * 2 / rays; 739 // Centroid of the umbra. 740 Vector2 centroid = ShadowTessellator::centroid2d(umbra, umbraLength); 741#if DEBUG_SHADOW 742 ALOGD("centroid2d = %f , %f", centroid.x, centroid.y); 743#endif 744 // Intersection to the penumbra. 745 float penumbraDistPerRay[rays]; 746 // Intersection to the umbra. 747 float umbraDistPerRay[rays]; 748 // Intersection to the occluded umbra area. 749 float occludedUmbraDistPerRay[rays]; 750 751 // convert CW polygons to ray distance encoding, aborting on conversion failure 752 if (!convertPolyToRayDist(umbra, umbraLength, centroid, umbraDistPerRay)) return; 753 if (!convertPolyToRayDist(penumbra, penumbraLength, centroid, penumbraDistPerRay)) return; 754 755 bool hasOccludedUmbraArea = false; 756 if (isCasterOpaque) { 757 Vector2 occludedUmbra[polyLength + umbraLength]; 758 int occludedUmbraLength = calculateOccludedUmbra(umbra, umbraLength, poly, polyLength, 759 occludedUmbra); 760 // Make sure the centroid is inside the umbra, otherwise, fall back to the 761 // approach as if there is no occluded umbra area. 762 if (testPointInsidePolygon(centroid, occludedUmbra, occludedUmbraLength)) { 763 hasOccludedUmbraArea = true; 764 // Shrink the occluded umbra area to avoid pixel level artifacts. 765 for (int i = 0; i < occludedUmbraLength; i ++) { 766 occludedUmbra[i] = centroid + (occludedUmbra[i] - centroid) * 767 OCLLUDED_UMBRA_SHRINK_FACTOR; 768 } 769 if (!convertPolyToRayDist(occludedUmbra, occludedUmbraLength, centroid, 770 occludedUmbraDistPerRay)) { 771 return; 772 } 773 } 774 } 775 776 AlphaVertex* shadowVertices = 777 shadowTriangleStrip.alloc<AlphaVertex>(SHADOW_VERTEX_COUNT); 778 779 // Calculate the vertices (x, y, alpha) in the shadow area. 780 AlphaVertex centroidXYA; 781 AlphaVertex::set(¢roidXYA, centroid.x, centroid.y, 1.0f); 782 for (int rayIndex = 0; rayIndex < rays; rayIndex++) { 783 float dx = cosf(step * rayIndex); 784 float dy = sinf(step * rayIndex); 785 786 // penumbra ring 787 float penumbraDistance = penumbraDistPerRay[rayIndex]; 788 AlphaVertex::set(&shadowVertices[rayIndex], 789 dx * penumbraDistance + centroid.x, 790 dy * penumbraDistance + centroid.y, 0.0f); 791 792 // umbra ring 793 float umbraDistance = umbraDistPerRay[rayIndex]; 794 AlphaVertex::set(&shadowVertices[rays + rayIndex], 795 dx * umbraDistance + centroid.x, dy * umbraDistance + centroid.y, 1.0f); 796 797 // occluded umbra ring 798 if (hasOccludedUmbraArea) { 799 float occludedUmbraDistance = occludedUmbraDistPerRay[rayIndex]; 800 AlphaVertex::set(&shadowVertices[2 * rays + rayIndex], 801 dx * occludedUmbraDistance + centroid.x, 802 dy * occludedUmbraDistance + centroid.y, 1.0f); 803 } else { 804 // Put all vertices of the occluded umbra ring at the centroid. 805 shadowVertices[2 * rays + rayIndex] = centroidXYA; 806 } 807 } 808} 809 810/** 811 * This is only for experimental purpose. 812 * After intersections are calculated, we could smooth the polygon if needed. 813 * So far, we don't think it is more appealing yet. 814 * 815 * @param level The level of smoothness. 816 * @param rays The total number of rays. 817 * @param rayDist (In and Out) The distance for each ray. 818 * 819 */ 820void SpotShadow::smoothPolygon(int level, int rays, float* rayDist) { 821 for (int k = 0; k < level; k++) { 822 for (int i = 0; i < rays; i++) { 823 float p1 = rayDist[(rays - 1 + i) % rays]; 824 float p2 = rayDist[i]; 825 float p3 = rayDist[(i + 1) % rays]; 826 rayDist[i] = (p1 + p2 * 2 + p3) / 4; 827 } 828 } 829} 830 831#if DEBUG_SHADOW 832 833#define TEST_POINT_NUMBER 128 834 835/** 836 * Calculate the bounds for generating random test points. 837 */ 838void SpotShadow::updateBound(const Vector2 inVector, Vector2& lowerBound, 839 Vector2& upperBound ) { 840 if (inVector.x < lowerBound.x) { 841 lowerBound.x = inVector.x; 842 } 843 844 if (inVector.y < lowerBound.y) { 845 lowerBound.y = inVector.y; 846 } 847 848 if (inVector.x > upperBound.x) { 849 upperBound.x = inVector.x; 850 } 851 852 if (inVector.y > upperBound.y) { 853 upperBound.y = inVector.y; 854 } 855} 856 857/** 858 * For debug purpose, when things go wrong, dump the whole polygon data. 859 */ 860static void dumpPolygon(const Vector2* poly, int polyLength, const char* polyName) { 861 for (int i = 0; i < polyLength; i++) { 862 ALOGD("polygon %s i %d x %f y %f", polyName, i, poly[i].x, poly[i].y); 863 } 864} 865 866/** 867 * Test whether the polygon is convex. 868 */ 869bool SpotShadow::testConvex(const Vector2* polygon, int polygonLength, 870 const char* name) { 871 bool isConvex = true; 872 for (int i = 0; i < polygonLength; i++) { 873 Vector2 start = polygon[i]; 874 Vector2 middle = polygon[(i + 1) % polygonLength]; 875 Vector2 end = polygon[(i + 2) % polygonLength]; 876 877 double delta = (double(middle.x) - start.x) * (double(end.y) - start.y) - 878 (double(middle.y) - start.y) * (double(end.x) - start.x); 879 bool isCCWOrCoLinear = (delta >= EPSILON); 880 881 if (isCCWOrCoLinear) { 882 ALOGW("(Error Type 2): polygon (%s) is not a convex b/c start (x %f, y %f)," 883 "middle (x %f, y %f) and end (x %f, y %f) , delta is %f !!!", 884 name, start.x, start.y, middle.x, middle.y, end.x, end.y, delta); 885 isConvex = false; 886 break; 887 } 888 } 889 return isConvex; 890} 891 892/** 893 * Test whether or not the polygon (intersection) is within the 2 input polygons. 894 * Using Marte Carlo method, we generate a random point, and if it is inside the 895 * intersection, then it must be inside both source polygons. 896 */ 897void SpotShadow::testIntersection(const Vector2* poly1, int poly1Length, 898 const Vector2* poly2, int poly2Length, 899 const Vector2* intersection, int intersectionLength) { 900 // Find the min and max of x and y. 901 Vector2 lowerBound(FLT_MAX, FLT_MAX); 902 Vector2 upperBound(-FLT_MAX, -FLT_MAX); 903 for (int i = 0; i < poly1Length; i++) { 904 updateBound(poly1[i], lowerBound, upperBound); 905 } 906 for (int i = 0; i < poly2Length; i++) { 907 updateBound(poly2[i], lowerBound, upperBound); 908 } 909 910 bool dumpPoly = false; 911 for (int k = 0; k < TEST_POINT_NUMBER; k++) { 912 // Generate a random point between minX, minY and maxX, maxY. 913 double randomX = rand() / double(RAND_MAX); 914 double randomY = rand() / double(RAND_MAX); 915 916 Vector2 testPoint; 917 testPoint.x = lowerBound.x + randomX * (upperBound.x - lowerBound.x); 918 testPoint.y = lowerBound.y + randomY * (upperBound.y - lowerBound.y); 919 920 // If the random point is in both poly 1 and 2, then it must be intersection. 921 if (testPointInsidePolygon(testPoint, intersection, intersectionLength)) { 922 if (!testPointInsidePolygon(testPoint, poly1, poly1Length)) { 923 dumpPoly = true; 924 ALOGW("(Error Type 1): one point (%f, %f) in the intersection is" 925 " not in the poly1", 926 testPoint.x, testPoint.y); 927 } 928 929 if (!testPointInsidePolygon(testPoint, poly2, poly2Length)) { 930 dumpPoly = true; 931 ALOGW("(Error Type 1): one point (%f, %f) in the intersection is" 932 " not in the poly2", 933 testPoint.x, testPoint.y); 934 } 935 } 936 } 937 938 if (dumpPoly) { 939 dumpPolygon(intersection, intersectionLength, "intersection"); 940 for (int i = 1; i < intersectionLength; i++) { 941 Vector2 delta = intersection[i] - intersection[i - 1]; 942 ALOGD("Intersetion i, %d Vs i-1 is delta %f", i, delta.lengthSquared()); 943 } 944 945 dumpPolygon(poly1, poly1Length, "poly 1"); 946 dumpPolygon(poly2, poly2Length, "poly 2"); 947 } 948} 949#endif 950 951}; // namespace uirenderer 952}; // namespace android 953