SpotShadow.cpp revision 50ecf849cb7ccc3482517b74d2214b347927791e
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) return -1.0f; // error, doesn't intersect between points 66#endif 67 68 double distance = (p1.x * (rayOrigin.y - p2.y) + p2.x * (p1.y - rayOrigin.y) + 69 rayOrigin.x * (p2.y - p1.y)) / divisor; 70 71 return distance; // may be negative in error cases 72} 73 74/** 75 * Sort points by their X coordinates 76 * 77 * @param points the points as a Vector2 array. 78 * @param pointsLength the number of vertices of the polygon. 79 */ 80void SpotShadow::xsort(Vector2* points, int pointsLength) { 81 quicksortX(points, 0, pointsLength - 1); 82} 83 84/** 85 * compute the convex hull of a collection of Points 86 * 87 * @param points the points as a Vector2 array. 88 * @param pointsLength the number of vertices of the polygon. 89 * @param retPoly pre allocated array of floats to put the vertices 90 * @return the number of points in the polygon 0 if no intersection 91 */ 92int SpotShadow::hull(Vector2* points, int pointsLength, Vector2* retPoly) { 93 xsort(points, pointsLength); 94 int n = pointsLength; 95 Vector2 lUpper[n]; 96 lUpper[0] = points[0]; 97 lUpper[1] = points[1]; 98 99 int lUpperSize = 2; 100 101 for (int i = 2; i < n; i++) { 102 lUpper[lUpperSize] = points[i]; 103 lUpperSize++; 104 105 while (lUpperSize > 2 && !ccw( 106 lUpper[lUpperSize - 3].x, lUpper[lUpperSize - 3].y, 107 lUpper[lUpperSize - 2].x, lUpper[lUpperSize - 2].y, 108 lUpper[lUpperSize - 1].x, lUpper[lUpperSize - 1].y)) { 109 // Remove the middle point of the three last 110 lUpper[lUpperSize - 2].x = lUpper[lUpperSize - 1].x; 111 lUpper[lUpperSize - 2].y = lUpper[lUpperSize - 1].y; 112 lUpperSize--; 113 } 114 } 115 116 Vector2 lLower[n]; 117 lLower[0] = points[n - 1]; 118 lLower[1] = points[n - 2]; 119 120 int lLowerSize = 2; 121 122 for (int i = n - 3; i >= 0; i--) { 123 lLower[lLowerSize] = points[i]; 124 lLowerSize++; 125 126 while (lLowerSize > 2 && !ccw( 127 lLower[lLowerSize - 3].x, lLower[lLowerSize - 3].y, 128 lLower[lLowerSize - 2].x, lLower[lLowerSize - 2].y, 129 lLower[lLowerSize - 1].x, lLower[lLowerSize - 1].y)) { 130 // Remove the middle point of the three last 131 lLower[lLowerSize - 2] = lLower[lLowerSize - 1]; 132 lLowerSize--; 133 } 134 } 135 136 // output points in CW ordering 137 const int total = lUpperSize + lLowerSize - 2; 138 int outIndex = total - 1; 139 for (int i = 0; i < lUpperSize; i++) { 140 retPoly[outIndex] = lUpper[i]; 141 outIndex--; 142 } 143 144 for (int i = 1; i < lLowerSize - 1; i++) { 145 retPoly[outIndex] = lLower[i]; 146 outIndex--; 147 } 148 // TODO: Add test harness which verify that all the points are inside the hull. 149 return total; 150} 151 152/** 153 * Test whether the 3 points form a counter clockwise turn. 154 * 155 * @return true if a right hand turn 156 */ 157bool SpotShadow::ccw(double ax, double ay, double bx, double by, 158 double cx, double cy) { 159 return (bx - ax) * (cy - ay) - (by - ay) * (cx - ax) > EPSILON; 160} 161 162/** 163 * Calculates the intersection of poly1 with poly2 and put in poly2. 164 * Note that both poly1 and poly2 must be in CW order already! 165 * 166 * @param poly1 The 1st polygon, as a Vector2 array. 167 * @param poly1Length The number of vertices of 1st polygon. 168 * @param poly2 The 2nd and output polygon, as a Vector2 array. 169 * @param poly2Length The number of vertices of 2nd polygon. 170 * @return number of vertices in output polygon as poly2. 171 */ 172int SpotShadow::intersection(const Vector2* poly1, int poly1Length, 173 Vector2* poly2, int poly2Length) { 174#if DEBUG_SHADOW 175 if (!isClockwise(poly1, poly1Length)) { 176 ALOGW("Poly1 is not clockwise! Intersection is wrong!"); 177 } 178 if (!isClockwise(poly2, poly2Length)) { 179 ALOGW("Poly2 is not clockwise! Intersection is wrong!"); 180 } 181#endif 182 Vector2 poly[poly1Length * poly2Length + 2]; 183 int count = 0; 184 int pcount = 0; 185 186 // If one vertex from one polygon sits inside another polygon, add it and 187 // count them. 188 for (int i = 0; i < poly1Length; i++) { 189 if (testPointInsidePolygon(poly1[i], poly2, poly2Length)) { 190 poly[count] = poly1[i]; 191 count++; 192 pcount++; 193 194 } 195 } 196 197 int insidePoly2 = pcount; 198 for (int i = 0; i < poly2Length; i++) { 199 if (testPointInsidePolygon(poly2[i], poly1, poly1Length)) { 200 poly[count] = poly2[i]; 201 count++; 202 } 203 } 204 205 int insidePoly1 = count - insidePoly2; 206 // If all vertices from poly1 are inside poly2, then just return poly1. 207 if (insidePoly2 == poly1Length) { 208 memcpy(poly2, poly1, poly1Length * sizeof(Vector2)); 209 return poly1Length; 210 } 211 212 // If all vertices from poly2 are inside poly1, then just return poly2. 213 if (insidePoly1 == poly2Length) { 214 return poly2Length; 215 } 216 217 // Since neither polygon fully contain the other one, we need to add all the 218 // intersection points. 219 Vector2 intersection; 220 for (int i = 0; i < poly2Length; i++) { 221 for (int j = 0; j < poly1Length; j++) { 222 int poly2LineStart = i; 223 int poly2LineEnd = ((i + 1) % poly2Length); 224 int poly1LineStart = j; 225 int poly1LineEnd = ((j + 1) % poly1Length); 226 bool found = lineIntersection( 227 poly2[poly2LineStart].x, poly2[poly2LineStart].y, 228 poly2[poly2LineEnd].x, poly2[poly2LineEnd].y, 229 poly1[poly1LineStart].x, poly1[poly1LineStart].y, 230 poly1[poly1LineEnd].x, poly1[poly1LineEnd].y, 231 intersection); 232 if (found) { 233 poly[count].x = intersection.x; 234 poly[count].y = intersection.y; 235 count++; 236 } else { 237 Vector2 delta = poly2[i] - poly1[j]; 238 if (delta.lengthSquared() < EPSILON) { 239 poly[count] = poly2[i]; 240 count++; 241 } 242 } 243 } 244 } 245 246 if (count == 0) { 247 return 0; 248 } 249 250 // Sort the result polygon around the center. 251 Vector2 center(0.0f, 0.0f); 252 for (int i = 0; i < count; i++) { 253 center += poly[i]; 254 } 255 center /= count; 256 sort(poly, count, center); 257 258#if DEBUG_SHADOW 259 // Since poly2 is overwritten as the result, we need to save a copy to do 260 // our verification. 261 Vector2 oldPoly2[poly2Length]; 262 int oldPoly2Length = poly2Length; 263 memcpy(oldPoly2, poly2, sizeof(Vector2) * poly2Length); 264#endif 265 266 // Filter the result out from poly and put it into poly2. 267 poly2[0] = poly[0]; 268 int lastOutputIndex = 0; 269 for (int i = 1; i < count; i++) { 270 Vector2 delta = poly[i] - poly2[lastOutputIndex]; 271 if (delta.lengthSquared() >= EPSILON) { 272 poly2[++lastOutputIndex] = poly[i]; 273 } else { 274 // If the vertices are too close, pick the inner one, because the 275 // inner one is more likely to be an intersection point. 276 Vector2 delta1 = poly[i] - center; 277 Vector2 delta2 = poly2[lastOutputIndex] - center; 278 if (delta1.lengthSquared() < delta2.lengthSquared()) { 279 poly2[lastOutputIndex] = poly[i]; 280 } 281 } 282 } 283 int resultLength = lastOutputIndex + 1; 284 285#if DEBUG_SHADOW 286 testConvex(poly2, resultLength, "intersection"); 287 testConvex(poly1, poly1Length, "input poly1"); 288 testConvex(oldPoly2, oldPoly2Length, "input poly2"); 289 290 testIntersection(poly1, poly1Length, oldPoly2, oldPoly2Length, poly2, resultLength); 291#endif 292 293 return resultLength; 294} 295 296/** 297 * Sort points about a center point 298 * 299 * @param poly The in and out polyogon as a Vector2 array. 300 * @param polyLength The number of vertices of the polygon. 301 * @param center the center ctr[0] = x , ctr[1] = y to sort around. 302 */ 303void SpotShadow::sort(Vector2* poly, int polyLength, const Vector2& center) { 304 quicksortCirc(poly, 0, polyLength - 1, center); 305} 306 307/** 308 * Swap points pointed to by i and j 309 */ 310void SpotShadow::swap(Vector2* points, int i, int j) { 311 Vector2 temp = points[i]; 312 points[i] = points[j]; 313 points[j] = temp; 314} 315 316/** 317 * quick sort implementation about the center. 318 */ 319void SpotShadow::quicksortCirc(Vector2* points, int low, int high, 320 const Vector2& center) { 321 int i = low, j = high; 322 int p = low + (high - low) / 2; 323 float pivot = angle(points[p], center); 324 while (i <= j) { 325 while (angle(points[i], center) > pivot) { 326 i++; 327 } 328 while (angle(points[j], center) < pivot) { 329 j--; 330 } 331 332 if (i <= j) { 333 swap(points, i, j); 334 i++; 335 j--; 336 } 337 } 338 if (low < j) quicksortCirc(points, low, j, center); 339 if (i < high) quicksortCirc(points, i, high, center); 340} 341 342/** 343 * Sort points by x axis 344 * 345 * @param points points to sort 346 * @param low start index 347 * @param high end index 348 */ 349void SpotShadow::quicksortX(Vector2* points, int low, int high) { 350 int i = low, j = high; 351 int p = low + (high - low) / 2; 352 float pivot = points[p].x; 353 while (i <= j) { 354 while (points[i].x < pivot) { 355 i++; 356 } 357 while (points[j].x > pivot) { 358 j--; 359 } 360 361 if (i <= j) { 362 swap(points, i, j); 363 i++; 364 j--; 365 } 366 } 367 if (low < j) quicksortX(points, low, j); 368 if (i < high) quicksortX(points, i, high); 369} 370 371/** 372 * Test whether a point is inside the polygon. 373 * 374 * @param testPoint the point to test 375 * @param poly the polygon 376 * @return true if the testPoint is inside the poly. 377 */ 378bool SpotShadow::testPointInsidePolygon(const Vector2 testPoint, 379 const Vector2* poly, int len) { 380 bool c = false; 381 double testx = testPoint.x; 382 double testy = testPoint.y; 383 for (int i = 0, j = len - 1; i < len; j = i++) { 384 double startX = poly[j].x; 385 double startY = poly[j].y; 386 double endX = poly[i].x; 387 double endY = poly[i].y; 388 389 if (((endY > testy) != (startY > testy)) && 390 (testx < (startX - endX) * (testy - endY) 391 / (startY - endY) + endX)) { 392 c = !c; 393 } 394 } 395 return c; 396} 397 398/** 399 * Make the polygon turn clockwise. 400 * 401 * @param polygon the polygon as a Vector2 array. 402 * @param len the number of points of the polygon 403 */ 404void SpotShadow::makeClockwise(Vector2* polygon, int len) { 405 if (polygon == 0 || len == 0) { 406 return; 407 } 408 if (!isClockwise(polygon, len)) { 409 reverse(polygon, len); 410 } 411} 412 413/** 414 * Test whether the polygon is order in clockwise. 415 * 416 * @param polygon the polygon as a Vector2 array 417 * @param len the number of points of the polygon 418 */ 419bool SpotShadow::isClockwise(const Vector2* polygon, int len) { 420 double sum = 0; 421 double p1x = polygon[len - 1].x; 422 double p1y = polygon[len - 1].y; 423 for (int i = 0; i < len; i++) { 424 425 double p2x = polygon[i].x; 426 double p2y = polygon[i].y; 427 sum += p1x * p2y - p2x * p1y; 428 p1x = p2x; 429 p1y = p2y; 430 } 431 return sum < 0; 432} 433 434/** 435 * Reverse the polygon 436 * 437 * @param polygon the polygon as a Vector2 array 438 * @param len the number of points of the polygon 439 */ 440void SpotShadow::reverse(Vector2* polygon, int len) { 441 int n = len / 2; 442 for (int i = 0; i < n; i++) { 443 Vector2 tmp = polygon[i]; 444 int k = len - 1 - i; 445 polygon[i] = polygon[k]; 446 polygon[k] = tmp; 447 } 448} 449 450/** 451 * Intersects two lines in parametric form. This function is called in a tight 452 * loop, and we need double precision to get things right. 453 * 454 * @param x1 the x coordinate point 1 of line 1 455 * @param y1 the y coordinate point 1 of line 1 456 * @param x2 the x coordinate point 2 of line 1 457 * @param y2 the y coordinate point 2 of line 1 458 * @param x3 the x coordinate point 1 of line 2 459 * @param y3 the y coordinate point 1 of line 2 460 * @param x4 the x coordinate point 2 of line 2 461 * @param y4 the y coordinate point 2 of line 2 462 * @param ret the x,y location of the intersection 463 * @return true if it found an intersection 464 */ 465inline bool SpotShadow::lineIntersection(double x1, double y1, double x2, double y2, 466 double x3, double y3, double x4, double y4, Vector2& ret) { 467 double d = (x1 - x2) * (y3 - y4) - (y1 - y2) * (x3 - x4); 468 if (d == 0.0) return false; 469 470 double dx = (x1 * y2 - y1 * x2); 471 double dy = (x3 * y4 - y3 * x4); 472 double x = (dx * (x3 - x4) - (x1 - x2) * dy) / d; 473 double y = (dx * (y3 - y4) - (y1 - y2) * dy) / d; 474 475 // The intersection should be in the middle of the point 1 and point 2, 476 // likewise point 3 and point 4. 477 if (((x - x1) * (x - x2) > EPSILON) 478 || ((x - x3) * (x - x4) > EPSILON) 479 || ((y - y1) * (y - y2) > EPSILON) 480 || ((y - y3) * (y - y4) > EPSILON)) { 481 // Not interesected 482 return false; 483 } 484 ret.x = x; 485 ret.y = y; 486 return true; 487 488} 489 490/** 491 * Compute a horizontal circular polygon about point (x , y , height) of radius 492 * (size) 493 * 494 * @param points number of the points of the output polygon. 495 * @param lightCenter the center of the light. 496 * @param size the light size. 497 * @param ret result polygon. 498 */ 499void SpotShadow::computeLightPolygon(int points, const Vector3& lightCenter, 500 float size, Vector3* ret) { 501 // TODO: Caching all the sin / cos values and store them in a look up table. 502 for (int i = 0; i < points; i++) { 503 double angle = 2 * i * M_PI / points; 504 ret[i].x = cosf(angle) * size + lightCenter.x; 505 ret[i].y = sinf(angle) * size + lightCenter.y; 506 ret[i].z = lightCenter.z; 507 } 508} 509 510/** 511* Generate the shadow from a spot light. 512* 513* @param poly x,y,z vertexes of a convex polygon that occludes the light source 514* @param polyLength number of vertexes of the occluding polygon 515* @param lightCenter the center of the light 516* @param lightSize the radius of the light source 517* @param lightVertexCount the vertex counter for the light polygon 518* @param shadowTriangleStrip return an (x,y,alpha) triangle strip representing the shadow. Return 519* empty strip if error. 520* 521*/ 522VertexBufferMode SpotShadow::createSpotShadow(bool isCasterOpaque, const Vector3* poly, 523 int polyLength, const Vector3& lightCenter, float lightSize, 524 int lightVertexCount, VertexBuffer& retStrips) { 525 Vector3 light[lightVertexCount * 3]; 526 computeLightPolygon(lightVertexCount, lightCenter, lightSize, light); 527 computeSpotShadow(isCasterOpaque, light, lightVertexCount, lightCenter, poly, 528 polyLength, retStrips); 529 return kVertexBufferMode_TwoPolyRingShadow; 530} 531 532/** 533 * Generate the shadow spot light of shape lightPoly and a object poly 534 * 535 * @param lightPoly x,y,z vertex of a convex polygon that is the light source 536 * @param lightPolyLength number of vertexes of the light source polygon 537 * @param poly x,y,z vertexes of a convex polygon that occludes the light source 538 * @param polyLength number of vertexes of the occluding polygon 539 * @param shadowTriangleStrip return an (x,y,alpha) triangle strip representing the shadow. Return 540 * empty strip if error. 541 */ 542void SpotShadow::computeSpotShadow(bool isCasterOpaque, const Vector3* lightPoly, 543 int lightPolyLength, const Vector3& lightCenter, const Vector3* poly, 544 int polyLength, VertexBuffer& shadowTriangleStrip) { 545 // Point clouds for all the shadowed vertices 546 Vector2 shadowRegion[lightPolyLength * polyLength]; 547 // Shadow polygon from one point light. 548 Vector2 outline[polyLength]; 549 Vector2 umbraMem[polyLength * lightPolyLength]; 550 Vector2* umbra = umbraMem; 551 552 int umbraLength = 0; 553 554 // Validate input, receiver is always at z = 0 plane. 555 bool inputPolyPositionValid = true; 556 for (int i = 0; i < polyLength; i++) { 557 if (poly[i].z >= lightPoly[0].z) { 558 inputPolyPositionValid = false; 559 ALOGW("polygon above the light"); 560 break; 561 } 562 } 563 564 // If the caster's position is invalid, don't draw anything. 565 if (!inputPolyPositionValid) { 566 return; 567 } 568 569 // Calculate the umbra polygon based on intersections of all outlines 570 int k = 0; 571 for (int j = 0; j < lightPolyLength; j++) { 572 int m = 0; 573 for (int i = 0; i < polyLength; i++) { 574 float deltaZ = lightPoly[j].z - poly[i].z; 575 if (deltaZ == 0) { 576 return; 577 } 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 if (deltaZ == 0) { 617 return; 618 } 619 float ratioZ = lightCenter.z / deltaZ; 620 float x = lightCenter.x - ratioZ * (lightCenter.x - poly[i].x); 621 float y = lightCenter.y - ratioZ * (lightCenter.y - poly[i].y); 622 623 fakeUmbra[i].x = x; 624 fakeUmbra[i].y = y; 625 } 626 627 // Shrink the centroid's shadow by 10%. 628 // TODO: Study the magic number of 10%. 629 Vector2 shadowCentroid = 630 ShadowTessellator::centroid2d(fakeUmbra, polyLength); 631 for (int i = 0; i < polyLength; i++) { 632 fakeUmbra[i] = shadowCentroid * (1.0f - SHADOW_SHRINK_SCALE) + 633 fakeUmbra[i] * SHADOW_SHRINK_SCALE; 634 } 635#if DEBUG_SHADOW 636 ALOGD("No real umbra make a fake one, centroid2d = %f , %f", 637 shadowCentroid.x, shadowCentroid.y); 638#endif 639 // Set the fake umbra, whose size is the same as the original polygon. 640 umbra = fakeUmbra; 641 umbraLength = polyLength; 642 } 643 644 generateTriangleStrip(isCasterOpaque, penumbra, penumbraLength, umbra, 645 umbraLength, poly, polyLength, shadowTriangleStrip); 646} 647 648/** 649 * Converts a polygon specified with CW vertices into an array of distance-from-centroid values. 650 * 651 * Returns false in error conditions 652 * 653 * @param poly Array of vertices. Note that these *must* be CW. 654 * @param polyLength The number of vertices in the polygon. 655 * @param polyCentroid The centroid of the polygon, from which rays will be cast 656 * @param rayDist The output array for the calculated distances, must be SHADOW_RAY_COUNT in size 657 */ 658bool convertPolyToRayDist(const Vector2* poly, int polyLength, const Vector2& polyCentroid, 659 float* rayDist) { 660 const int rays = SHADOW_RAY_COUNT; 661 const float step = M_PI * 2 / rays; 662 663 const Vector2* lastVertex = &(poly[polyLength - 1]); 664 float startAngle = angle(*lastVertex, polyCentroid); 665 666 // Start with the ray that's closest to and less than startAngle 667 int rayIndex = floor((startAngle - EPSILON) / step); 668 rayIndex = (rayIndex + rays) % rays; // ensure positive 669 670 for (int polyIndex = 0; polyIndex < polyLength; polyIndex++) { 671 /* 672 * For a given pair of vertices on the polygon, poly[i-1] and poly[i], the rays that 673 * intersect these will be those that are between the two angles from the centroid that the 674 * vertices define. 675 * 676 * Because the polygon vertices are stored clockwise, the closest ray with an angle 677 * *smaller* than that defined by angle(poly[i], centroid) will be the first ray that does 678 * not intersect with poly[i-1], poly[i]. 679 */ 680 float currentAngle = angle(poly[polyIndex], polyCentroid); 681 682 // find first ray that will not intersect the line segment poly[i-1] & poly[i] 683 int firstRayIndexOnNextSegment = floor((currentAngle - EPSILON) / step); 684 firstRayIndexOnNextSegment = (firstRayIndexOnNextSegment + rays) % rays; // ensure positive 685 686 // Iterate through all rays that intersect with poly[i-1], poly[i] line segment. 687 // This may be 0 rays. 688 while (rayIndex != firstRayIndexOnNextSegment) { 689 float distanceToIntersect = rayIntersectPoints(polyCentroid, 690 cos(rayIndex * step), 691 sin(rayIndex * step), 692 *lastVertex, poly[polyIndex]); 693 if (distanceToIntersect < 0) { 694#if DEBUG_SHADOW 695 ALOGW("ERROR: convertPolyToRayDist failed"); 696#endif 697 return false; // error case, abort 698 } 699 700 rayDist[rayIndex] = distanceToIntersect; 701 702 rayIndex = (rayIndex - 1 + rays) % rays; 703 } 704 lastVertex = &poly[polyIndex]; 705 } 706 707 return true; 708} 709 710int SpotShadow::calculateOccludedUmbra(const Vector2* umbra, int umbraLength, 711 const Vector3* poly, int polyLength, Vector2* occludedUmbra) { 712 // Occluded umbra area is computed as the intersection of the projected 2D 713 // poly and umbra. 714 for (int i = 0; i < polyLength; i++) { 715 occludedUmbra[i].x = poly[i].x; 716 occludedUmbra[i].y = poly[i].y; 717 } 718 719 // Both umbra and incoming polygon are guaranteed to be CW, so we can call 720 // intersection() directly. 721 return intersection(umbra, umbraLength, 722 occludedUmbra, polyLength); 723} 724 725#define OCLLUDED_UMBRA_SHRINK_FACTOR 0.95f 726/** 727 * Generate a triangle strip given two convex polygons 728 * 729 * @param penumbra The outer polygon x,y vertexes 730 * @param penumbraLength The number of vertexes in the outer polygon 731 * @param umbra The inner outer polygon x,y vertexes 732 * @param umbraLength The number of vertexes in the inner polygon 733 * @param shadowTriangleStrip return an (x,y,alpha) triangle strip representing the shadow. Return 734 * empty strip if error. 735**/ 736void SpotShadow::generateTriangleStrip(bool isCasterOpaque, const Vector2* penumbra, 737 int penumbraLength, const Vector2* umbra, int umbraLength, 738 const Vector3* poly, int polyLength, VertexBuffer& shadowTriangleStrip) { 739 const int rays = SHADOW_RAY_COUNT; 740 const int size = 2 * rays; 741 const float step = M_PI * 2 / rays; 742 // Centroid of the umbra. 743 Vector2 centroid = ShadowTessellator::centroid2d(umbra, umbraLength); 744#if DEBUG_SHADOW 745 ALOGD("centroid2d = %f , %f", centroid.x, centroid.y); 746#endif 747 // Intersection to the penumbra. 748 float penumbraDistPerRay[rays]; 749 // Intersection to the umbra. 750 float umbraDistPerRay[rays]; 751 // Intersection to the occluded umbra area. 752 float occludedUmbraDistPerRay[rays]; 753 754 // convert CW polygons to ray distance encoding, aborting on conversion failure 755 if (!convertPolyToRayDist(umbra, umbraLength, centroid, umbraDistPerRay)) return; 756 if (!convertPolyToRayDist(penumbra, penumbraLength, centroid, penumbraDistPerRay)) return; 757 758 bool hasOccludedUmbraArea = false; 759 if (isCasterOpaque) { 760 Vector2 occludedUmbra[polyLength + umbraLength]; 761 int occludedUmbraLength = calculateOccludedUmbra(umbra, umbraLength, poly, polyLength, 762 occludedUmbra); 763 // Make sure the centroid is inside the umbra, otherwise, fall back to the 764 // approach as if there is no occluded umbra area. 765 if (testPointInsidePolygon(centroid, occludedUmbra, occludedUmbraLength)) { 766 hasOccludedUmbraArea = true; 767 // Shrink the occluded umbra area to avoid pixel level artifacts. 768 for (int i = 0; i < occludedUmbraLength; i ++) { 769 occludedUmbra[i] = centroid + (occludedUmbra[i] - centroid) * 770 OCLLUDED_UMBRA_SHRINK_FACTOR; 771 } 772 if (!convertPolyToRayDist(occludedUmbra, occludedUmbraLength, centroid, 773 occludedUmbraDistPerRay)) { 774 return; 775 } 776 } 777 } 778 779 AlphaVertex* shadowVertices = 780 shadowTriangleStrip.alloc<AlphaVertex>(SHADOW_VERTEX_COUNT); 781 782 // Calculate the vertices (x, y, alpha) in the shadow area. 783 AlphaVertex centroidXYA; 784 AlphaVertex::set(¢roidXYA, centroid.x, centroid.y, 1.0f); 785 for (int rayIndex = 0; rayIndex < rays; rayIndex++) { 786 float dx = cosf(step * rayIndex); 787 float dy = sinf(step * rayIndex); 788 789 // penumbra ring 790 float penumbraDistance = penumbraDistPerRay[rayIndex]; 791 AlphaVertex::set(&shadowVertices[rayIndex], 792 dx * penumbraDistance + centroid.x, 793 dy * penumbraDistance + centroid.y, 0.0f); 794 795 // umbra ring 796 float umbraDistance = umbraDistPerRay[rayIndex]; 797 AlphaVertex::set(&shadowVertices[rays + rayIndex], 798 dx * umbraDistance + centroid.x, dy * umbraDistance + centroid.y, 1.0f); 799 800 // occluded umbra ring 801 if (hasOccludedUmbraArea) { 802 float occludedUmbraDistance = occludedUmbraDistPerRay[rayIndex]; 803 AlphaVertex::set(&shadowVertices[2 * rays + rayIndex], 804 dx * occludedUmbraDistance + centroid.x, 805 dy * occludedUmbraDistance + centroid.y, 1.0f); 806 } else { 807 // Put all vertices of the occluded umbra ring at the centroid. 808 shadowVertices[2 * rays + rayIndex] = centroidXYA; 809 } 810 } 811} 812 813/** 814 * This is only for experimental purpose. 815 * After intersections are calculated, we could smooth the polygon if needed. 816 * So far, we don't think it is more appealing yet. 817 * 818 * @param level The level of smoothness. 819 * @param rays The total number of rays. 820 * @param rayDist (In and Out) The distance for each ray. 821 * 822 */ 823void SpotShadow::smoothPolygon(int level, int rays, float* rayDist) { 824 for (int k = 0; k < level; k++) { 825 for (int i = 0; i < rays; i++) { 826 float p1 = rayDist[(rays - 1 + i) % rays]; 827 float p2 = rayDist[i]; 828 float p3 = rayDist[(i + 1) % rays]; 829 rayDist[i] = (p1 + p2 * 2 + p3) / 4; 830 } 831 } 832} 833 834#if DEBUG_SHADOW 835 836#define TEST_POINT_NUMBER 128 837 838/** 839 * Calculate the bounds for generating random test points. 840 */ 841void SpotShadow::updateBound(const Vector2 inVector, Vector2& lowerBound, 842 Vector2& upperBound ) { 843 if (inVector.x < lowerBound.x) { 844 lowerBound.x = inVector.x; 845 } 846 847 if (inVector.y < lowerBound.y) { 848 lowerBound.y = inVector.y; 849 } 850 851 if (inVector.x > upperBound.x) { 852 upperBound.x = inVector.x; 853 } 854 855 if (inVector.y > upperBound.y) { 856 upperBound.y = inVector.y; 857 } 858} 859 860/** 861 * For debug purpose, when things go wrong, dump the whole polygon data. 862 */ 863static void dumpPolygon(const Vector2* poly, int polyLength, const char* polyName) { 864 for (int i = 0; i < polyLength; i++) { 865 ALOGD("polygon %s i %d x %f y %f", polyName, i, poly[i].x, poly[i].y); 866 } 867} 868 869/** 870 * Test whether the polygon is convex. 871 */ 872bool SpotShadow::testConvex(const Vector2* polygon, int polygonLength, 873 const char* name) { 874 bool isConvex = true; 875 for (int i = 0; i < polygonLength; i++) { 876 Vector2 start = polygon[i]; 877 Vector2 middle = polygon[(i + 1) % polygonLength]; 878 Vector2 end = polygon[(i + 2) % polygonLength]; 879 880 double delta = (double(middle.x) - start.x) * (double(end.y) - start.y) - 881 (double(middle.y) - start.y) * (double(end.x) - start.x); 882 bool isCCWOrCoLinear = (delta >= EPSILON); 883 884 if (isCCWOrCoLinear) { 885 ALOGW("(Error Type 2): polygon (%s) is not a convex b/c start (x %f, y %f)," 886 "middle (x %f, y %f) and end (x %f, y %f) , delta is %f !!!", 887 name, start.x, start.y, middle.x, middle.y, end.x, end.y, delta); 888 isConvex = false; 889 break; 890 } 891 } 892 return isConvex; 893} 894 895/** 896 * Test whether or not the polygon (intersection) is within the 2 input polygons. 897 * Using Marte Carlo method, we generate a random point, and if it is inside the 898 * intersection, then it must be inside both source polygons. 899 */ 900void SpotShadow::testIntersection(const Vector2* poly1, int poly1Length, 901 const Vector2* poly2, int poly2Length, 902 const Vector2* intersection, int intersectionLength) { 903 // Find the min and max of x and y. 904 Vector2 lowerBound(FLT_MAX, FLT_MAX); 905 Vector2 upperBound(-FLT_MAX, -FLT_MAX); 906 for (int i = 0; i < poly1Length; i++) { 907 updateBound(poly1[i], lowerBound, upperBound); 908 } 909 for (int i = 0; i < poly2Length; i++) { 910 updateBound(poly2[i], lowerBound, upperBound); 911 } 912 913 bool dumpPoly = false; 914 for (int k = 0; k < TEST_POINT_NUMBER; k++) { 915 // Generate a random point between minX, minY and maxX, maxY. 916 double randomX = rand() / double(RAND_MAX); 917 double randomY = rand() / double(RAND_MAX); 918 919 Vector2 testPoint; 920 testPoint.x = lowerBound.x + randomX * (upperBound.x - lowerBound.x); 921 testPoint.y = lowerBound.y + randomY * (upperBound.y - lowerBound.y); 922 923 // If the random point is in both poly 1 and 2, then it must be intersection. 924 if (testPointInsidePolygon(testPoint, intersection, intersectionLength)) { 925 if (!testPointInsidePolygon(testPoint, poly1, poly1Length)) { 926 dumpPoly = true; 927 ALOGW("(Error Type 1): one point (%f, %f) in the intersection is" 928 " not in the poly1", 929 testPoint.x, testPoint.y); 930 } 931 932 if (!testPointInsidePolygon(testPoint, poly2, poly2Length)) { 933 dumpPoly = true; 934 ALOGW("(Error Type 1): one point (%f, %f) in the intersection is" 935 " not in the poly2", 936 testPoint.x, testPoint.y); 937 } 938 } 939 } 940 941 if (dumpPoly) { 942 dumpPolygon(intersection, intersectionLength, "intersection"); 943 for (int i = 1; i < intersectionLength; i++) { 944 Vector2 delta = intersection[i] - intersection[i - 1]; 945 ALOGD("Intersetion i, %d Vs i-1 is delta %f", i, delta.lengthSquared()); 946 } 947 948 dumpPolygon(poly1, poly1Length, "poly 1"); 949 dumpPolygon(poly2, poly2Length, "poly 2"); 950 } 951} 952#endif 953 954}; // namespace uirenderer 955}; // namespace android 956