SpotShadow.cpp revision b79a3e301a8d89b9e1b1f6f3d7fd6aa56610a6f0
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 * 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(Vector2* poly1, int poly1Length, 173 Vector2* poly2, int poly2Length) { 174 makeClockwise(poly1, poly1Length); 175 makeClockwise(poly2, poly2Length); 176 177 Vector2 poly[poly1Length * poly2Length + 2]; 178 int count = 0; 179 int pcount = 0; 180 181 // If one vertex from one polygon sits inside another polygon, add it and 182 // count them. 183 for (int i = 0; i < poly1Length; i++) { 184 if (testPointInsidePolygon(poly1[i], poly2, poly2Length)) { 185 poly[count] = poly1[i]; 186 count++; 187 pcount++; 188 189 } 190 } 191 192 int insidePoly2 = pcount; 193 for (int i = 0; i < poly2Length; i++) { 194 if (testPointInsidePolygon(poly2[i], poly1, poly1Length)) { 195 poly[count] = poly2[i]; 196 count++; 197 } 198 } 199 200 int insidePoly1 = count - insidePoly2; 201 // If all vertices from poly1 are inside poly2, then just return poly1. 202 if (insidePoly2 == poly1Length) { 203 memcpy(poly2, poly1, poly1Length * sizeof(Vector2)); 204 return poly1Length; 205 } 206 207 // If all vertices from poly2 are inside poly1, then just return poly2. 208 if (insidePoly1 == poly2Length) { 209 return poly2Length; 210 } 211 212 // Since neither polygon fully contain the other one, we need to add all the 213 // intersection points. 214 Vector2 intersection; 215 for (int i = 0; i < poly2Length; i++) { 216 for (int j = 0; j < poly1Length; j++) { 217 int poly2LineStart = i; 218 int poly2LineEnd = ((i + 1) % poly2Length); 219 int poly1LineStart = j; 220 int poly1LineEnd = ((j + 1) % poly1Length); 221 bool found = lineIntersection( 222 poly2[poly2LineStart].x, poly2[poly2LineStart].y, 223 poly2[poly2LineEnd].x, poly2[poly2LineEnd].y, 224 poly1[poly1LineStart].x, poly1[poly1LineStart].y, 225 poly1[poly1LineEnd].x, poly1[poly1LineEnd].y, 226 intersection); 227 if (found) { 228 poly[count].x = intersection.x; 229 poly[count].y = intersection.y; 230 count++; 231 } else { 232 Vector2 delta = poly2[i] - poly1[j]; 233 if (delta.lengthSquared() < EPSILON) { 234 poly[count] = poly2[i]; 235 count++; 236 } 237 } 238 } 239 } 240 241 if (count == 0) { 242 return 0; 243 } 244 245 // Sort the result polygon around the center. 246 Vector2 center(0.0f, 0.0f); 247 for (int i = 0; i < count; i++) { 248 center += poly[i]; 249 } 250 center /= count; 251 sort(poly, count, center); 252 253#if DEBUG_SHADOW 254 // Since poly2 is overwritten as the result, we need to save a copy to do 255 // our verification. 256 Vector2 oldPoly2[poly2Length]; 257 int oldPoly2Length = poly2Length; 258 memcpy(oldPoly2, poly2, sizeof(Vector2) * poly2Length); 259#endif 260 261 // Filter the result out from poly and put it into poly2. 262 poly2[0] = poly[0]; 263 int lastOutputIndex = 0; 264 for (int i = 1; i < count; i++) { 265 Vector2 delta = poly[i] - poly2[lastOutputIndex]; 266 if (delta.lengthSquared() >= EPSILON) { 267 poly2[++lastOutputIndex] = poly[i]; 268 } else { 269 // If the vertices are too close, pick the inner one, because the 270 // inner one is more likely to be an intersection point. 271 Vector2 delta1 = poly[i] - center; 272 Vector2 delta2 = poly2[lastOutputIndex] - center; 273 if (delta1.lengthSquared() < delta2.lengthSquared()) { 274 poly2[lastOutputIndex] = poly[i]; 275 } 276 } 277 } 278 int resultLength = lastOutputIndex + 1; 279 280#if DEBUG_SHADOW 281 testConvex(poly2, resultLength, "intersection"); 282 testConvex(poly1, poly1Length, "input poly1"); 283 testConvex(oldPoly2, oldPoly2Length, "input poly2"); 284 285 testIntersection(poly1, poly1Length, oldPoly2, oldPoly2Length, poly2, resultLength); 286#endif 287 288 return resultLength; 289} 290 291/** 292 * Sort points about a center point 293 * 294 * @param poly The in and out polyogon as a Vector2 array. 295 * @param polyLength The number of vertices of the polygon. 296 * @param center the center ctr[0] = x , ctr[1] = y to sort around. 297 */ 298void SpotShadow::sort(Vector2* poly, int polyLength, const Vector2& center) { 299 quicksortCirc(poly, 0, polyLength - 1, center); 300} 301 302/** 303 * Swap points pointed to by i and j 304 */ 305void SpotShadow::swap(Vector2* points, int i, int j) { 306 Vector2 temp = points[i]; 307 points[i] = points[j]; 308 points[j] = temp; 309} 310 311/** 312 * quick sort implementation about the center. 313 */ 314void SpotShadow::quicksortCirc(Vector2* points, int low, int high, 315 const Vector2& center) { 316 int i = low, j = high; 317 int p = low + (high - low) / 2; 318 float pivot = angle(points[p], center); 319 while (i <= j) { 320 while (angle(points[i], center) > pivot) { 321 i++; 322 } 323 while (angle(points[j], center) < pivot) { 324 j--; 325 } 326 327 if (i <= j) { 328 swap(points, i, j); 329 i++; 330 j--; 331 } 332 } 333 if (low < j) quicksortCirc(points, low, j, center); 334 if (i < high) quicksortCirc(points, i, high, center); 335} 336 337/** 338 * Sort points by x axis 339 * 340 * @param points points to sort 341 * @param low start index 342 * @param high end index 343 */ 344void SpotShadow::quicksortX(Vector2* points, int low, int high) { 345 int i = low, j = high; 346 int p = low + (high - low) / 2; 347 float pivot = points[p].x; 348 while (i <= j) { 349 while (points[i].x < pivot) { 350 i++; 351 } 352 while (points[j].x > pivot) { 353 j--; 354 } 355 356 if (i <= j) { 357 swap(points, i, j); 358 i++; 359 j--; 360 } 361 } 362 if (low < j) quicksortX(points, low, j); 363 if (i < high) quicksortX(points, i, high); 364} 365 366/** 367 * Test whether a point is inside the polygon. 368 * 369 * @param testPoint the point to test 370 * @param poly the polygon 371 * @return true if the testPoint is inside the poly. 372 */ 373bool SpotShadow::testPointInsidePolygon(const Vector2 testPoint, 374 const Vector2* poly, int len) { 375 bool c = false; 376 double testx = testPoint.x; 377 double testy = testPoint.y; 378 for (int i = 0, j = len - 1; i < len; j = i++) { 379 double startX = poly[j].x; 380 double startY = poly[j].y; 381 double endX = poly[i].x; 382 double endY = poly[i].y; 383 384 if (((endY > testy) != (startY > testy)) && 385 (testx < (startX - endX) * (testy - endY) 386 / (startY - endY) + endX)) { 387 c = !c; 388 } 389 } 390 return c; 391} 392 393/** 394 * Make the polygon turn clockwise. 395 * 396 * @param polygon the polygon as a Vector2 array. 397 * @param len the number of points of the polygon 398 */ 399void SpotShadow::makeClockwise(Vector2* polygon, int len) { 400 if (polygon == 0 || len == 0) { 401 return; 402 } 403 if (!isClockwise(polygon, len)) { 404 reverse(polygon, len); 405 } 406} 407 408/** 409 * Test whether the polygon is order in clockwise. 410 * 411 * @param polygon the polygon as a Vector2 array 412 * @param len the number of points of the polygon 413 */ 414bool SpotShadow::isClockwise(Vector2* polygon, int len) { 415 double sum = 0; 416 double p1x = polygon[len - 1].x; 417 double p1y = polygon[len - 1].y; 418 for (int i = 0; i < len; i++) { 419 420 double p2x = polygon[i].x; 421 double p2y = polygon[i].y; 422 sum += p1x * p2y - p2x * p1y; 423 p1x = p2x; 424 p1y = p2y; 425 } 426 return sum < 0; 427} 428 429/** 430 * Reverse the polygon 431 * 432 * @param polygon the polygon as a Vector2 array 433 * @param len the number of points of the polygon 434 */ 435void SpotShadow::reverse(Vector2* polygon, int len) { 436 int n = len / 2; 437 for (int i = 0; i < n; i++) { 438 Vector2 tmp = polygon[i]; 439 int k = len - 1 - i; 440 polygon[i] = polygon[k]; 441 polygon[k] = tmp; 442 } 443} 444 445/** 446 * Intersects two lines in parametric form. This function is called in a tight 447 * loop, and we need double precision to get things right. 448 * 449 * @param x1 the x coordinate point 1 of line 1 450 * @param y1 the y coordinate point 1 of line 1 451 * @param x2 the x coordinate point 2 of line 1 452 * @param y2 the y coordinate point 2 of line 1 453 * @param x3 the x coordinate point 1 of line 2 454 * @param y3 the y coordinate point 1 of line 2 455 * @param x4 the x coordinate point 2 of line 2 456 * @param y4 the y coordinate point 2 of line 2 457 * @param ret the x,y location of the intersection 458 * @return true if it found an intersection 459 */ 460inline bool SpotShadow::lineIntersection(double x1, double y1, double x2, double y2, 461 double x3, double y3, double x4, double y4, Vector2& ret) { 462 double d = (x1 - x2) * (y3 - y4) - (y1 - y2) * (x3 - x4); 463 if (d == 0.0) return false; 464 465 double dx = (x1 * y2 - y1 * x2); 466 double dy = (x3 * y4 - y3 * x4); 467 double x = (dx * (x3 - x4) - (x1 - x2) * dy) / d; 468 double y = (dx * (y3 - y4) - (y1 - y2) * dy) / d; 469 470 // The intersection should be in the middle of the point 1 and point 2, 471 // likewise point 3 and point 4. 472 if (((x - x1) * (x - x2) > EPSILON) 473 || ((x - x3) * (x - x4) > EPSILON) 474 || ((y - y1) * (y - y2) > EPSILON) 475 || ((y - y3) * (y - y4) > EPSILON)) { 476 // Not interesected 477 return false; 478 } 479 ret.x = x; 480 ret.y = y; 481 return true; 482 483} 484 485/** 486 * Compute a horizontal circular polygon about point (x , y , height) of radius 487 * (size) 488 * 489 * @param points number of the points of the output polygon. 490 * @param lightCenter the center of the light. 491 * @param size the light size. 492 * @param ret result polygon. 493 */ 494void SpotShadow::computeLightPolygon(int points, const Vector3& lightCenter, 495 float size, Vector3* ret) { 496 // TODO: Caching all the sin / cos values and store them in a look up table. 497 for (int i = 0; i < points; i++) { 498 double angle = 2 * i * M_PI / points; 499 ret[i].x = cosf(angle) * size + lightCenter.x; 500 ret[i].y = sinf(angle) * size + lightCenter.y; 501 ret[i].z = lightCenter.z; 502 } 503} 504 505/** 506* Generate the shadow from a spot light. 507* 508* @param poly x,y,z vertexes of a convex polygon that occludes the light source 509* @param polyLength number of vertexes of the occluding polygon 510* @param lightCenter the center of the light 511* @param lightSize the radius of the light source 512* @param lightVertexCount the vertex counter for the light polygon 513* @param shadowTriangleStrip return an (x,y,alpha) triangle strip representing the shadow. Return 514* empty strip if error. 515* 516*/ 517void SpotShadow::createSpotShadow(const Vector3* poly, int polyLength, 518 const Vector3& lightCenter, float lightSize, int lightVertexCount, 519 VertexBuffer& retStrips) { 520 Vector3 light[lightVertexCount * 3]; 521 computeLightPolygon(lightVertexCount, lightCenter, lightSize, light); 522 computeSpotShadow(light, lightVertexCount, lightCenter, poly, polyLength, 523 retStrips); 524} 525 526/** 527 * Generate the shadow spot light of shape lightPoly and a object poly 528 * 529 * @param lightPoly x,y,z vertex of a convex polygon that is the light source 530 * @param lightPolyLength number of vertexes of the light source polygon 531 * @param poly x,y,z vertexes of a convex polygon that occludes the light source 532 * @param polyLength number of vertexes of the occluding polygon 533 * @param shadowTriangleStrip return an (x,y,alpha) triangle strip representing the shadow. Return 534 * empty strip if error. 535 */ 536void SpotShadow::computeSpotShadow(const Vector3* lightPoly, int lightPolyLength, 537 const Vector3& lightCenter, const Vector3* poly, int polyLength, 538 VertexBuffer& shadowTriangleStrip) { 539 // Point clouds for all the shadowed vertices 540 Vector2 shadowRegion[lightPolyLength * polyLength]; 541 // Shadow polygon from one point light. 542 Vector2 outline[polyLength]; 543 Vector2 umbraMem[polyLength * lightPolyLength]; 544 Vector2* umbra = umbraMem; 545 546 int umbraLength = 0; 547 548 // Validate input, receiver is always at z = 0 plane. 549 bool inputPolyPositionValid = true; 550 for (int i = 0; i < polyLength; i++) { 551 if (poly[i].z <= 0.00001) { 552 inputPolyPositionValid = false; 553 ALOGW("polygon below the surface"); 554 break; 555 } 556 if (poly[i].z >= lightPoly[0].z) { 557 inputPolyPositionValid = false; 558 ALOGW("polygon above the light"); 559 break; 560 } 561 } 562 563 // If the caster's position is invalid, don't draw anything. 564 if (!inputPolyPositionValid) { 565 return; 566 } 567 568 // Calculate the umbra polygon based on intersections of all outlines 569 int k = 0; 570 for (int j = 0; j < lightPolyLength; j++) { 571 int m = 0; 572 for (int i = 0; i < polyLength; i++) { 573 float t = lightPoly[j].z - poly[i].z; 574 if (t == 0) { 575 return; 576 } 577 t = lightPoly[j].z / t; 578 float x = lightPoly[j].x - t * (lightPoly[j].x - poly[i].x); 579 float y = lightPoly[j].y - t * (lightPoly[j].y - poly[i].y); 580 581 Vector2 newPoint = Vector2(x, y); 582 shadowRegion[k] = newPoint; 583 outline[m] = newPoint; 584 585 k++; 586 m++; 587 } 588 589 // For the first light polygon's vertex, use the outline as the umbra. 590 // Later on, use the intersection of the outline and existing umbra. 591 if (umbraLength == 0) { 592 for (int i = 0; i < polyLength; i++) { 593 umbra[i] = outline[i]; 594 } 595 umbraLength = polyLength; 596 } else { 597 int col = ((j * 255) / lightPolyLength); 598 umbraLength = intersection(outline, polyLength, umbra, umbraLength); 599 if (umbraLength == 0) { 600 break; 601 } 602 } 603 } 604 605 // Generate the penumbra area using the hull of all shadow regions. 606 int shadowRegionLength = k; 607 Vector2 penumbra[k]; 608 int penumbraLength = hull(shadowRegion, shadowRegionLength, penumbra); 609 610 Vector2 fakeUmbra[polyLength]; 611 if (umbraLength < 3) { 612 // If there is no real umbra, make a fake one. 613 for (int i = 0; i < polyLength; i++) { 614 float t = lightCenter.z - poly[i].z; 615 if (t == 0) { 616 return; 617 } 618 t = lightCenter.z / t; 619 float x = lightCenter.x - t * (lightCenter.x - poly[i].x); 620 float y = lightCenter.y - t * (lightCenter.y - poly[i].y); 621 622 fakeUmbra[i].x = x; 623 fakeUmbra[i].y = y; 624 } 625 626 // Shrink the centroid's shadow by 10%. 627 // TODO: Study the magic number of 10%. 628 Vector2 shadowCentroid = 629 ShadowTessellator::centroid2d(fakeUmbra, polyLength); 630 for (int i = 0; i < polyLength; i++) { 631 fakeUmbra[i] = shadowCentroid * (1.0f - SHADOW_SHRINK_SCALE) + 632 fakeUmbra[i] * SHADOW_SHRINK_SCALE; 633 } 634#if DEBUG_SHADOW 635 ALOGD("No real umbra make a fake one, centroid2d = %f , %f", 636 shadowCentroid.x, shadowCentroid.y); 637#endif 638 // Set the fake umbra, whose size is the same as the original polygon. 639 umbra = fakeUmbra; 640 umbraLength = polyLength; 641 } 642 643 generateTriangleStrip(penumbra, penumbraLength, umbra, umbraLength, 644 shadowTriangleStrip); 645} 646 647/** 648 * Converts a polygon specified with CW vertices into an array of distance-from-centroid values. 649 * 650 * Returns false in error conditions 651 * 652 * @param poly Array of vertices. Note that these *must* be CW. 653 * @param polyLength The number of vertices in the polygon. 654 * @param polyCentroid The centroid of the polygon, from which rays will be cast 655 * @param rayDist The output array for the calculated distances, must be SHADOW_RAY_COUNT in size 656 */ 657bool convertPolyToRayDist(const Vector2* poly, int polyLength, const Vector2& polyCentroid, 658 float* rayDist) { 659 const int rays = SHADOW_RAY_COUNT; 660 const float step = M_PI * 2 / rays; 661 662 const Vector2* lastVertex = &(poly[polyLength - 1]); 663 float startAngle = angle(*lastVertex, polyCentroid); 664 665 // Start with the ray that's closest to and less than startAngle 666 int rayIndex = floor((startAngle - EPSILON) / step); 667 rayIndex = (rayIndex + rays) % rays; // ensure positive 668 669 for (int polyIndex = 0; polyIndex < polyLength; polyIndex++) { 670 /* 671 * For a given pair of vertices on the polygon, poly[i-1] and poly[i], the rays that 672 * intersect these will be those that are between the two angles from the centroid that the 673 * vertices define. 674 * 675 * Because the polygon vertices are stored clockwise, the closest ray with an angle 676 * *smaller* than that defined by angle(poly[i], centroid) will be the first ray that does 677 * not intersect with poly[i-1], poly[i]. 678 */ 679 float currentAngle = angle(poly[polyIndex], polyCentroid); 680 681 // find first ray that will not intersect the line segment poly[i-1] & poly[i] 682 int firstRayIndexOnNextSegment = floor((currentAngle - EPSILON) / step); 683 firstRayIndexOnNextSegment = (firstRayIndexOnNextSegment + rays) % rays; // ensure positive 684 685 // Iterate through all rays that intersect with poly[i-1], poly[i] line segment. 686 // This may be 0 rays. 687 while (rayIndex != firstRayIndexOnNextSegment) { 688 float distanceToIntersect = rayIntersectPoints(polyCentroid, 689 cos(rayIndex * step), 690 sin(rayIndex * step), 691 *lastVertex, poly[polyIndex]); 692 if (distanceToIntersect < 0) return false; // error case, abort 693 694 rayDist[rayIndex] = distanceToIntersect; 695 696 rayIndex = (rayIndex - 1 + rays) % rays; 697 } 698 lastVertex = &poly[polyIndex]; 699 } 700 701 return true; 702} 703 704/** 705 * Generate a triangle strip given two convex polygons 706 * 707 * @param penumbra The outer polygon x,y vertexes 708 * @param penumbraLength The number of vertexes in the outer polygon 709 * @param umbra The inner outer polygon x,y vertexes 710 * @param umbraLength The number of vertexes in the inner polygon 711 * @param shadowTriangleStrip return an (x,y,alpha) triangle strip representing the shadow. Return 712 * empty strip if error. 713**/ 714void SpotShadow::generateTriangleStrip(const Vector2* penumbra, int penumbraLength, 715 const Vector2* umbra, int umbraLength, VertexBuffer& shadowTriangleStrip) { 716 const int rays = SHADOW_RAY_COUNT; 717 718 const int size = 2 * rays; 719 const float step = M_PI * 2 / rays; 720 // Centroid of the umbra. 721 Vector2 centroid = ShadowTessellator::centroid2d(umbra, umbraLength); 722#if DEBUG_SHADOW 723 ALOGD("centroid2d = %f , %f", centroid.x, centroid.y); 724#endif 725 // Intersection to the penumbra. 726 float penumbraDistPerRay[rays]; 727 // Intersection to the umbra. 728 float umbraDistPerRay[rays]; 729 730 // convert CW polygons to ray distance encoding, aborting on conversion failure 731 if (!convertPolyToRayDist(umbra, umbraLength, centroid, umbraDistPerRay)) return; 732 if (!convertPolyToRayDist(penumbra, penumbraLength, centroid, penumbraDistPerRay)) return; 733 734 AlphaVertex* shadowVertices = shadowTriangleStrip.alloc<AlphaVertex>(getStripSize(rays)); 735 736 // Calculate the vertices (x, y, alpha) in the shadow area. 737 for (int rayIndex = 0; rayIndex < rays; rayIndex++) { 738 float dx = cosf(step * rayIndex); 739 float dy = sinf(step * rayIndex); 740 741 // outer ring 742 float currentDist = penumbraDistPerRay[rayIndex]; 743 AlphaVertex::set(&shadowVertices[rayIndex], 744 dx * currentDist + centroid.x, dy * currentDist + centroid.y, 0.0f); 745 746 // inner ring 747 float deltaDist = umbraDistPerRay[rayIndex] - penumbraDistPerRay[rayIndex]; 748 currentDist += deltaDist; 749 AlphaVertex::set(&shadowVertices[rays + rayIndex], 750 dx * currentDist + centroid.x, dy * currentDist + centroid.y, 1.0f); 751 } 752 // The centroid is in the umbra area, so the opacity is considered as 1.0. 753 AlphaVertex::set(&shadowVertices[SHADOW_VERTEX_COUNT - 1], centroid.x, centroid.y, 1.0f); 754#if DEBUG_SHADOW 755 for (int i = 0; i < currentIndex; i++) { 756 ALOGD("spot shadow value: i %d, (x:%f, y:%f, a:%f)", i, shadowVertices[i].x, 757 shadowVertices[i].y, shadowVertices[i].alpha); 758 } 759#endif 760} 761 762/** 763 * This is only for experimental purpose. 764 * After intersections are calculated, we could smooth the polygon if needed. 765 * So far, we don't think it is more appealing yet. 766 * 767 * @param level The level of smoothness. 768 * @param rays The total number of rays. 769 * @param rayDist (In and Out) The distance for each ray. 770 * 771 */ 772void SpotShadow::smoothPolygon(int level, int rays, float* rayDist) { 773 for (int k = 0; k < level; k++) { 774 for (int i = 0; i < rays; i++) { 775 float p1 = rayDist[(rays - 1 + i) % rays]; 776 float p2 = rayDist[i]; 777 float p3 = rayDist[(i + 1) % rays]; 778 rayDist[i] = (p1 + p2 * 2 + p3) / 4; 779 } 780 } 781} 782 783/** 784 * Calculate the number of vertex we will create given a number of rays and layers 785 * 786 * @param rays number of points around the polygons you want 787 * @param layers number of layers of triangle strips you need 788 * @return number of vertex (multiply by 3 for number of floats) 789 */ 790int SpotShadow::getStripSize(int rays) { 791 return (2 + rays + (2 * (rays + 1))); 792} 793 794#if DEBUG_SHADOW 795 796#define TEST_POINT_NUMBER 128 797 798/** 799 * Calculate the bounds for generating random test points. 800 */ 801void SpotShadow::updateBound(const Vector2 inVector, Vector2& lowerBound, 802 Vector2& upperBound ) { 803 if (inVector.x < lowerBound.x) { 804 lowerBound.x = inVector.x; 805 } 806 807 if (inVector.y < lowerBound.y) { 808 lowerBound.y = inVector.y; 809 } 810 811 if (inVector.x > upperBound.x) { 812 upperBound.x = inVector.x; 813 } 814 815 if (inVector.y > upperBound.y) { 816 upperBound.y = inVector.y; 817 } 818} 819 820/** 821 * For debug purpose, when things go wrong, dump the whole polygon data. 822 */ 823static void dumpPolygon(const Vector2* poly, int polyLength, const char* polyName) { 824 for (int i = 0; i < polyLength; i++) { 825 ALOGD("polygon %s i %d x %f y %f", polyName, i, poly[i].x, poly[i].y); 826 } 827} 828 829/** 830 * Test whether the polygon is convex. 831 */ 832bool SpotShadow::testConvex(const Vector2* polygon, int polygonLength, 833 const char* name) { 834 bool isConvex = true; 835 for (int i = 0; i < polygonLength; i++) { 836 Vector2 start = polygon[i]; 837 Vector2 middle = polygon[(i + 1) % polygonLength]; 838 Vector2 end = polygon[(i + 2) % polygonLength]; 839 840 double delta = (double(middle.x) - start.x) * (double(end.y) - start.y) - 841 (double(middle.y) - start.y) * (double(end.x) - start.x); 842 bool isCCWOrCoLinear = (delta >= EPSILON); 843 844 if (isCCWOrCoLinear) { 845 ALOGE("(Error Type 2): polygon (%s) is not a convex b/c start (x %f, y %f)," 846 "middle (x %f, y %f) and end (x %f, y %f) , delta is %f !!!", 847 name, start.x, start.y, middle.x, middle.y, end.x, end.y, delta); 848 isConvex = false; 849 break; 850 } 851 } 852 return isConvex; 853} 854 855/** 856 * Test whether or not the polygon (intersection) is within the 2 input polygons. 857 * Using Marte Carlo method, we generate a random point, and if it is inside the 858 * intersection, then it must be inside both source polygons. 859 */ 860void SpotShadow::testIntersection(const Vector2* poly1, int poly1Length, 861 const Vector2* poly2, int poly2Length, 862 const Vector2* intersection, int intersectionLength) { 863 // Find the min and max of x and y. 864 Vector2 lowerBound(FLT_MAX, FLT_MAX); 865 Vector2 upperBound(-FLT_MAX, -FLT_MAX); 866 for (int i = 0; i < poly1Length; i++) { 867 updateBound(poly1[i], lowerBound, upperBound); 868 } 869 for (int i = 0; i < poly2Length; i++) { 870 updateBound(poly2[i], lowerBound, upperBound); 871 } 872 873 bool dumpPoly = false; 874 for (int k = 0; k < TEST_POINT_NUMBER; k++) { 875 // Generate a random point between minX, minY and maxX, maxY. 876 double randomX = rand() / double(RAND_MAX); 877 double randomY = rand() / double(RAND_MAX); 878 879 Vector2 testPoint; 880 testPoint.x = lowerBound.x + randomX * (upperBound.x - lowerBound.x); 881 testPoint.y = lowerBound.y + randomY * (upperBound.y - lowerBound.y); 882 883 // If the random point is in both poly 1 and 2, then it must be intersection. 884 if (testPointInsidePolygon(testPoint, intersection, intersectionLength)) { 885 if (!testPointInsidePolygon(testPoint, poly1, poly1Length)) { 886 dumpPoly = true; 887 ALOGE("(Error Type 1): one point (%f, %f) in the intersection is" 888 " not in the poly1", 889 testPoint.x, testPoint.y); 890 } 891 892 if (!testPointInsidePolygon(testPoint, poly2, poly2Length)) { 893 dumpPoly = true; 894 ALOGE("(Error Type 1): one point (%f, %f) in the intersection is" 895 " not in the poly2", 896 testPoint.x, testPoint.y); 897 } 898 } 899 } 900 901 if (dumpPoly) { 902 dumpPolygon(intersection, intersectionLength, "intersection"); 903 for (int i = 1; i < intersectionLength; i++) { 904 Vector2 delta = intersection[i] - intersection[i - 1]; 905 ALOGD("Intersetion i, %d Vs i-1 is delta %f", i, delta.lengthSquared()); 906 } 907 908 dumpPolygon(poly1, poly1Length, "poly 1"); 909 dumpPolygon(poly2, poly2Length, "poly 2"); 910 } 911} 912#endif 913 914}; // namespace uirenderer 915}; // namespace android 916