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// The highest z value can't be higher than (CASTER_Z_CAP_RATIO * light.z) 18#define CASTER_Z_CAP_RATIO 0.95f 19 20// When there is no umbra, then just fake the umbra using 21// centroid * (1 - FAKE_UMBRA_SIZE_RATIO) + outline * FAKE_UMBRA_SIZE_RATIO 22#define FAKE_UMBRA_SIZE_RATIO 0.05f 23 24// When the polygon is about 90 vertices, the penumbra + umbra can reach 270 rays. 25// That is consider pretty fine tessllated polygon so far. 26// This is just to prevent using too much some memory when edge slicing is not 27// needed any more. 28#define FINE_TESSELLATED_POLYGON_RAY_NUMBER 270 29/** 30 * Extra vertices for the corner for smoother corner. 31 * Only for outer loop. 32 * Note that we use such extra memory to avoid an extra loop. 33 */ 34// For half circle, we could add EXTRA_VERTEX_PER_PI vertices. 35// Set to 1 if we don't want to have any. 36#define SPOT_EXTRA_CORNER_VERTEX_PER_PI 18 37 38// For the whole polygon, the sum of all the deltas b/t normals is 2 * M_PI, 39// therefore, the maximum number of extra vertices will be twice bigger. 40#define SPOT_MAX_EXTRA_CORNER_VERTEX_NUMBER (2 * SPOT_EXTRA_CORNER_VERTEX_PER_PI) 41 42// For each RADIANS_DIVISOR, we would allocate one more vertex b/t the normals. 43#define SPOT_CORNER_RADIANS_DIVISOR (M_PI / SPOT_EXTRA_CORNER_VERTEX_PER_PI) 44 45#define PENUMBRA_ALPHA 0.0f 46#define UMBRA_ALPHA 1.0f 47 48#include "SpotShadow.h" 49 50#include "ShadowTessellator.h" 51#include "Vertex.h" 52#include "VertexBuffer.h" 53#include "utils/MathUtils.h" 54 55#include <algorithm> 56#include <math.h> 57#include <stdlib.h> 58#include <utils/Log.h> 59 60// TODO: After we settle down the new algorithm, we can remove the old one and 61// its utility functions. 62// Right now, we still need to keep it for comparison purpose and future expansion. 63namespace android { 64namespace uirenderer { 65 66static const float EPSILON = 1e-7; 67 68/** 69 * For each polygon's vertex, the light center will project it to the receiver 70 * as one of the outline vertex. 71 * For each outline vertex, we need to store the position and normal. 72 * Normal here is defined against the edge by the current vertex and the next vertex. 73 */ 74struct OutlineData { 75 Vector2 position; 76 Vector2 normal; 77 float radius; 78}; 79 80/** 81 * For each vertex, we need to keep track of its angle, whether it is penumbra or 82 * umbra, and its corresponding vertex index. 83 */ 84struct SpotShadow::VertexAngleData { 85 // The angle to the vertex from the centroid. 86 float mAngle; 87 // True is the vertex comes from penumbra, otherwise it comes from umbra. 88 bool mIsPenumbra; 89 // The index of the vertex described by this data. 90 int mVertexIndex; 91 void set(float angle, bool isPenumbra, int index) { 92 mAngle = angle; 93 mIsPenumbra = isPenumbra; 94 mVertexIndex = index; 95 } 96}; 97 98/** 99 * Calculate the angle between and x and a y coordinate. 100 * The atan2 range from -PI to PI. 101 */ 102static float angle(const Vector2& point, const Vector2& center) { 103 return atan2(point.y - center.y, point.x - center.x); 104} 105 106/** 107 * Calculate the intersection of a ray with the line segment defined by two points. 108 * 109 * Returns a negative value in error conditions. 110 111 * @param rayOrigin The start of the ray 112 * @param dx The x vector of the ray 113 * @param dy The y vector of the ray 114 * @param p1 The first point defining the line segment 115 * @param p2 The second point defining the line segment 116 * @return The distance along the ray if it intersects with the line segment, negative if otherwise 117 */ 118static float rayIntersectPoints(const Vector2& rayOrigin, float dx, float dy, 119 const Vector2& p1, const Vector2& p2) { 120 // The math below is derived from solving this formula, basically the 121 // intersection point should stay on both the ray and the edge of (p1, p2). 122 // solve([p1x+t*(p2x-p1x)=dx*t2+px,p1y+t*(p2y-p1y)=dy*t2+py],[t,t2]); 123 124 float divisor = (dx * (p1.y - p2.y) + dy * p2.x - dy * p1.x); 125 if (divisor == 0) return -1.0f; // error, invalid divisor 126 127#if DEBUG_SHADOW 128 float interpVal = (dx * (p1.y - rayOrigin.y) + dy * rayOrigin.x - dy * p1.x) / divisor; 129 if (interpVal < 0 || interpVal > 1) { 130 ALOGW("rayIntersectPoints is hitting outside the segment %f", interpVal); 131 } 132#endif 133 134 float distance = (p1.x * (rayOrigin.y - p2.y) + p2.x * (p1.y - rayOrigin.y) + 135 rayOrigin.x * (p2.y - p1.y)) / divisor; 136 137 return distance; // may be negative in error cases 138} 139 140/** 141 * Sort points by their X coordinates 142 * 143 * @param points the points as a Vector2 array. 144 * @param pointsLength the number of vertices of the polygon. 145 */ 146void SpotShadow::xsort(Vector2* points, int pointsLength) { 147 auto cmp = [](const Vector2& a, const Vector2& b) -> bool { 148 return a.x < b.x; 149 }; 150 std::sort(points, points + pointsLength, cmp); 151} 152 153/** 154 * compute the convex hull of a collection of Points 155 * 156 * @param points the points as a Vector2 array. 157 * @param pointsLength the number of vertices of the polygon. 158 * @param retPoly pre allocated array of floats to put the vertices 159 * @return the number of points in the polygon 0 if no intersection 160 */ 161int SpotShadow::hull(Vector2* points, int pointsLength, Vector2* retPoly) { 162 xsort(points, pointsLength); 163 int n = pointsLength; 164 Vector2 lUpper[n]; 165 lUpper[0] = points[0]; 166 lUpper[1] = points[1]; 167 168 int lUpperSize = 2; 169 170 for (int i = 2; i < n; i++) { 171 lUpper[lUpperSize] = points[i]; 172 lUpperSize++; 173 174 while (lUpperSize > 2 && !ccw( 175 lUpper[lUpperSize - 3].x, lUpper[lUpperSize - 3].y, 176 lUpper[lUpperSize - 2].x, lUpper[lUpperSize - 2].y, 177 lUpper[lUpperSize - 1].x, lUpper[lUpperSize - 1].y)) { 178 // Remove the middle point of the three last 179 lUpper[lUpperSize - 2].x = lUpper[lUpperSize - 1].x; 180 lUpper[lUpperSize - 2].y = lUpper[lUpperSize - 1].y; 181 lUpperSize--; 182 } 183 } 184 185 Vector2 lLower[n]; 186 lLower[0] = points[n - 1]; 187 lLower[1] = points[n - 2]; 188 189 int lLowerSize = 2; 190 191 for (int i = n - 3; i >= 0; i--) { 192 lLower[lLowerSize] = points[i]; 193 lLowerSize++; 194 195 while (lLowerSize > 2 && !ccw( 196 lLower[lLowerSize - 3].x, lLower[lLowerSize - 3].y, 197 lLower[lLowerSize - 2].x, lLower[lLowerSize - 2].y, 198 lLower[lLowerSize - 1].x, lLower[lLowerSize - 1].y)) { 199 // Remove the middle point of the three last 200 lLower[lLowerSize - 2] = lLower[lLowerSize - 1]; 201 lLowerSize--; 202 } 203 } 204 205 // output points in CW ordering 206 const int total = lUpperSize + lLowerSize - 2; 207 int outIndex = total - 1; 208 for (int i = 0; i < lUpperSize; i++) { 209 retPoly[outIndex] = lUpper[i]; 210 outIndex--; 211 } 212 213 for (int i = 1; i < lLowerSize - 1; i++) { 214 retPoly[outIndex] = lLower[i]; 215 outIndex--; 216 } 217 // TODO: Add test harness which verify that all the points are inside the hull. 218 return total; 219} 220 221/** 222 * Test whether the 3 points form a counter clockwise turn. 223 * 224 * @return true if a right hand turn 225 */ 226bool SpotShadow::ccw(float ax, float ay, float bx, float by, 227 float cx, float cy) { 228 return (bx - ax) * (cy - ay) - (by - ay) * (cx - ax) > EPSILON; 229} 230 231/** 232 * Sort points about a center point 233 * 234 * @param poly The in and out polyogon as a Vector2 array. 235 * @param polyLength The number of vertices of the polygon. 236 * @param center the center ctr[0] = x , ctr[1] = y to sort around. 237 */ 238void SpotShadow::sort(Vector2* poly, int polyLength, const Vector2& center) { 239 quicksortCirc(poly, 0, polyLength - 1, center); 240} 241 242/** 243 * Swap points pointed to by i and j 244 */ 245void SpotShadow::swap(Vector2* points, int i, int j) { 246 Vector2 temp = points[i]; 247 points[i] = points[j]; 248 points[j] = temp; 249} 250 251/** 252 * quick sort implementation about the center. 253 */ 254void SpotShadow::quicksortCirc(Vector2* points, int low, int high, 255 const Vector2& center) { 256 int i = low, j = high; 257 int p = low + (high - low) / 2; 258 float pivot = angle(points[p], center); 259 while (i <= j) { 260 while (angle(points[i], center) > pivot) { 261 i++; 262 } 263 while (angle(points[j], center) < pivot) { 264 j--; 265 } 266 267 if (i <= j) { 268 swap(points, i, j); 269 i++; 270 j--; 271 } 272 } 273 if (low < j) quicksortCirc(points, low, j, center); 274 if (i < high) quicksortCirc(points, i, high, center); 275} 276 277/** 278 * Test whether a point is inside the polygon. 279 * 280 * @param testPoint the point to test 281 * @param poly the polygon 282 * @return true if the testPoint is inside the poly. 283 */ 284bool SpotShadow::testPointInsidePolygon(const Vector2 testPoint, 285 const Vector2* poly, int len) { 286 bool c = false; 287 float testx = testPoint.x; 288 float testy = testPoint.y; 289 for (int i = 0, j = len - 1; i < len; j = i++) { 290 float startX = poly[j].x; 291 float startY = poly[j].y; 292 float endX = poly[i].x; 293 float endY = poly[i].y; 294 295 if (((endY > testy) != (startY > testy)) 296 && (testx < (startX - endX) * (testy - endY) 297 / (startY - endY) + endX)) { 298 c = !c; 299 } 300 } 301 return c; 302} 303 304/** 305 * Make the polygon turn clockwise. 306 * 307 * @param polygon the polygon as a Vector2 array. 308 * @param len the number of points of the polygon 309 */ 310void SpotShadow::makeClockwise(Vector2* polygon, int len) { 311 if (polygon == nullptr || len == 0) { 312 return; 313 } 314 if (!ShadowTessellator::isClockwise(polygon, len)) { 315 reverse(polygon, len); 316 } 317} 318 319/** 320 * Reverse the polygon 321 * 322 * @param polygon the polygon as a Vector2 array 323 * @param len the number of points of the polygon 324 */ 325void SpotShadow::reverse(Vector2* polygon, int len) { 326 int n = len / 2; 327 for (int i = 0; i < n; i++) { 328 Vector2 tmp = polygon[i]; 329 int k = len - 1 - i; 330 polygon[i] = polygon[k]; 331 polygon[k] = tmp; 332 } 333} 334 335/** 336 * Compute a horizontal circular polygon about point (x , y , height) of radius 337 * (size) 338 * 339 * @param points number of the points of the output polygon. 340 * @param lightCenter the center of the light. 341 * @param size the light size. 342 * @param ret result polygon. 343 */ 344void SpotShadow::computeLightPolygon(int points, const Vector3& lightCenter, 345 float size, Vector3* ret) { 346 // TODO: Caching all the sin / cos values and store them in a look up table. 347 for (int i = 0; i < points; i++) { 348 float angle = 2 * i * M_PI / points; 349 ret[i].x = cosf(angle) * size + lightCenter.x; 350 ret[i].y = sinf(angle) * size + lightCenter.y; 351 ret[i].z = lightCenter.z; 352 } 353} 354 355/** 356 * From light center, project one vertex to the z=0 surface and get the outline. 357 * 358 * @param outline The result which is the outline position. 359 * @param lightCenter The center of light. 360 * @param polyVertex The input polygon's vertex. 361 * 362 * @return float The ratio of (polygon.z / light.z - polygon.z) 363 */ 364float SpotShadow::projectCasterToOutline(Vector2& outline, 365 const Vector3& lightCenter, const Vector3& polyVertex) { 366 float lightToPolyZ = lightCenter.z - polyVertex.z; 367 float ratioZ = CASTER_Z_CAP_RATIO; 368 if (lightToPolyZ != 0) { 369 // If any caster's vertex is almost above the light, we just keep it as 95% 370 // of the height of the light. 371 ratioZ = MathUtils::clamp(polyVertex.z / lightToPolyZ, 0.0f, CASTER_Z_CAP_RATIO); 372 } 373 374 outline.x = polyVertex.x - ratioZ * (lightCenter.x - polyVertex.x); 375 outline.y = polyVertex.y - ratioZ * (lightCenter.y - polyVertex.y); 376 return ratioZ; 377} 378 379/** 380 * Generate the shadow spot light of shape lightPoly and a object poly 381 * 382 * @param isCasterOpaque whether the caster is opaque 383 * @param lightCenter the center of the light 384 * @param lightSize the radius of the light 385 * @param poly x,y,z vertexes of a convex polygon that occludes the light source 386 * @param polyLength number of vertexes of the occluding polygon 387 * @param shadowTriangleStrip return an (x,y,alpha) triangle strip representing the shadow. Return 388 * empty strip if error. 389 */ 390void SpotShadow::createSpotShadow(bool isCasterOpaque, const Vector3& lightCenter, 391 float lightSize, const Vector3* poly, int polyLength, const Vector3& polyCentroid, 392 VertexBuffer& shadowTriangleStrip) { 393 if (CC_UNLIKELY(lightCenter.z <= 0)) { 394 ALOGW("Relative Light Z is not positive. No spot shadow!"); 395 return; 396 } 397 if (CC_UNLIKELY(polyLength < 3)) { 398#if DEBUG_SHADOW 399 ALOGW("Invalid polygon length. No spot shadow!"); 400#endif 401 return; 402 } 403 OutlineData outlineData[polyLength]; 404 Vector2 outlineCentroid; 405 // Calculate the projected outline for each polygon's vertices from the light center. 406 // 407 // O Light 408 // / 409 // / 410 // . Polygon vertex 411 // / 412 // / 413 // O Outline vertices 414 // 415 // Ratio = (Poly - Outline) / (Light - Poly) 416 // Outline.x = Poly.x - Ratio * (Light.x - Poly.x) 417 // Outline's radius / Light's radius = Ratio 418 419 // Compute the last outline vertex to make sure we can get the normal and outline 420 // in one single loop. 421 projectCasterToOutline(outlineData[polyLength - 1].position, lightCenter, 422 poly[polyLength - 1]); 423 424 // Take the outline's polygon, calculate the normal for each outline edge. 425 int currentNormalIndex = polyLength - 1; 426 int nextNormalIndex = 0; 427 428 for (int i = 0; i < polyLength; i++) { 429 float ratioZ = projectCasterToOutline(outlineData[i].position, 430 lightCenter, poly[i]); 431 outlineData[i].radius = ratioZ * lightSize; 432 433 outlineData[currentNormalIndex].normal = ShadowTessellator::calculateNormal( 434 outlineData[currentNormalIndex].position, 435 outlineData[nextNormalIndex].position); 436 currentNormalIndex = (currentNormalIndex + 1) % polyLength; 437 nextNormalIndex++; 438 } 439 440 projectCasterToOutline(outlineCentroid, lightCenter, polyCentroid); 441 442 int penumbraIndex = 0; 443 // Then each polygon's vertex produce at minmal 2 penumbra vertices. 444 // Since the size can be dynamic here, we keep track of the size and update 445 // the real size at the end. 446 int allocatedPenumbraLength = 2 * polyLength + SPOT_MAX_EXTRA_CORNER_VERTEX_NUMBER; 447 Vector2 penumbra[allocatedPenumbraLength]; 448 int totalExtraCornerSliceNumber = 0; 449 450 Vector2 umbra[polyLength]; 451 452 // When centroid is covered by all circles from outline, then we consider 453 // the umbra is invalid, and we will tune down the shadow strength. 454 bool hasValidUmbra = true; 455 // We need the minimal of RaitoVI to decrease the spot shadow strength accordingly. 456 float minRaitoVI = FLT_MAX; 457 458 for (int i = 0; i < polyLength; i++) { 459 // Generate all the penumbra's vertices only using the (outline vertex + normal * radius) 460 // There is no guarantee that the penumbra is still convex, but for 461 // each outline vertex, it will connect to all its corresponding penumbra vertices as 462 // triangle fans. And for neighber penumbra vertex, it will be a trapezoid. 463 // 464 // Penumbra Vertices marked as Pi 465 // Outline Vertices marked as Vi 466 // (P3) 467 // (P2) | ' (P4) 468 // (P1)' | | ' 469 // ' | | ' 470 // (P0) ------------------------------------------------(P5) 471 // | (V0) |(V1) 472 // | | 473 // | | 474 // | | 475 // | | 476 // | | 477 // | | 478 // | | 479 // | | 480 // (V3)-----------------------------------(V2) 481 int preNormalIndex = (i + polyLength - 1) % polyLength; 482 483 const Vector2& previousNormal = outlineData[preNormalIndex].normal; 484 const Vector2& currentNormal = outlineData[i].normal; 485 486 // Depending on how roundness we want for each corner, we can subdivide 487 // further here and/or introduce some heuristic to decide how much the 488 // subdivision should be. 489 int currentExtraSliceNumber = ShadowTessellator::getExtraVertexNumber( 490 previousNormal, currentNormal, SPOT_CORNER_RADIANS_DIVISOR); 491 492 int currentCornerSliceNumber = 1 + currentExtraSliceNumber; 493 totalExtraCornerSliceNumber += currentExtraSliceNumber; 494#if DEBUG_SHADOW 495 ALOGD("currentExtraSliceNumber should be %d", currentExtraSliceNumber); 496 ALOGD("currentCornerSliceNumber should be %d", currentCornerSliceNumber); 497 ALOGD("totalCornerSliceNumber is %d", totalExtraCornerSliceNumber); 498#endif 499 if (CC_UNLIKELY(totalExtraCornerSliceNumber > SPOT_MAX_EXTRA_CORNER_VERTEX_NUMBER)) { 500 currentCornerSliceNumber = 1; 501 } 502 for (int k = 0; k <= currentCornerSliceNumber; k++) { 503 Vector2 avgNormal = 504 (previousNormal * (currentCornerSliceNumber - k) + currentNormal * k) / 505 currentCornerSliceNumber; 506 avgNormal.normalize(); 507 penumbra[penumbraIndex++] = outlineData[i].position + 508 avgNormal * outlineData[i].radius; 509 } 510 511 512 // Compute the umbra by the intersection from the outline's centroid! 513 // 514 // (V) ------------------------------------ 515 // | ' | 516 // | ' | 517 // | ' (I) | 518 // | ' | 519 // | ' (C) | 520 // | | 521 // | | 522 // | | 523 // | | 524 // ------------------------------------ 525 // 526 // Connect a line b/t the outline vertex (V) and the centroid (C), it will 527 // intersect with the outline vertex's circle at point (I). 528 // Now, ratioVI = VI / VC, ratioIC = IC / VC 529 // Then the intersetion point can be computed as Ixy = Vxy * ratioIC + Cxy * ratioVI; 530 // 531 // When all of the outline circles cover the the outline centroid, (like I is 532 // on the other side of C), there is no real umbra any more, so we just fake 533 // a small area around the centroid as the umbra, and tune down the spot 534 // shadow's umbra strength to simulate the effect the whole shadow will 535 // become lighter in this case. 536 // The ratio can be simulated by using the inverse of maximum of ratioVI for 537 // all (V). 538 float distOutline = (outlineData[i].position - outlineCentroid).length(); 539 if (CC_UNLIKELY(distOutline == 0)) { 540 // If the outline has 0 area, then there is no spot shadow anyway. 541 ALOGW("Outline has 0 area, no spot shadow!"); 542 return; 543 } 544 545 float ratioVI = outlineData[i].radius / distOutline; 546 minRaitoVI = std::min(minRaitoVI, ratioVI); 547 if (ratioVI >= (1 - FAKE_UMBRA_SIZE_RATIO)) { 548 ratioVI = (1 - FAKE_UMBRA_SIZE_RATIO); 549 } 550 // When we know we don't have valid umbra, don't bother to compute the 551 // values below. But we can't skip the loop yet since we want to know the 552 // maximum ratio. 553 float ratioIC = 1 - ratioVI; 554 umbra[i] = outlineData[i].position * ratioIC + outlineCentroid * ratioVI; 555 } 556 557 hasValidUmbra = (minRaitoVI <= 1.0); 558 float shadowStrengthScale = 1.0; 559 if (!hasValidUmbra) { 560#if DEBUG_SHADOW 561 ALOGW("The object is too close to the light or too small, no real umbra!"); 562#endif 563 for (int i = 0; i < polyLength; i++) { 564 umbra[i] = outlineData[i].position * FAKE_UMBRA_SIZE_RATIO + 565 outlineCentroid * (1 - FAKE_UMBRA_SIZE_RATIO); 566 } 567 shadowStrengthScale = 1.0 / minRaitoVI; 568 } 569 570 int penumbraLength = penumbraIndex; 571 int umbraLength = polyLength; 572 573#if DEBUG_SHADOW 574 ALOGD("penumbraLength is %d , allocatedPenumbraLength %d", penumbraLength, allocatedPenumbraLength); 575 dumpPolygon(poly, polyLength, "input poly"); 576 dumpPolygon(penumbra, penumbraLength, "penumbra"); 577 dumpPolygon(umbra, umbraLength, "umbra"); 578 ALOGD("hasValidUmbra is %d and shadowStrengthScale is %f", hasValidUmbra, shadowStrengthScale); 579#endif 580 581 // The penumbra and umbra needs to be in convex shape to keep consistency 582 // and quality. 583 // Since we are still shooting rays to penumbra, it needs to be convex. 584 // Umbra can be represented as a fan from the centroid, but visually umbra 585 // looks nicer when it is convex. 586 Vector2 finalUmbra[umbraLength]; 587 Vector2 finalPenumbra[penumbraLength]; 588 int finalUmbraLength = hull(umbra, umbraLength, finalUmbra); 589 int finalPenumbraLength = hull(penumbra, penumbraLength, finalPenumbra); 590 591 generateTriangleStrip(isCasterOpaque, shadowStrengthScale, finalPenumbra, 592 finalPenumbraLength, finalUmbra, finalUmbraLength, poly, polyLength, 593 shadowTriangleStrip, outlineCentroid); 594 595} 596 597/** 598 * This is only for experimental purpose. 599 * After intersections are calculated, we could smooth the polygon if needed. 600 * So far, we don't think it is more appealing yet. 601 * 602 * @param level The level of smoothness. 603 * @param rays The total number of rays. 604 * @param rayDist (In and Out) The distance for each ray. 605 * 606 */ 607void SpotShadow::smoothPolygon(int level, int rays, float* rayDist) { 608 for (int k = 0; k < level; k++) { 609 for (int i = 0; i < rays; i++) { 610 float p1 = rayDist[(rays - 1 + i) % rays]; 611 float p2 = rayDist[i]; 612 float p3 = rayDist[(i + 1) % rays]; 613 rayDist[i] = (p1 + p2 * 2 + p3) / 4; 614 } 615 } 616} 617 618// Index pair is meant for storing the tessellation information for the penumbra 619// area. One index must come from exterior tangent of the circles, the other one 620// must come from the interior tangent of the circles. 621struct IndexPair { 622 int outerIndex; 623 int innerIndex; 624}; 625 626// For one penumbra vertex, find the cloest umbra vertex and return its index. 627inline int getClosestUmbraIndex(const Vector2& pivot, const Vector2* polygon, int polygonLength) { 628 float minLengthSquared = FLT_MAX; 629 int resultIndex = -1; 630 bool hasDecreased = false; 631 // Starting with some negative offset, assuming both umbra and penumbra are starting 632 // at the same angle, this can help to find the result faster. 633 // Normally, loop 3 times, we can find the closest point. 634 int offset = polygonLength - 2; 635 for (int i = 0; i < polygonLength; i++) { 636 int currentIndex = (i + offset) % polygonLength; 637 float currentLengthSquared = (pivot - polygon[currentIndex]).lengthSquared(); 638 if (currentLengthSquared < minLengthSquared) { 639 if (minLengthSquared != FLT_MAX) { 640 hasDecreased = true; 641 } 642 minLengthSquared = currentLengthSquared; 643 resultIndex = currentIndex; 644 } else if (currentLengthSquared > minLengthSquared && hasDecreased) { 645 // Early break b/c we have found the closet one and now the length 646 // is increasing again. 647 break; 648 } 649 } 650 if(resultIndex == -1) { 651 ALOGE("resultIndex is -1, the polygon must be invalid!"); 652 resultIndex = 0; 653 } 654 return resultIndex; 655} 656 657// Allow some epsilon here since the later ray intersection did allow for some small 658// floating point error, when the intersection point is slightly outside the segment. 659inline bool sameDirections(bool isPositiveCross, float a, float b) { 660 if (isPositiveCross) { 661 return a >= -EPSILON && b >= -EPSILON; 662 } else { 663 return a <= EPSILON && b <= EPSILON; 664 } 665} 666 667// Find the right polygon edge to shoot the ray at. 668inline int findPolyIndex(bool isPositiveCross, int startPolyIndex, const Vector2& umbraDir, 669 const Vector2* polyToCentroid, int polyLength) { 670 // Make sure we loop with a bound. 671 for (int i = 0; i < polyLength; i++) { 672 int currentIndex = (i + startPolyIndex) % polyLength; 673 const Vector2& currentToCentroid = polyToCentroid[currentIndex]; 674 const Vector2& nextToCentroid = polyToCentroid[(currentIndex + 1) % polyLength]; 675 676 float currentCrossUmbra = currentToCentroid.cross(umbraDir); 677 float umbraCrossNext = umbraDir.cross(nextToCentroid); 678 if (sameDirections(isPositiveCross, currentCrossUmbra, umbraCrossNext)) { 679#if DEBUG_SHADOW 680 ALOGD("findPolyIndex loop %d times , index %d", i, currentIndex ); 681#endif 682 return currentIndex; 683 } 684 } 685 LOG_ALWAYS_FATAL("Can't find the right polygon's edge from startPolyIndex %d", startPolyIndex); 686 return -1; 687} 688 689// Generate the index pair for penumbra / umbra vertices, and more penumbra vertices 690// if needed. 691inline void genNewPenumbraAndPairWithUmbra(const Vector2* penumbra, int penumbraLength, 692 const Vector2* umbra, int umbraLength, Vector2* newPenumbra, int& newPenumbraIndex, 693 IndexPair* verticesPair, int& verticesPairIndex) { 694 // In order to keep everything in just one loop, we need to pre-compute the 695 // closest umbra vertex for the last penumbra vertex. 696 int previousClosestUmbraIndex = getClosestUmbraIndex(penumbra[penumbraLength - 1], 697 umbra, umbraLength); 698 for (int i = 0; i < penumbraLength; i++) { 699 const Vector2& currentPenumbraVertex = penumbra[i]; 700 // For current penumbra vertex, starting from previousClosestUmbraIndex, 701 // then check the next one until the distance increase. 702 // The last one before the increase is the umbra vertex we need to pair with. 703 float currentLengthSquared = 704 (currentPenumbraVertex - umbra[previousClosestUmbraIndex]).lengthSquared(); 705 int currentClosestUmbraIndex = previousClosestUmbraIndex; 706 int indexDelta = 0; 707 for (int j = 1; j < umbraLength; j++) { 708 int newUmbraIndex = (previousClosestUmbraIndex + j) % umbraLength; 709 float newLengthSquared = (currentPenumbraVertex - umbra[newUmbraIndex]).lengthSquared(); 710 if (newLengthSquared > currentLengthSquared) { 711 // currentClosestUmbraIndex is the umbra vertex's index which has 712 // currently found smallest distance, so we can simply break here. 713 break; 714 } else { 715 currentLengthSquared = newLengthSquared; 716 indexDelta++; 717 currentClosestUmbraIndex = newUmbraIndex; 718 } 719 } 720 721 if (indexDelta > 1) { 722 // For those umbra don't have penumbra, generate new penumbra vertices by interpolation. 723 // 724 // Assuming Pi for penumbra vertices, and Ui for umbra vertices. 725 // In the case like below P1 paired with U1 and P2 paired with U5. 726 // U2 to U4 are unpaired umbra vertices. 727 // 728 // P1 P2 729 // | | 730 // U1 U2 U3 U4 U5 731 // 732 // We will need to generate 3 more penumbra vertices P1.1, P1.2, P1.3 733 // to pair with U2 to U4. 734 // 735 // P1 P1.1 P1.2 P1.3 P2 736 // | | | | | 737 // U1 U2 U3 U4 U5 738 // 739 // That distance ratio b/t Ui to U1 and Ui to U5 decides its paired penumbra 740 // vertex's location. 741 int newPenumbraNumber = indexDelta - 1; 742 743 float accumulatedDeltaLength[indexDelta]; 744 float totalDeltaLength = 0; 745 746 // To save time, cache the previous umbra vertex info outside the loop 747 // and update each loop. 748 Vector2 previousClosestUmbra = umbra[previousClosestUmbraIndex]; 749 Vector2 skippedUmbra; 750 // Use umbra data to precompute the length b/t unpaired umbra vertices, 751 // and its ratio against the total length. 752 for (int k = 0; k < indexDelta; k++) { 753 int skippedUmbraIndex = (previousClosestUmbraIndex + k + 1) % umbraLength; 754 skippedUmbra = umbra[skippedUmbraIndex]; 755 float currentDeltaLength = (skippedUmbra - previousClosestUmbra).length(); 756 757 totalDeltaLength += currentDeltaLength; 758 accumulatedDeltaLength[k] = totalDeltaLength; 759 760 previousClosestUmbra = skippedUmbra; 761 } 762 763 const Vector2& previousPenumbra = penumbra[(i + penumbraLength - 1) % penumbraLength]; 764 // Then for each unpaired umbra vertex, create a new penumbra by the ratio, 765 // and pair them togehter. 766 for (int k = 0; k < newPenumbraNumber; k++) { 767 float weightForCurrentPenumbra = 1.0f; 768 if (totalDeltaLength != 0.0f) { 769 weightForCurrentPenumbra = accumulatedDeltaLength[k] / totalDeltaLength; 770 } 771 float weightForPreviousPenumbra = 1.0f - weightForCurrentPenumbra; 772 773 Vector2 interpolatedPenumbra = currentPenumbraVertex * weightForCurrentPenumbra + 774 previousPenumbra * weightForPreviousPenumbra; 775 776 int skippedUmbraIndex = (previousClosestUmbraIndex + k + 1) % umbraLength; 777 verticesPair[verticesPairIndex].outerIndex = newPenumbraIndex; 778 verticesPair[verticesPairIndex].innerIndex = skippedUmbraIndex; 779 verticesPairIndex++; 780 newPenumbra[newPenumbraIndex++] = interpolatedPenumbra; 781 } 782 } 783 verticesPair[verticesPairIndex].outerIndex = newPenumbraIndex; 784 verticesPair[verticesPairIndex].innerIndex = currentClosestUmbraIndex; 785 verticesPairIndex++; 786 newPenumbra[newPenumbraIndex++] = currentPenumbraVertex; 787 788 previousClosestUmbraIndex = currentClosestUmbraIndex; 789 } 790} 791 792// Precompute all the polygon's vector, return true if the reference cross product is positive. 793inline bool genPolyToCentroid(const Vector2* poly2d, int polyLength, 794 const Vector2& centroid, Vector2* polyToCentroid) { 795 for (int j = 0; j < polyLength; j++) { 796 polyToCentroid[j] = poly2d[j] - centroid; 797 // Normalize these vectors such that we can use epsilon comparison after 798 // computing their cross products with another normalized vector. 799 polyToCentroid[j].normalize(); 800 } 801 float refCrossProduct = 0; 802 for (int j = 0; j < polyLength; j++) { 803 refCrossProduct = polyToCentroid[j].cross(polyToCentroid[(j + 1) % polyLength]); 804 if (refCrossProduct != 0) { 805 break; 806 } 807 } 808 809 return refCrossProduct > 0; 810} 811 812// For one umbra vertex, shoot an ray from centroid to it. 813// If the ray hit the polygon first, then return the intersection point as the 814// closer vertex. 815inline Vector2 getCloserVertex(const Vector2& umbraVertex, const Vector2& centroid, 816 const Vector2* poly2d, int polyLength, const Vector2* polyToCentroid, 817 bool isPositiveCross, int& previousPolyIndex) { 818 Vector2 umbraToCentroid = umbraVertex - centroid; 819 float distanceToUmbra = umbraToCentroid.length(); 820 umbraToCentroid = umbraToCentroid / distanceToUmbra; 821 822 // previousPolyIndex is updated for each item such that we can minimize the 823 // looping inside findPolyIndex(); 824 previousPolyIndex = findPolyIndex(isPositiveCross, previousPolyIndex, 825 umbraToCentroid, polyToCentroid, polyLength); 826 827 float dx = umbraToCentroid.x; 828 float dy = umbraToCentroid.y; 829 float distanceToIntersectPoly = rayIntersectPoints(centroid, dx, dy, 830 poly2d[previousPolyIndex], poly2d[(previousPolyIndex + 1) % polyLength]); 831 if (distanceToIntersectPoly < 0) { 832 distanceToIntersectPoly = 0; 833 } 834 835 // Pick the closer one as the occluded area vertex. 836 Vector2 closerVertex; 837 if (distanceToIntersectPoly < distanceToUmbra) { 838 closerVertex.x = centroid.x + dx * distanceToIntersectPoly; 839 closerVertex.y = centroid.y + dy * distanceToIntersectPoly; 840 } else { 841 closerVertex = umbraVertex; 842 } 843 844 return closerVertex; 845} 846 847/** 848 * Generate a triangle strip given two convex polygon 849**/ 850void SpotShadow::generateTriangleStrip(bool isCasterOpaque, float shadowStrengthScale, 851 Vector2* penumbra, int penumbraLength, Vector2* umbra, int umbraLength, 852 const Vector3* poly, int polyLength, VertexBuffer& shadowTriangleStrip, 853 const Vector2& centroid) { 854 bool hasOccludedUmbraArea = false; 855 Vector2 poly2d[polyLength]; 856 857 if (isCasterOpaque) { 858 for (int i = 0; i < polyLength; i++) { 859 poly2d[i].x = poly[i].x; 860 poly2d[i].y = poly[i].y; 861 } 862 // Make sure the centroid is inside the umbra, otherwise, fall back to the 863 // approach as if there is no occluded umbra area. 864 if (testPointInsidePolygon(centroid, poly2d, polyLength)) { 865 hasOccludedUmbraArea = true; 866 } 867 } 868 869 // For each penumbra vertex, find its corresponding closest umbra vertex index. 870 // 871 // Penumbra Vertices marked as Pi 872 // Umbra Vertices marked as Ui 873 // (P3) 874 // (P2) | ' (P4) 875 // (P1)' | | ' 876 // ' | | ' 877 // (P0) ------------------------------------------------(P5) 878 // | (U0) |(U1) 879 // | | 880 // | |(U2) (P5.1) 881 // | | 882 // | | 883 // | | 884 // | | 885 // | | 886 // | | 887 // (U4)-----------------------------------(U3) (P6) 888 // 889 // At least, like P0, P1, P2, they will find the matching umbra as U0. 890 // If we jump over some umbra vertex without matching penumbra vertex, then 891 // we will generate some new penumbra vertex by interpolation. Like P6 is 892 // matching U3, but U2 is not matched with any penumbra vertex. 893 // So interpolate P5.1 out and match U2. 894 // In this way, every umbra vertex will have a matching penumbra vertex. 895 // 896 // The total pair number can be as high as umbraLength + penumbraLength. 897 const int maxNewPenumbraLength = umbraLength + penumbraLength; 898 IndexPair verticesPair[maxNewPenumbraLength]; 899 int verticesPairIndex = 0; 900 901 // Cache all the existing penumbra vertices and newly interpolated vertices into a 902 // a new array. 903 Vector2 newPenumbra[maxNewPenumbraLength]; 904 int newPenumbraIndex = 0; 905 906 // For each penumbra vertex, find its closet umbra vertex by comparing the 907 // neighbor umbra vertices. 908 genNewPenumbraAndPairWithUmbra(penumbra, penumbraLength, umbra, umbraLength, newPenumbra, 909 newPenumbraIndex, verticesPair, verticesPairIndex); 910 ShadowTessellator::checkOverflow(verticesPairIndex, maxNewPenumbraLength, "Spot pair"); 911 ShadowTessellator::checkOverflow(newPenumbraIndex, maxNewPenumbraLength, "Spot new penumbra"); 912#if DEBUG_SHADOW 913 for (int i = 0; i < umbraLength; i++) { 914 ALOGD("umbra i %d, [%f, %f]", i, umbra[i].x, umbra[i].y); 915 } 916 for (int i = 0; i < newPenumbraIndex; i++) { 917 ALOGD("new penumbra i %d, [%f, %f]", i, newPenumbra[i].x, newPenumbra[i].y); 918 } 919 for (int i = 0; i < verticesPairIndex; i++) { 920 ALOGD("index i %d, [%d, %d]", i, verticesPair[i].outerIndex, verticesPair[i].innerIndex); 921 } 922#endif 923 924 // For the size of vertex buffer, we need 3 rings, one has newPenumbraSize, 925 // one has umbraLength, the last one has at most umbraLength. 926 // 927 // For the size of index buffer, the umbra area needs (2 * umbraLength + 2). 928 // The penumbra one can vary a bit, but it is bounded by (2 * verticesPairIndex + 2). 929 // And 2 more for jumping between penumbra to umbra. 930 const int newPenumbraLength = newPenumbraIndex; 931 const int totalVertexCount = newPenumbraLength + umbraLength * 2; 932 const int totalIndexCount = 2 * umbraLength + 2 * verticesPairIndex + 6; 933 AlphaVertex* shadowVertices = 934 shadowTriangleStrip.alloc<AlphaVertex>(totalVertexCount); 935 uint16_t* indexBuffer = 936 shadowTriangleStrip.allocIndices<uint16_t>(totalIndexCount); 937 int vertexBufferIndex = 0; 938 int indexBufferIndex = 0; 939 940 // Fill the IB and VB for the penumbra area. 941 for (int i = 0; i < newPenumbraLength; i++) { 942 AlphaVertex::set(&shadowVertices[vertexBufferIndex++], newPenumbra[i].x, 943 newPenumbra[i].y, PENUMBRA_ALPHA); 944 } 945 for (int i = 0; i < umbraLength; i++) { 946 AlphaVertex::set(&shadowVertices[vertexBufferIndex++], umbra[i].x, umbra[i].y, 947 UMBRA_ALPHA); 948 } 949 950 for (int i = 0; i < verticesPairIndex; i++) { 951 indexBuffer[indexBufferIndex++] = verticesPair[i].outerIndex; 952 // All umbra index need to be offseted by newPenumbraSize. 953 indexBuffer[indexBufferIndex++] = verticesPair[i].innerIndex + newPenumbraLength; 954 } 955 indexBuffer[indexBufferIndex++] = verticesPair[0].outerIndex; 956 indexBuffer[indexBufferIndex++] = verticesPair[0].innerIndex + newPenumbraLength; 957 958 // Now fill the IB and VB for the umbra area. 959 // First duplicated the index from previous strip and the first one for the 960 // degenerated triangles. 961 indexBuffer[indexBufferIndex] = indexBuffer[indexBufferIndex - 1]; 962 indexBufferIndex++; 963 indexBuffer[indexBufferIndex++] = newPenumbraLength + 0; 964 // Save the first VB index for umbra area in order to close the loop. 965 int savedStartIndex = vertexBufferIndex; 966 967 if (hasOccludedUmbraArea) { 968 // Precompute all the polygon's vector, and the reference cross product, 969 // in order to find the right polygon edge for the ray to intersect. 970 Vector2 polyToCentroid[polyLength]; 971 bool isPositiveCross = genPolyToCentroid(poly2d, polyLength, centroid, polyToCentroid); 972 973 // Because both the umbra and polygon are going in the same direction, 974 // we can save the previous polygon index to make sure we have less polygon 975 // vertex to compute for each ray. 976 int previousPolyIndex = 0; 977 for (int i = 0; i < umbraLength; i++) { 978 // Shoot a ray from centroid to each umbra vertices and pick the one with 979 // shorter distance to the centroid, b/t the umbra vertex or the intersection point. 980 Vector2 closerVertex = getCloserVertex(umbra[i], centroid, poly2d, polyLength, 981 polyToCentroid, isPositiveCross, previousPolyIndex); 982 983 // We already stored the umbra vertices, just need to add the occlued umbra's ones. 984 indexBuffer[indexBufferIndex++] = newPenumbraLength + i; 985 indexBuffer[indexBufferIndex++] = vertexBufferIndex; 986 AlphaVertex::set(&shadowVertices[vertexBufferIndex++], 987 closerVertex.x, closerVertex.y, UMBRA_ALPHA); 988 } 989 } else { 990 // If there is no occluded umbra at all, then draw the triangle fan 991 // starting from the centroid to all umbra vertices. 992 int lastCentroidIndex = vertexBufferIndex; 993 AlphaVertex::set(&shadowVertices[vertexBufferIndex++], centroid.x, 994 centroid.y, UMBRA_ALPHA); 995 for (int i = 0; i < umbraLength; i++) { 996 indexBuffer[indexBufferIndex++] = newPenumbraLength + i; 997 indexBuffer[indexBufferIndex++] = lastCentroidIndex; 998 } 999 } 1000 // Closing the umbra area triangle's loop here. 1001 indexBuffer[indexBufferIndex++] = newPenumbraLength; 1002 indexBuffer[indexBufferIndex++] = savedStartIndex; 1003 1004 // At the end, update the real index and vertex buffer size. 1005 shadowTriangleStrip.updateVertexCount(vertexBufferIndex); 1006 shadowTriangleStrip.updateIndexCount(indexBufferIndex); 1007 ShadowTessellator::checkOverflow(vertexBufferIndex, totalVertexCount, "Spot Vertex Buffer"); 1008 ShadowTessellator::checkOverflow(indexBufferIndex, totalIndexCount, "Spot Index Buffer"); 1009 1010 shadowTriangleStrip.setMeshFeatureFlags(VertexBuffer::kAlpha | VertexBuffer::kIndices); 1011 shadowTriangleStrip.computeBounds<AlphaVertex>(); 1012} 1013 1014#if DEBUG_SHADOW 1015 1016#define TEST_POINT_NUMBER 128 1017/** 1018 * Calculate the bounds for generating random test points. 1019 */ 1020void SpotShadow::updateBound(const Vector2 inVector, Vector2& lowerBound, 1021 Vector2& upperBound) { 1022 if (inVector.x < lowerBound.x) { 1023 lowerBound.x = inVector.x; 1024 } 1025 1026 if (inVector.y < lowerBound.y) { 1027 lowerBound.y = inVector.y; 1028 } 1029 1030 if (inVector.x > upperBound.x) { 1031 upperBound.x = inVector.x; 1032 } 1033 1034 if (inVector.y > upperBound.y) { 1035 upperBound.y = inVector.y; 1036 } 1037} 1038 1039/** 1040 * For debug purpose, when things go wrong, dump the whole polygon data. 1041 */ 1042void SpotShadow::dumpPolygon(const Vector2* poly, int polyLength, const char* polyName) { 1043 for (int i = 0; i < polyLength; i++) { 1044 ALOGD("polygon %s i %d x %f y %f", polyName, i, poly[i].x, poly[i].y); 1045 } 1046} 1047 1048/** 1049 * For debug purpose, when things go wrong, dump the whole polygon data. 1050 */ 1051void SpotShadow::dumpPolygon(const Vector3* poly, int polyLength, const char* polyName) { 1052 for (int i = 0; i < polyLength; i++) { 1053 ALOGD("polygon %s i %d x %f y %f z %f", polyName, i, poly[i].x, poly[i].y, poly[i].z); 1054 } 1055} 1056 1057/** 1058 * Test whether the polygon is convex. 1059 */ 1060bool SpotShadow::testConvex(const Vector2* polygon, int polygonLength, 1061 const char* name) { 1062 bool isConvex = true; 1063 for (int i = 0; i < polygonLength; i++) { 1064 Vector2 start = polygon[i]; 1065 Vector2 middle = polygon[(i + 1) % polygonLength]; 1066 Vector2 end = polygon[(i + 2) % polygonLength]; 1067 1068 float delta = (float(middle.x) - start.x) * (float(end.y) - start.y) - 1069 (float(middle.y) - start.y) * (float(end.x) - start.x); 1070 bool isCCWOrCoLinear = (delta >= EPSILON); 1071 1072 if (isCCWOrCoLinear) { 1073 ALOGW("(Error Type 2): polygon (%s) is not a convex b/c start (x %f, y %f)," 1074 "middle (x %f, y %f) and end (x %f, y %f) , delta is %f !!!", 1075 name, start.x, start.y, middle.x, middle.y, end.x, end.y, delta); 1076 isConvex = false; 1077 break; 1078 } 1079 } 1080 return isConvex; 1081} 1082 1083/** 1084 * Test whether or not the polygon (intersection) is within the 2 input polygons. 1085 * Using Marte Carlo method, we generate a random point, and if it is inside the 1086 * intersection, then it must be inside both source polygons. 1087 */ 1088void SpotShadow::testIntersection(const Vector2* poly1, int poly1Length, 1089 const Vector2* poly2, int poly2Length, 1090 const Vector2* intersection, int intersectionLength) { 1091 // Find the min and max of x and y. 1092 Vector2 lowerBound = {FLT_MAX, FLT_MAX}; 1093 Vector2 upperBound = {-FLT_MAX, -FLT_MAX}; 1094 for (int i = 0; i < poly1Length; i++) { 1095 updateBound(poly1[i], lowerBound, upperBound); 1096 } 1097 for (int i = 0; i < poly2Length; i++) { 1098 updateBound(poly2[i], lowerBound, upperBound); 1099 } 1100 1101 bool dumpPoly = false; 1102 for (int k = 0; k < TEST_POINT_NUMBER; k++) { 1103 // Generate a random point between minX, minY and maxX, maxY. 1104 float randomX = rand() / float(RAND_MAX); 1105 float randomY = rand() / float(RAND_MAX); 1106 1107 Vector2 testPoint; 1108 testPoint.x = lowerBound.x + randomX * (upperBound.x - lowerBound.x); 1109 testPoint.y = lowerBound.y + randomY * (upperBound.y - lowerBound.y); 1110 1111 // If the random point is in both poly 1 and 2, then it must be intersection. 1112 if (testPointInsidePolygon(testPoint, intersection, intersectionLength)) { 1113 if (!testPointInsidePolygon(testPoint, poly1, poly1Length)) { 1114 dumpPoly = true; 1115 ALOGW("(Error Type 1): one point (%f, %f) in the intersection is" 1116 " not in the poly1", 1117 testPoint.x, testPoint.y); 1118 } 1119 1120 if (!testPointInsidePolygon(testPoint, poly2, poly2Length)) { 1121 dumpPoly = true; 1122 ALOGW("(Error Type 1): one point (%f, %f) in the intersection is" 1123 " not in the poly2", 1124 testPoint.x, testPoint.y); 1125 } 1126 } 1127 } 1128 1129 if (dumpPoly) { 1130 dumpPolygon(intersection, intersectionLength, "intersection"); 1131 for (int i = 1; i < intersectionLength; i++) { 1132 Vector2 delta = intersection[i] - intersection[i - 1]; 1133 ALOGD("Intersetion i, %d Vs i-1 is delta %f", i, delta.lengthSquared()); 1134 } 1135 1136 dumpPolygon(poly1, poly1Length, "poly 1"); 1137 dumpPolygon(poly2, poly2Length, "poly 2"); 1138 } 1139} 1140#endif 1141 1142}; // namespace uirenderer 1143}; // namespace android 1144