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// The highest z value can't be higher than (CASTER_Z_CAP_RATIO * light.z) 20#define CASTER_Z_CAP_RATIO 0.95f 21 22// When there is no umbra, then just fake the umbra using 23// centroid * (1 - FAKE_UMBRA_SIZE_RATIO) + outline * FAKE_UMBRA_SIZE_RATIO 24#define FAKE_UMBRA_SIZE_RATIO 0.05f 25 26// When the polygon is about 90 vertices, the penumbra + umbra can reach 270 rays. 27// That is consider pretty fine tessllated polygon so far. 28// This is just to prevent using too much some memory when edge slicing is not 29// needed any more. 30#define FINE_TESSELLATED_POLYGON_RAY_NUMBER 270 31/** 32 * Extra vertices for the corner for smoother corner. 33 * Only for outer loop. 34 * Note that we use such extra memory to avoid an extra loop. 35 */ 36// For half circle, we could add EXTRA_VERTEX_PER_PI vertices. 37// Set to 1 if we don't want to have any. 38#define SPOT_EXTRA_CORNER_VERTEX_PER_PI 18 39 40// For the whole polygon, the sum of all the deltas b/t normals is 2 * M_PI, 41// therefore, the maximum number of extra vertices will be twice bigger. 42#define SPOT_MAX_EXTRA_CORNER_VERTEX_NUMBER (2 * SPOT_EXTRA_CORNER_VERTEX_PER_PI) 43 44// For each RADIANS_DIVISOR, we would allocate one more vertex b/t the normals. 45#define SPOT_CORNER_RADIANS_DIVISOR (M_PI / SPOT_EXTRA_CORNER_VERTEX_PER_PI) 46 47 48#include <math.h> 49#include <stdlib.h> 50#include <utils/Log.h> 51 52#include "ShadowTessellator.h" 53#include "SpotShadow.h" 54#include "Vertex.h" 55#include "utils/MathUtils.h" 56 57// TODO: After we settle down the new algorithm, we can remove the old one and 58// its utility functions. 59// Right now, we still need to keep it for comparison purpose and future expansion. 60namespace android { 61namespace uirenderer { 62 63static const float EPSILON = 1e-7; 64 65/** 66 * For each polygon's vertex, the light center will project it to the receiver 67 * as one of the outline vertex. 68 * For each outline vertex, we need to store the position and normal. 69 * Normal here is defined against the edge by the current vertex and the next vertex. 70 */ 71struct OutlineData { 72 Vector2 position; 73 Vector2 normal; 74 float radius; 75}; 76 77/** 78 * For each vertex, we need to keep track of its angle, whether it is penumbra or 79 * umbra, and its corresponding vertex index. 80 */ 81struct SpotShadow::VertexAngleData { 82 // The angle to the vertex from the centroid. 83 float mAngle; 84 // True is the vertex comes from penumbra, otherwise it comes from umbra. 85 bool mIsPenumbra; 86 // The index of the vertex described by this data. 87 int mVertexIndex; 88 void set(float angle, bool isPenumbra, int index) { 89 mAngle = angle; 90 mIsPenumbra = isPenumbra; 91 mVertexIndex = index; 92 } 93}; 94 95/** 96 * Calculate the angle between and x and a y coordinate. 97 * The atan2 range from -PI to PI. 98 */ 99static float angle(const Vector2& point, const Vector2& center) { 100 return atan2(point.y - center.y, point.x - center.x); 101} 102 103/** 104 * Calculate the intersection of a ray with the line segment defined by two points. 105 * 106 * Returns a negative value in error conditions. 107 108 * @param rayOrigin The start of the ray 109 * @param dx The x vector of the ray 110 * @param dy The y vector of the ray 111 * @param p1 The first point defining the line segment 112 * @param p2 The second point defining the line segment 113 * @return The distance along the ray if it intersects with the line segment, negative if otherwise 114 */ 115static float rayIntersectPoints(const Vector2& rayOrigin, float dx, float dy, 116 const Vector2& p1, const Vector2& p2) { 117 // The math below is derived from solving this formula, basically the 118 // intersection point should stay on both the ray and the edge of (p1, p2). 119 // solve([p1x+t*(p2x-p1x)=dx*t2+px,p1y+t*(p2y-p1y)=dy*t2+py],[t,t2]); 120 121 float divisor = (dx * (p1.y - p2.y) + dy * p2.x - dy * p1.x); 122 if (divisor == 0) return -1.0f; // error, invalid divisor 123 124#if DEBUG_SHADOW 125 float interpVal = (dx * (p1.y - rayOrigin.y) + dy * rayOrigin.x - dy * p1.x) / divisor; 126 if (interpVal < 0 || interpVal > 1) { 127 ALOGW("rayIntersectPoints is hitting outside the segment %f", interpVal); 128 } 129#endif 130 131 float distance = (p1.x * (rayOrigin.y - p2.y) + p2.x * (p1.y - rayOrigin.y) + 132 rayOrigin.x * (p2.y - p1.y)) / divisor; 133 134 return distance; // may be negative in error cases 135} 136 137/** 138 * Sort points by their X coordinates 139 * 140 * @param points the points as a Vector2 array. 141 * @param pointsLength the number of vertices of the polygon. 142 */ 143void SpotShadow::xsort(Vector2* points, int pointsLength) { 144 quicksortX(points, 0, pointsLength - 1); 145} 146 147/** 148 * compute the convex hull of a collection of Points 149 * 150 * @param points the points as a Vector2 array. 151 * @param pointsLength the number of vertices of the polygon. 152 * @param retPoly pre allocated array of floats to put the vertices 153 * @return the number of points in the polygon 0 if no intersection 154 */ 155int SpotShadow::hull(Vector2* points, int pointsLength, Vector2* retPoly) { 156 xsort(points, pointsLength); 157 int n = pointsLength; 158 Vector2 lUpper[n]; 159 lUpper[0] = points[0]; 160 lUpper[1] = points[1]; 161 162 int lUpperSize = 2; 163 164 for (int i = 2; i < n; i++) { 165 lUpper[lUpperSize] = points[i]; 166 lUpperSize++; 167 168 while (lUpperSize > 2 && !ccw( 169 lUpper[lUpperSize - 3].x, lUpper[lUpperSize - 3].y, 170 lUpper[lUpperSize - 2].x, lUpper[lUpperSize - 2].y, 171 lUpper[lUpperSize - 1].x, lUpper[lUpperSize - 1].y)) { 172 // Remove the middle point of the three last 173 lUpper[lUpperSize - 2].x = lUpper[lUpperSize - 1].x; 174 lUpper[lUpperSize - 2].y = lUpper[lUpperSize - 1].y; 175 lUpperSize--; 176 } 177 } 178 179 Vector2 lLower[n]; 180 lLower[0] = points[n - 1]; 181 lLower[1] = points[n - 2]; 182 183 int lLowerSize = 2; 184 185 for (int i = n - 3; i >= 0; i--) { 186 lLower[lLowerSize] = points[i]; 187 lLowerSize++; 188 189 while (lLowerSize > 2 && !ccw( 190 lLower[lLowerSize - 3].x, lLower[lLowerSize - 3].y, 191 lLower[lLowerSize - 2].x, lLower[lLowerSize - 2].y, 192 lLower[lLowerSize - 1].x, lLower[lLowerSize - 1].y)) { 193 // Remove the middle point of the three last 194 lLower[lLowerSize - 2] = lLower[lLowerSize - 1]; 195 lLowerSize--; 196 } 197 } 198 199 // output points in CW ordering 200 const int total = lUpperSize + lLowerSize - 2; 201 int outIndex = total - 1; 202 for (int i = 0; i < lUpperSize; i++) { 203 retPoly[outIndex] = lUpper[i]; 204 outIndex--; 205 } 206 207 for (int i = 1; i < lLowerSize - 1; i++) { 208 retPoly[outIndex] = lLower[i]; 209 outIndex--; 210 } 211 // TODO: Add test harness which verify that all the points are inside the hull. 212 return total; 213} 214 215/** 216 * Test whether the 3 points form a counter clockwise turn. 217 * 218 * @return true if a right hand turn 219 */ 220bool SpotShadow::ccw(float ax, float ay, float bx, float by, 221 float cx, float cy) { 222 return (bx - ax) * (cy - ay) - (by - ay) * (cx - ax) > EPSILON; 223} 224 225/** 226 * Sort points about a center point 227 * 228 * @param poly The in and out polyogon as a Vector2 array. 229 * @param polyLength The number of vertices of the polygon. 230 * @param center the center ctr[0] = x , ctr[1] = y to sort around. 231 */ 232void SpotShadow::sort(Vector2* poly, int polyLength, const Vector2& center) { 233 quicksortCirc(poly, 0, polyLength - 1, center); 234} 235 236/** 237 * Swap points pointed to by i and j 238 */ 239void SpotShadow::swap(Vector2* points, int i, int j) { 240 Vector2 temp = points[i]; 241 points[i] = points[j]; 242 points[j] = temp; 243} 244 245/** 246 * quick sort implementation about the center. 247 */ 248void SpotShadow::quicksortCirc(Vector2* points, int low, int high, 249 const Vector2& center) { 250 int i = low, j = high; 251 int p = low + (high - low) / 2; 252 float pivot = angle(points[p], center); 253 while (i <= j) { 254 while (angle(points[i], center) > pivot) { 255 i++; 256 } 257 while (angle(points[j], center) < pivot) { 258 j--; 259 } 260 261 if (i <= j) { 262 swap(points, i, j); 263 i++; 264 j--; 265 } 266 } 267 if (low < j) quicksortCirc(points, low, j, center); 268 if (i < high) quicksortCirc(points, i, high, center); 269} 270 271/** 272 * Sort points by x axis 273 * 274 * @param points points to sort 275 * @param low start index 276 * @param high end index 277 */ 278void SpotShadow::quicksortX(Vector2* points, int low, int high) { 279 int i = low, j = high; 280 int p = low + (high - low) / 2; 281 float pivot = points[p].x; 282 while (i <= j) { 283 while (points[i].x < pivot) { 284 i++; 285 } 286 while (points[j].x > pivot) { 287 j--; 288 } 289 290 if (i <= j) { 291 swap(points, i, j); 292 i++; 293 j--; 294 } 295 } 296 if (low < j) quicksortX(points, low, j); 297 if (i < high) quicksortX(points, i, high); 298} 299 300/** 301 * Test whether a point is inside the polygon. 302 * 303 * @param testPoint the point to test 304 * @param poly the polygon 305 * @return true if the testPoint is inside the poly. 306 */ 307bool SpotShadow::testPointInsidePolygon(const Vector2 testPoint, 308 const Vector2* poly, int len) { 309 bool c = false; 310 float testx = testPoint.x; 311 float testy = testPoint.y; 312 for (int i = 0, j = len - 1; i < len; j = i++) { 313 float startX = poly[j].x; 314 float startY = poly[j].y; 315 float endX = poly[i].x; 316 float endY = poly[i].y; 317 318 if (((endY > testy) != (startY > testy)) 319 && (testx < (startX - endX) * (testy - endY) 320 / (startY - endY) + endX)) { 321 c = !c; 322 } 323 } 324 return c; 325} 326 327/** 328 * Make the polygon turn clockwise. 329 * 330 * @param polygon the polygon as a Vector2 array. 331 * @param len the number of points of the polygon 332 */ 333void SpotShadow::makeClockwise(Vector2* polygon, int len) { 334 if (polygon == 0 || len == 0) { 335 return; 336 } 337 if (!ShadowTessellator::isClockwise(polygon, len)) { 338 reverse(polygon, len); 339 } 340} 341 342/** 343 * Reverse the polygon 344 * 345 * @param polygon the polygon as a Vector2 array 346 * @param len the number of points of the polygon 347 */ 348void SpotShadow::reverse(Vector2* polygon, int len) { 349 int n = len / 2; 350 for (int i = 0; i < n; i++) { 351 Vector2 tmp = polygon[i]; 352 int k = len - 1 - i; 353 polygon[i] = polygon[k]; 354 polygon[k] = tmp; 355 } 356} 357 358/** 359 * Compute a horizontal circular polygon about point (x , y , height) of radius 360 * (size) 361 * 362 * @param points number of the points of the output polygon. 363 * @param lightCenter the center of the light. 364 * @param size the light size. 365 * @param ret result polygon. 366 */ 367void SpotShadow::computeLightPolygon(int points, const Vector3& lightCenter, 368 float size, Vector3* ret) { 369 // TODO: Caching all the sin / cos values and store them in a look up table. 370 for (int i = 0; i < points; i++) { 371 float angle = 2 * i * M_PI / points; 372 ret[i].x = cosf(angle) * size + lightCenter.x; 373 ret[i].y = sinf(angle) * size + lightCenter.y; 374 ret[i].z = lightCenter.z; 375 } 376} 377 378/** 379 * From light center, project one vertex to the z=0 surface and get the outline. 380 * 381 * @param outline The result which is the outline position. 382 * @param lightCenter The center of light. 383 * @param polyVertex The input polygon's vertex. 384 * 385 * @return float The ratio of (polygon.z / light.z - polygon.z) 386 */ 387float SpotShadow::projectCasterToOutline(Vector2& outline, 388 const Vector3& lightCenter, const Vector3& polyVertex) { 389 float lightToPolyZ = lightCenter.z - polyVertex.z; 390 float ratioZ = CASTER_Z_CAP_RATIO; 391 if (lightToPolyZ != 0) { 392 // If any caster's vertex is almost above the light, we just keep it as 95% 393 // of the height of the light. 394 ratioZ = MathUtils::clamp(polyVertex.z / lightToPolyZ, 0.0f, CASTER_Z_CAP_RATIO); 395 } 396 397 outline.x = polyVertex.x - ratioZ * (lightCenter.x - polyVertex.x); 398 outline.y = polyVertex.y - ratioZ * (lightCenter.y - polyVertex.y); 399 return ratioZ; 400} 401 402/** 403 * Generate the shadow spot light of shape lightPoly and a object poly 404 * 405 * @param isCasterOpaque whether the caster is opaque 406 * @param lightCenter the center of the light 407 * @param lightSize the radius of the light 408 * @param poly x,y,z vertexes of a convex polygon that occludes the light source 409 * @param polyLength number of vertexes of the occluding polygon 410 * @param shadowTriangleStrip return an (x,y,alpha) triangle strip representing the shadow. Return 411 * empty strip if error. 412 */ 413void SpotShadow::createSpotShadow(bool isCasterOpaque, const Vector3& lightCenter, 414 float lightSize, const Vector3* poly, int polyLength, const Vector3& polyCentroid, 415 VertexBuffer& shadowTriangleStrip) { 416 if (CC_UNLIKELY(lightCenter.z <= 0)) { 417 ALOGW("Relative Light Z is not positive. No spot shadow!"); 418 return; 419 } 420 if (CC_UNLIKELY(polyLength < 3)) { 421#if DEBUG_SHADOW 422 ALOGW("Invalid polygon length. No spot shadow!"); 423#endif 424 return; 425 } 426 OutlineData outlineData[polyLength]; 427 Vector2 outlineCentroid; 428 // Calculate the projected outline for each polygon's vertices from the light center. 429 // 430 // O Light 431 // / 432 // / 433 // . Polygon vertex 434 // / 435 // / 436 // O Outline vertices 437 // 438 // Ratio = (Poly - Outline) / (Light - Poly) 439 // Outline.x = Poly.x - Ratio * (Light.x - Poly.x) 440 // Outline's radius / Light's radius = Ratio 441 442 // Compute the last outline vertex to make sure we can get the normal and outline 443 // in one single loop. 444 projectCasterToOutline(outlineData[polyLength - 1].position, lightCenter, 445 poly[polyLength - 1]); 446 447 // Take the outline's polygon, calculate the normal for each outline edge. 448 int currentNormalIndex = polyLength - 1; 449 int nextNormalIndex = 0; 450 451 for (int i = 0; i < polyLength; i++) { 452 float ratioZ = projectCasterToOutline(outlineData[i].position, 453 lightCenter, poly[i]); 454 outlineData[i].radius = ratioZ * lightSize; 455 456 outlineData[currentNormalIndex].normal = ShadowTessellator::calculateNormal( 457 outlineData[currentNormalIndex].position, 458 outlineData[nextNormalIndex].position); 459 currentNormalIndex = (currentNormalIndex + 1) % polyLength; 460 nextNormalIndex++; 461 } 462 463 projectCasterToOutline(outlineCentroid, lightCenter, polyCentroid); 464 465 int penumbraIndex = 0; 466 // Then each polygon's vertex produce at minmal 2 penumbra vertices. 467 // Since the size can be dynamic here, we keep track of the size and update 468 // the real size at the end. 469 int allocatedPenumbraLength = 2 * polyLength + SPOT_MAX_EXTRA_CORNER_VERTEX_NUMBER; 470 Vector2 penumbra[allocatedPenumbraLength]; 471 int totalExtraCornerSliceNumber = 0; 472 473 Vector2 umbra[polyLength]; 474 475 // When centroid is covered by all circles from outline, then we consider 476 // the umbra is invalid, and we will tune down the shadow strength. 477 bool hasValidUmbra = true; 478 // We need the minimal of RaitoVI to decrease the spot shadow strength accordingly. 479 float minRaitoVI = FLT_MAX; 480 481 for (int i = 0; i < polyLength; i++) { 482 // Generate all the penumbra's vertices only using the (outline vertex + normal * radius) 483 // There is no guarantee that the penumbra is still convex, but for 484 // each outline vertex, it will connect to all its corresponding penumbra vertices as 485 // triangle fans. And for neighber penumbra vertex, it will be a trapezoid. 486 // 487 // Penumbra Vertices marked as Pi 488 // Outline Vertices marked as Vi 489 // (P3) 490 // (P2) | ' (P4) 491 // (P1)' | | ' 492 // ' | | ' 493 // (P0) ------------------------------------------------(P5) 494 // | (V0) |(V1) 495 // | | 496 // | | 497 // | | 498 // | | 499 // | | 500 // | | 501 // | | 502 // | | 503 // (V3)-----------------------------------(V2) 504 int preNormalIndex = (i + polyLength - 1) % polyLength; 505 506 const Vector2& previousNormal = outlineData[preNormalIndex].normal; 507 const Vector2& currentNormal = outlineData[i].normal; 508 509 // Depending on how roundness we want for each corner, we can subdivide 510 // further here and/or introduce some heuristic to decide how much the 511 // subdivision should be. 512 int currentExtraSliceNumber = ShadowTessellator::getExtraVertexNumber( 513 previousNormal, currentNormal, SPOT_CORNER_RADIANS_DIVISOR); 514 515 int currentCornerSliceNumber = 1 + currentExtraSliceNumber; 516 totalExtraCornerSliceNumber += currentExtraSliceNumber; 517#if DEBUG_SHADOW 518 ALOGD("currentExtraSliceNumber should be %d", currentExtraSliceNumber); 519 ALOGD("currentCornerSliceNumber should be %d", currentCornerSliceNumber); 520 ALOGD("totalCornerSliceNumber is %d", totalExtraCornerSliceNumber); 521#endif 522 if (CC_UNLIKELY(totalExtraCornerSliceNumber > SPOT_MAX_EXTRA_CORNER_VERTEX_NUMBER)) { 523 currentCornerSliceNumber = 1; 524 } 525 for (int k = 0; k <= currentCornerSliceNumber; k++) { 526 Vector2 avgNormal = 527 (previousNormal * (currentCornerSliceNumber - k) + currentNormal * k) / 528 currentCornerSliceNumber; 529 avgNormal.normalize(); 530 penumbra[penumbraIndex++] = outlineData[i].position + 531 avgNormal * outlineData[i].radius; 532 } 533 534 535 // Compute the umbra by the intersection from the outline's centroid! 536 // 537 // (V) ------------------------------------ 538 // | ' | 539 // | ' | 540 // | ' (I) | 541 // | ' | 542 // | ' (C) | 543 // | | 544 // | | 545 // | | 546 // | | 547 // ------------------------------------ 548 // 549 // Connect a line b/t the outline vertex (V) and the centroid (C), it will 550 // intersect with the outline vertex's circle at point (I). 551 // Now, ratioVI = VI / VC, ratioIC = IC / VC 552 // Then the intersetion point can be computed as Ixy = Vxy * ratioIC + Cxy * ratioVI; 553 // 554 // When all of the outline circles cover the the outline centroid, (like I is 555 // on the other side of C), there is no real umbra any more, so we just fake 556 // a small area around the centroid as the umbra, and tune down the spot 557 // shadow's umbra strength to simulate the effect the whole shadow will 558 // become lighter in this case. 559 // The ratio can be simulated by using the inverse of maximum of ratioVI for 560 // all (V). 561 float distOutline = (outlineData[i].position - outlineCentroid).length(); 562 if (CC_UNLIKELY(distOutline == 0)) { 563 // If the outline has 0 area, then there is no spot shadow anyway. 564 ALOGW("Outline has 0 area, no spot shadow!"); 565 return; 566 } 567 568 float ratioVI = outlineData[i].radius / distOutline; 569 minRaitoVI = MathUtils::min(minRaitoVI, ratioVI); 570 if (ratioVI >= (1 - FAKE_UMBRA_SIZE_RATIO)) { 571 ratioVI = (1 - FAKE_UMBRA_SIZE_RATIO); 572 } 573 // When we know we don't have valid umbra, don't bother to compute the 574 // values below. But we can't skip the loop yet since we want to know the 575 // maximum ratio. 576 float ratioIC = 1 - ratioVI; 577 umbra[i] = outlineData[i].position * ratioIC + outlineCentroid * ratioVI; 578 } 579 580 hasValidUmbra = (minRaitoVI <= 1.0); 581 float shadowStrengthScale = 1.0; 582 if (!hasValidUmbra) { 583#if DEBUG_SHADOW 584 ALOGW("The object is too close to the light or too small, no real umbra!"); 585#endif 586 for (int i = 0; i < polyLength; i++) { 587 umbra[i] = outlineData[i].position * FAKE_UMBRA_SIZE_RATIO + 588 outlineCentroid * (1 - FAKE_UMBRA_SIZE_RATIO); 589 } 590 shadowStrengthScale = 1.0 / minRaitoVI; 591 } 592 593 int penumbraLength = penumbraIndex; 594 int umbraLength = polyLength; 595 596#if DEBUG_SHADOW 597 ALOGD("penumbraLength is %d , allocatedPenumbraLength %d", penumbraLength, allocatedPenumbraLength); 598 dumpPolygon(poly, polyLength, "input poly"); 599 dumpPolygon(penumbra, penumbraLength, "penumbra"); 600 dumpPolygon(umbra, umbraLength, "umbra"); 601 ALOGD("hasValidUmbra is %d and shadowStrengthScale is %f", hasValidUmbra, shadowStrengthScale); 602#endif 603 604 // The penumbra and umbra needs to be in convex shape to keep consistency 605 // and quality. 606 // Since we are still shooting rays to penumbra, it needs to be convex. 607 // Umbra can be represented as a fan from the centroid, but visually umbra 608 // looks nicer when it is convex. 609 Vector2 finalUmbra[umbraLength]; 610 Vector2 finalPenumbra[penumbraLength]; 611 int finalUmbraLength = hull(umbra, umbraLength, finalUmbra); 612 int finalPenumbraLength = hull(penumbra, penumbraLength, finalPenumbra); 613 614 generateTriangleStrip(isCasterOpaque, shadowStrengthScale, finalPenumbra, 615 finalPenumbraLength, finalUmbra, finalUmbraLength, poly, polyLength, 616 shadowTriangleStrip, outlineCentroid); 617 618} 619 620/** 621 * This is only for experimental purpose. 622 * After intersections are calculated, we could smooth the polygon if needed. 623 * So far, we don't think it is more appealing yet. 624 * 625 * @param level The level of smoothness. 626 * @param rays The total number of rays. 627 * @param rayDist (In and Out) The distance for each ray. 628 * 629 */ 630void SpotShadow::smoothPolygon(int level, int rays, float* rayDist) { 631 for (int k = 0; k < level; k++) { 632 for (int i = 0; i < rays; i++) { 633 float p1 = rayDist[(rays - 1 + i) % rays]; 634 float p2 = rayDist[i]; 635 float p3 = rayDist[(i + 1) % rays]; 636 rayDist[i] = (p1 + p2 * 2 + p3) / 4; 637 } 638 } 639} 640 641// Index pair is meant for storing the tessellation information for the penumbra 642// area. One index must come from exterior tangent of the circles, the other one 643// must come from the interior tangent of the circles. 644struct IndexPair { 645 int outerIndex; 646 int innerIndex; 647}; 648 649// For one penumbra vertex, find the cloest umbra vertex and return its index. 650inline int getClosestUmbraIndex(const Vector2& pivot, const Vector2* polygon, int polygonLength) { 651 float minLengthSquared = FLT_MAX; 652 int resultIndex = -1; 653 bool hasDecreased = false; 654 // Starting with some negative offset, assuming both umbra and penumbra are starting 655 // at the same angle, this can help to find the result faster. 656 // Normally, loop 3 times, we can find the closest point. 657 int offset = polygonLength - 2; 658 for (int i = 0; i < polygonLength; i++) { 659 int currentIndex = (i + offset) % polygonLength; 660 float currentLengthSquared = (pivot - polygon[currentIndex]).lengthSquared(); 661 if (currentLengthSquared < minLengthSquared) { 662 if (minLengthSquared != FLT_MAX) { 663 hasDecreased = true; 664 } 665 minLengthSquared = currentLengthSquared; 666 resultIndex = currentIndex; 667 } else if (currentLengthSquared > minLengthSquared && hasDecreased) { 668 // Early break b/c we have found the closet one and now the length 669 // is increasing again. 670 break; 671 } 672 } 673 if(resultIndex == -1) { 674 ALOGE("resultIndex is -1, the polygon must be invalid!"); 675 resultIndex = 0; 676 } 677 return resultIndex; 678} 679 680// Allow some epsilon here since the later ray intersection did allow for some small 681// floating point error, when the intersection point is slightly outside the segment. 682inline bool sameDirections(bool isPositiveCross, float a, float b) { 683 if (isPositiveCross) { 684 return a >= -EPSILON && b >= -EPSILON; 685 } else { 686 return a <= EPSILON && b <= EPSILON; 687 } 688} 689 690// Find the right polygon edge to shoot the ray at. 691inline int findPolyIndex(bool isPositiveCross, int startPolyIndex, const Vector2& umbraDir, 692 const Vector2* polyToCentroid, int polyLength) { 693 // Make sure we loop with a bound. 694 for (int i = 0; i < polyLength; i++) { 695 int currentIndex = (i + startPolyIndex) % polyLength; 696 const Vector2& currentToCentroid = polyToCentroid[currentIndex]; 697 const Vector2& nextToCentroid = polyToCentroid[(currentIndex + 1) % polyLength]; 698 699 float currentCrossUmbra = currentToCentroid.cross(umbraDir); 700 float umbraCrossNext = umbraDir.cross(nextToCentroid); 701 if (sameDirections(isPositiveCross, currentCrossUmbra, umbraCrossNext)) { 702#if DEBUG_SHADOW 703 ALOGD("findPolyIndex loop %d times , index %d", i, currentIndex ); 704#endif 705 return currentIndex; 706 } 707 } 708 LOG_ALWAYS_FATAL("Can't find the right polygon's edge from startPolyIndex %d", startPolyIndex); 709 return -1; 710} 711 712// Generate the index pair for penumbra / umbra vertices, and more penumbra vertices 713// if needed. 714inline void genNewPenumbraAndPairWithUmbra(const Vector2* penumbra, int penumbraLength, 715 const Vector2* umbra, int umbraLength, Vector2* newPenumbra, int& newPenumbraIndex, 716 IndexPair* verticesPair, int& verticesPairIndex) { 717 // In order to keep everything in just one loop, we need to pre-compute the 718 // closest umbra vertex for the last penumbra vertex. 719 int previousClosestUmbraIndex = getClosestUmbraIndex(penumbra[penumbraLength - 1], 720 umbra, umbraLength); 721 for (int i = 0; i < penumbraLength; i++) { 722 const Vector2& currentPenumbraVertex = penumbra[i]; 723 // For current penumbra vertex, starting from previousClosestUmbraIndex, 724 // then check the next one until the distance increase. 725 // The last one before the increase is the umbra vertex we need to pair with. 726 float currentLengthSquared = 727 (currentPenumbraVertex - umbra[previousClosestUmbraIndex]).lengthSquared(); 728 int currentClosestUmbraIndex = previousClosestUmbraIndex; 729 int indexDelta = 0; 730 for (int j = 1; j < umbraLength; j++) { 731 int newUmbraIndex = (previousClosestUmbraIndex + j) % umbraLength; 732 float newLengthSquared = (currentPenumbraVertex - umbra[newUmbraIndex]).lengthSquared(); 733 if (newLengthSquared > currentLengthSquared) { 734 // currentClosestUmbraIndex is the umbra vertex's index which has 735 // currently found smallest distance, so we can simply break here. 736 break; 737 } else { 738 currentLengthSquared = newLengthSquared; 739 indexDelta++; 740 currentClosestUmbraIndex = newUmbraIndex; 741 } 742 } 743 744 if (indexDelta > 1) { 745 // For those umbra don't have penumbra, generate new penumbra vertices by interpolation. 746 // 747 // Assuming Pi for penumbra vertices, and Ui for umbra vertices. 748 // In the case like below P1 paired with U1 and P2 paired with U5. 749 // U2 to U4 are unpaired umbra vertices. 750 // 751 // P1 P2 752 // | | 753 // U1 U2 U3 U4 U5 754 // 755 // We will need to generate 3 more penumbra vertices P1.1, P1.2, P1.3 756 // to pair with U2 to U4. 757 // 758 // P1 P1.1 P1.2 P1.3 P2 759 // | | | | | 760 // U1 U2 U3 U4 U5 761 // 762 // That distance ratio b/t Ui to U1 and Ui to U5 decides its paired penumbra 763 // vertex's location. 764 int newPenumbraNumber = indexDelta - 1; 765 766 float accumulatedDeltaLength[newPenumbraNumber]; 767 float totalDeltaLength = 0; 768 769 // To save time, cache the previous umbra vertex info outside the loop 770 // and update each loop. 771 Vector2 previousClosestUmbra = umbra[previousClosestUmbraIndex]; 772 Vector2 skippedUmbra; 773 // Use umbra data to precompute the length b/t unpaired umbra vertices, 774 // and its ratio against the total length. 775 for (int k = 0; k < indexDelta; k++) { 776 int skippedUmbraIndex = (previousClosestUmbraIndex + k + 1) % umbraLength; 777 skippedUmbra = umbra[skippedUmbraIndex]; 778 float currentDeltaLength = (skippedUmbra - previousClosestUmbra).length(); 779 780 totalDeltaLength += currentDeltaLength; 781 accumulatedDeltaLength[k] = totalDeltaLength; 782 783 previousClosestUmbra = skippedUmbra; 784 } 785 786 const Vector2& previousPenumbra = penumbra[(i + penumbraLength - 1) % penumbraLength]; 787 // Then for each unpaired umbra vertex, create a new penumbra by the ratio, 788 // and pair them togehter. 789 for (int k = 0; k < newPenumbraNumber; k++) { 790 float weightForCurrentPenumbra = 1.0f; 791 if (totalDeltaLength != 0.0f) { 792 weightForCurrentPenumbra = accumulatedDeltaLength[k] / totalDeltaLength; 793 } 794 float weightForPreviousPenumbra = 1.0f - weightForCurrentPenumbra; 795 796 Vector2 interpolatedPenumbra = currentPenumbraVertex * weightForCurrentPenumbra + 797 previousPenumbra * weightForPreviousPenumbra; 798 799 int skippedUmbraIndex = (previousClosestUmbraIndex + k + 1) % umbraLength; 800 verticesPair[verticesPairIndex++] = {newPenumbraIndex, skippedUmbraIndex}; 801 newPenumbra[newPenumbraIndex++] = interpolatedPenumbra; 802 } 803 } 804 verticesPair[verticesPairIndex++] = {newPenumbraIndex, currentClosestUmbraIndex}; 805 newPenumbra[newPenumbraIndex++] = currentPenumbraVertex; 806 807 previousClosestUmbraIndex = currentClosestUmbraIndex; 808 } 809} 810 811// Precompute all the polygon's vector, return true if the reference cross product is positive. 812inline bool genPolyToCentroid(const Vector2* poly2d, int polyLength, 813 const Vector2& centroid, Vector2* polyToCentroid) { 814 for (int j = 0; j < polyLength; j++) { 815 polyToCentroid[j] = poly2d[j] - centroid; 816 // Normalize these vectors such that we can use epsilon comparison after 817 // computing their cross products with another normalized vector. 818 polyToCentroid[j].normalize(); 819 } 820 float refCrossProduct = 0; 821 for (int j = 0; j < polyLength; j++) { 822 refCrossProduct = polyToCentroid[j].cross(polyToCentroid[(j + 1) % polyLength]); 823 if (refCrossProduct != 0) { 824 break; 825 } 826 } 827 828 return refCrossProduct > 0; 829} 830 831// For one umbra vertex, shoot an ray from centroid to it. 832// If the ray hit the polygon first, then return the intersection point as the 833// closer vertex. 834inline Vector2 getCloserVertex(const Vector2& umbraVertex, const Vector2& centroid, 835 const Vector2* poly2d, int polyLength, const Vector2* polyToCentroid, 836 bool isPositiveCross, int& previousPolyIndex) { 837 Vector2 umbraToCentroid = umbraVertex - centroid; 838 float distanceToUmbra = umbraToCentroid.length(); 839 umbraToCentroid = umbraToCentroid / distanceToUmbra; 840 841 // previousPolyIndex is updated for each item such that we can minimize the 842 // looping inside findPolyIndex(); 843 previousPolyIndex = findPolyIndex(isPositiveCross, previousPolyIndex, 844 umbraToCentroid, polyToCentroid, polyLength); 845 846 float dx = umbraToCentroid.x; 847 float dy = umbraToCentroid.y; 848 float distanceToIntersectPoly = rayIntersectPoints(centroid, dx, dy, 849 poly2d[previousPolyIndex], poly2d[(previousPolyIndex + 1) % polyLength]); 850 if (distanceToIntersectPoly < 0) { 851 distanceToIntersectPoly = 0; 852 } 853 854 // Pick the closer one as the occluded area vertex. 855 Vector2 closerVertex; 856 if (distanceToIntersectPoly < distanceToUmbra) { 857 closerVertex.x = centroid.x + dx * distanceToIntersectPoly; 858 closerVertex.y = centroid.y + dy * distanceToIntersectPoly; 859 } else { 860 closerVertex = umbraVertex; 861 } 862 863 return closerVertex; 864} 865 866/** 867 * Generate a triangle strip given two convex polygon 868**/ 869void SpotShadow::generateTriangleStrip(bool isCasterOpaque, float shadowStrengthScale, 870 Vector2* penumbra, int penumbraLength, Vector2* umbra, int umbraLength, 871 const Vector3* poly, int polyLength, VertexBuffer& shadowTriangleStrip, 872 const Vector2& centroid) { 873 bool hasOccludedUmbraArea = false; 874 Vector2 poly2d[polyLength]; 875 876 if (isCasterOpaque) { 877 for (int i = 0; i < polyLength; i++) { 878 poly2d[i].x = poly[i].x; 879 poly2d[i].y = poly[i].y; 880 } 881 // Make sure the centroid is inside the umbra, otherwise, fall back to the 882 // approach as if there is no occluded umbra area. 883 if (testPointInsidePolygon(centroid, poly2d, polyLength)) { 884 hasOccludedUmbraArea = true; 885 } 886 } 887 888 // For each penumbra vertex, find its corresponding closest umbra vertex index. 889 // 890 // Penumbra Vertices marked as Pi 891 // Umbra Vertices marked as Ui 892 // (P3) 893 // (P2) | ' (P4) 894 // (P1)' | | ' 895 // ' | | ' 896 // (P0) ------------------------------------------------(P5) 897 // | (U0) |(U1) 898 // | | 899 // | |(U2) (P5.1) 900 // | | 901 // | | 902 // | | 903 // | | 904 // | | 905 // | | 906 // (U4)-----------------------------------(U3) (P6) 907 // 908 // At least, like P0, P1, P2, they will find the matching umbra as U0. 909 // If we jump over some umbra vertex without matching penumbra vertex, then 910 // we will generate some new penumbra vertex by interpolation. Like P6 is 911 // matching U3, but U2 is not matched with any penumbra vertex. 912 // So interpolate P5.1 out and match U2. 913 // In this way, every umbra vertex will have a matching penumbra vertex. 914 // 915 // The total pair number can be as high as umbraLength + penumbraLength. 916 const int maxNewPenumbraLength = umbraLength + penumbraLength; 917 IndexPair verticesPair[maxNewPenumbraLength]; 918 int verticesPairIndex = 0; 919 920 // Cache all the existing penumbra vertices and newly interpolated vertices into a 921 // a new array. 922 Vector2 newPenumbra[maxNewPenumbraLength]; 923 int newPenumbraIndex = 0; 924 925 // For each penumbra vertex, find its closet umbra vertex by comparing the 926 // neighbor umbra vertices. 927 genNewPenumbraAndPairWithUmbra(penumbra, penumbraLength, umbra, umbraLength, newPenumbra, 928 newPenumbraIndex, verticesPair, verticesPairIndex); 929 ShadowTessellator::checkOverflow(verticesPairIndex, maxNewPenumbraLength, "Spot pair"); 930 ShadowTessellator::checkOverflow(newPenumbraIndex, maxNewPenumbraLength, "Spot new penumbra"); 931#if DEBUG_SHADOW 932 for (int i = 0; i < umbraLength; i++) { 933 ALOGD("umbra i %d, [%f, %f]", i, umbra[i].x, umbra[i].y); 934 } 935 for (int i = 0; i < newPenumbraIndex; i++) { 936 ALOGD("new penumbra i %d, [%f, %f]", i, newPenumbra[i].x, newPenumbra[i].y); 937 } 938 for (int i = 0; i < verticesPairIndex; i++) { 939 ALOGD("index i %d, [%d, %d]", i, verticesPair[i].outerIndex, verticesPair[i].innerIndex); 940 } 941#endif 942 943 // For the size of vertex buffer, we need 3 rings, one has newPenumbraSize, 944 // one has umbraLength, the last one has at most umbraLength. 945 // 946 // For the size of index buffer, the umbra area needs (2 * umbraLength + 2). 947 // The penumbra one can vary a bit, but it is bounded by (2 * verticesPairIndex + 2). 948 // And 2 more for jumping between penumbra to umbra. 949 const int newPenumbraLength = newPenumbraIndex; 950 const int totalVertexCount = newPenumbraLength + umbraLength * 2; 951 const int totalIndexCount = 2 * umbraLength + 2 * verticesPairIndex + 6; 952 AlphaVertex* shadowVertices = 953 shadowTriangleStrip.alloc<AlphaVertex>(totalVertexCount); 954 uint16_t* indexBuffer = 955 shadowTriangleStrip.allocIndices<uint16_t>(totalIndexCount); 956 int vertexBufferIndex = 0; 957 int indexBufferIndex = 0; 958 959 // Fill the IB and VB for the penumbra area. 960 for (int i = 0; i < newPenumbraLength; i++) { 961 AlphaVertex::set(&shadowVertices[vertexBufferIndex++], newPenumbra[i].x, 962 newPenumbra[i].y, 0.0f); 963 } 964 for (int i = 0; i < umbraLength; i++) { 965 AlphaVertex::set(&shadowVertices[vertexBufferIndex++], umbra[i].x, umbra[i].y, 966 M_PI); 967 } 968 969 for (int i = 0; i < verticesPairIndex; i++) { 970 indexBuffer[indexBufferIndex++] = verticesPair[i].outerIndex; 971 // All umbra index need to be offseted by newPenumbraSize. 972 indexBuffer[indexBufferIndex++] = verticesPair[i].innerIndex + newPenumbraLength; 973 } 974 indexBuffer[indexBufferIndex++] = verticesPair[0].outerIndex; 975 indexBuffer[indexBufferIndex++] = verticesPair[0].innerIndex + newPenumbraLength; 976 977 // Now fill the IB and VB for the umbra area. 978 // First duplicated the index from previous strip and the first one for the 979 // degenerated triangles. 980 indexBuffer[indexBufferIndex] = indexBuffer[indexBufferIndex - 1]; 981 indexBufferIndex++; 982 indexBuffer[indexBufferIndex++] = newPenumbraLength + 0; 983 // Save the first VB index for umbra area in order to close the loop. 984 int savedStartIndex = vertexBufferIndex; 985 986 if (hasOccludedUmbraArea) { 987 // Precompute all the polygon's vector, and the reference cross product, 988 // in order to find the right polygon edge for the ray to intersect. 989 Vector2 polyToCentroid[polyLength]; 990 bool isPositiveCross = genPolyToCentroid(poly2d, polyLength, centroid, polyToCentroid); 991 992 // Because both the umbra and polygon are going in the same direction, 993 // we can save the previous polygon index to make sure we have less polygon 994 // vertex to compute for each ray. 995 int previousPolyIndex = 0; 996 for (int i = 0; i < umbraLength; i++) { 997 // Shoot a ray from centroid to each umbra vertices and pick the one with 998 // shorter distance to the centroid, b/t the umbra vertex or the intersection point. 999 Vector2 closerVertex = getCloserVertex(umbra[i], centroid, poly2d, polyLength, 1000 polyToCentroid, isPositiveCross, previousPolyIndex); 1001 1002 // We already stored the umbra vertices, just need to add the occlued umbra's ones. 1003 indexBuffer[indexBufferIndex++] = newPenumbraLength + i; 1004 indexBuffer[indexBufferIndex++] = vertexBufferIndex; 1005 AlphaVertex::set(&shadowVertices[vertexBufferIndex++], 1006 closerVertex.x, closerVertex.y, M_PI); 1007 } 1008 } else { 1009 // If there is no occluded umbra at all, then draw the triangle fan 1010 // starting from the centroid to all umbra vertices. 1011 int lastCentroidIndex = vertexBufferIndex; 1012 AlphaVertex::set(&shadowVertices[vertexBufferIndex++], centroid.x, 1013 centroid.y, M_PI); 1014 for (int i = 0; i < umbraLength; i++) { 1015 indexBuffer[indexBufferIndex++] = newPenumbraLength + i; 1016 indexBuffer[indexBufferIndex++] = lastCentroidIndex; 1017 } 1018 } 1019 // Closing the umbra area triangle's loop here. 1020 indexBuffer[indexBufferIndex++] = newPenumbraLength; 1021 indexBuffer[indexBufferIndex++] = savedStartIndex; 1022 1023 // At the end, update the real index and vertex buffer size. 1024 shadowTriangleStrip.updateVertexCount(vertexBufferIndex); 1025 shadowTriangleStrip.updateIndexCount(indexBufferIndex); 1026 ShadowTessellator::checkOverflow(vertexBufferIndex, totalVertexCount, "Spot Vertex Buffer"); 1027 ShadowTessellator::checkOverflow(indexBufferIndex, totalIndexCount, "Spot Index Buffer"); 1028 1029 shadowTriangleStrip.setMode(VertexBuffer::kIndices); 1030 shadowTriangleStrip.computeBounds<AlphaVertex>(); 1031} 1032 1033#if DEBUG_SHADOW 1034 1035#define TEST_POINT_NUMBER 128 1036/** 1037 * Calculate the bounds for generating random test points. 1038 */ 1039void SpotShadow::updateBound(const Vector2 inVector, Vector2& lowerBound, 1040 Vector2& upperBound) { 1041 if (inVector.x < lowerBound.x) { 1042 lowerBound.x = inVector.x; 1043 } 1044 1045 if (inVector.y < lowerBound.y) { 1046 lowerBound.y = inVector.y; 1047 } 1048 1049 if (inVector.x > upperBound.x) { 1050 upperBound.x = inVector.x; 1051 } 1052 1053 if (inVector.y > upperBound.y) { 1054 upperBound.y = inVector.y; 1055 } 1056} 1057 1058/** 1059 * For debug purpose, when things go wrong, dump the whole polygon data. 1060 */ 1061void SpotShadow::dumpPolygon(const Vector2* poly, int polyLength, const char* polyName) { 1062 for (int i = 0; i < polyLength; i++) { 1063 ALOGD("polygon %s i %d x %f y %f", polyName, i, poly[i].x, poly[i].y); 1064 } 1065} 1066 1067/** 1068 * For debug purpose, when things go wrong, dump the whole polygon data. 1069 */ 1070void SpotShadow::dumpPolygon(const Vector3* poly, int polyLength, const char* polyName) { 1071 for (int i = 0; i < polyLength; i++) { 1072 ALOGD("polygon %s i %d x %f y %f", polyName, i, poly[i].x, poly[i].y); 1073 } 1074} 1075 1076/** 1077 * Test whether the polygon is convex. 1078 */ 1079bool SpotShadow::testConvex(const Vector2* polygon, int polygonLength, 1080 const char* name) { 1081 bool isConvex = true; 1082 for (int i = 0; i < polygonLength; i++) { 1083 Vector2 start = polygon[i]; 1084 Vector2 middle = polygon[(i + 1) % polygonLength]; 1085 Vector2 end = polygon[(i + 2) % polygonLength]; 1086 1087 float delta = (float(middle.x) - start.x) * (float(end.y) - start.y) - 1088 (float(middle.y) - start.y) * (float(end.x) - start.x); 1089 bool isCCWOrCoLinear = (delta >= EPSILON); 1090 1091 if (isCCWOrCoLinear) { 1092 ALOGW("(Error Type 2): polygon (%s) is not a convex b/c start (x %f, y %f)," 1093 "middle (x %f, y %f) and end (x %f, y %f) , delta is %f !!!", 1094 name, start.x, start.y, middle.x, middle.y, end.x, end.y, delta); 1095 isConvex = false; 1096 break; 1097 } 1098 } 1099 return isConvex; 1100} 1101 1102/** 1103 * Test whether or not the polygon (intersection) is within the 2 input polygons. 1104 * Using Marte Carlo method, we generate a random point, and if it is inside the 1105 * intersection, then it must be inside both source polygons. 1106 */ 1107void SpotShadow::testIntersection(const Vector2* poly1, int poly1Length, 1108 const Vector2* poly2, int poly2Length, 1109 const Vector2* intersection, int intersectionLength) { 1110 // Find the min and max of x and y. 1111 Vector2 lowerBound = {FLT_MAX, FLT_MAX}; 1112 Vector2 upperBound = {-FLT_MAX, -FLT_MAX}; 1113 for (int i = 0; i < poly1Length; i++) { 1114 updateBound(poly1[i], lowerBound, upperBound); 1115 } 1116 for (int i = 0; i < poly2Length; i++) { 1117 updateBound(poly2[i], lowerBound, upperBound); 1118 } 1119 1120 bool dumpPoly = false; 1121 for (int k = 0; k < TEST_POINT_NUMBER; k++) { 1122 // Generate a random point between minX, minY and maxX, maxY. 1123 float randomX = rand() / float(RAND_MAX); 1124 float randomY = rand() / float(RAND_MAX); 1125 1126 Vector2 testPoint; 1127 testPoint.x = lowerBound.x + randomX * (upperBound.x - lowerBound.x); 1128 testPoint.y = lowerBound.y + randomY * (upperBound.y - lowerBound.y); 1129 1130 // If the random point is in both poly 1 and 2, then it must be intersection. 1131 if (testPointInsidePolygon(testPoint, intersection, intersectionLength)) { 1132 if (!testPointInsidePolygon(testPoint, poly1, poly1Length)) { 1133 dumpPoly = true; 1134 ALOGW("(Error Type 1): one point (%f, %f) in the intersection is" 1135 " not in the poly1", 1136 testPoint.x, testPoint.y); 1137 } 1138 1139 if (!testPointInsidePolygon(testPoint, poly2, poly2Length)) { 1140 dumpPoly = true; 1141 ALOGW("(Error Type 1): one point (%f, %f) in the intersection is" 1142 " not in the poly2", 1143 testPoint.x, testPoint.y); 1144 } 1145 } 1146 } 1147 1148 if (dumpPoly) { 1149 dumpPolygon(intersection, intersectionLength, "intersection"); 1150 for (int i = 1; i < intersectionLength; i++) { 1151 Vector2 delta = intersection[i] - intersection[i - 1]; 1152 ALOGD("Intersetion i, %d Vs i-1 is delta %f", i, delta.lengthSquared()); 1153 } 1154 1155 dumpPolygon(poly1, poly1Length, "poly 1"); 1156 dumpPolygon(poly2, poly2Length, "poly 2"); 1157 } 1158} 1159#endif 1160 1161}; // namespace uirenderer 1162}; // namespace android 1163