SpotShadow.cpp revision a989cb29c35149b35bf8c332ba39d7167bd95d6b
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 "SpotShadow.h" 26#include "Vertex.h" 27 28namespace android { 29namespace uirenderer { 30 31/** 32 * Calculate the intersection of a ray with a polygon. 33 * It assumes the ray originates inside the polygon. 34 * 35 * @param poly The polygon, which is represented in a Vector2 array. 36 * @param polyLength The length of caster's polygon in terms of number of 37 * vertices. 38 * @param point the start of the ray 39 * @param dx the x vector of the ray 40 * @param dy the y vector of the ray 41 * @return the distance along the ray if it intersects with the polygon FP_NAN if otherwise 42 */ 43float SpotShadow::rayIntersectPoly(const Vector2* poly, int polyLength, 44 const Vector2& point, float dx, float dy) { 45 double px = point.x; 46 double py = point.y; 47 int p1 = polyLength - 1; 48 for (int p2 = 0; p2 < polyLength; p2++) { 49 double p1x = poly[p1].x; 50 double p1y = poly[p1].y; 51 double p2x = poly[p2].x; 52 double p2y = poly[p2].y; 53 // The math below is derived from solving this formula, basically the 54 // intersection point should stay on both the ray and the edge of (p1, p2). 55 // solve([p1x+t*(p2x-p1x)=dx*t2+px,p1y+t*(p2y-p1y)=dy*t2+py],[t,t2]); 56 double div = (dx * (p1y - p2y) + dy * p2x - dy * p1x); 57 if (div != 0) { 58 double t = (dx * (p1y - py) + dy * px - dy * p1x) / (div); 59 if (t >= 0 && t <= 1) { 60 double t2 = (p1x * (py - p2y) + p2x * (p1y - py) + 61 px * (p2y - p1y)) / div; 62 if (t2 > 0) { 63 return (float)t2; 64 } 65 } 66 } 67 p1 = p2; 68 } 69 return FP_NAN; 70} 71 72/** 73 * Calculate the centroid of a 2d polygon. 74 * 75 * @param poly The polygon, which is represented in a Vector2 array. 76 * @param polyLength The length of the polygon in terms of number of vertices. 77 * @return the centroid of the polygon. 78 */ 79Vector2 SpotShadow::centroid2d(const Vector2* poly, int polyLength) { 80 double sumx = 0; 81 double sumy = 0; 82 int p1 = polyLength - 1; 83 double area = 0; 84 for (int p2 = 0; p2 < polyLength; p2++) { 85 double x1 = poly[p1].x; 86 double y1 = poly[p1].y; 87 double x2 = poly[p2].x; 88 double y2 = poly[p2].y; 89 double a = (x1 * y2 - x2 * y1); 90 sumx += (x1 + x2) * a; 91 sumy += (y1 + y2) * a; 92 area += a; 93 p1 = p2; 94 } 95 96 double centroidx = sumx / (3 * area); 97 double centroidy = sumy / (3 * area); 98 return Vector2((float)centroidx, (float)centroidy); 99} 100 101/** 102 * Sort points by their X coordinates 103 * 104 * @param points the points as a Vector2 array. 105 * @param pointsLength the number of vertices of the polygon. 106 */ 107void SpotShadow::xsort(Vector2* points, int pointsLength) { 108 quicksortX(points, 0, pointsLength - 1); 109} 110 111/** 112 * compute the convex hull of a collection of Points 113 * 114 * @param points the points as a Vector2 array. 115 * @param pointsLength the number of vertices of the polygon. 116 * @param retPoly pre allocated array of floats to put the vertices 117 * @return the number of points in the polygon 0 if no intersection 118 */ 119int SpotShadow::hull(Vector2* points, int pointsLength, Vector2* retPoly) { 120 xsort(points, pointsLength); 121 int n = pointsLength; 122 Vector2 lUpper[n]; 123 lUpper[0] = points[0]; 124 lUpper[1] = points[1]; 125 126 int lUpperSize = 2; 127 128 for (int i = 2; i < n; i++) { 129 lUpper[lUpperSize] = points[i]; 130 lUpperSize++; 131 132 while (lUpperSize > 2 && !ccw( 133 lUpper[lUpperSize - 3].x, lUpper[lUpperSize - 3].y, 134 lUpper[lUpperSize - 2].x, lUpper[lUpperSize - 2].y, 135 lUpper[lUpperSize - 1].x, lUpper[lUpperSize - 1].y)) { 136 // Remove the middle point of the three last 137 lUpper[lUpperSize - 2].x = lUpper[lUpperSize - 1].x; 138 lUpper[lUpperSize - 2].y = lUpper[lUpperSize - 1].y; 139 lUpperSize--; 140 } 141 } 142 143 Vector2 lLower[n]; 144 lLower[0] = points[n - 1]; 145 lLower[1] = points[n - 2]; 146 147 int lLowerSize = 2; 148 149 for (int i = n - 3; i >= 0; i--) { 150 lLower[lLowerSize] = points[i]; 151 lLowerSize++; 152 153 while (lLowerSize > 2 && !ccw( 154 lLower[lLowerSize - 3].x, lLower[lLowerSize - 3].y, 155 lLower[lLowerSize - 2].x, lLower[lLowerSize - 2].y, 156 lLower[lLowerSize - 1].x, lLower[lLowerSize - 1].y)) { 157 // Remove the middle point of the three last 158 lLower[lLowerSize - 2] = lLower[lLowerSize - 1]; 159 lLowerSize--; 160 } 161 } 162 int count = 0; 163 164 for (int i = 0; i < lUpperSize; i++) { 165 retPoly[count] = lUpper[i]; 166 count++; 167 } 168 169 for (int i = 1; i < lLowerSize - 1; i++) { 170 retPoly[count] = lLower[i]; 171 count++; 172 } 173 // TODO: Add test harness which verify that all the points are inside the hull. 174 return count; 175} 176 177/** 178 * Test whether the 3 points form a counter clockwise turn. 179 * 180 * @param ax the x coordinate of point a 181 * @param ay the y coordinate of point a 182 * @param bx the x coordinate of point b 183 * @param by the y coordinate of point b 184 * @param cx the x coordinate of point c 185 * @param cy the y coordinate of point c 186 * @return true if a right hand turn 187 */ 188bool SpotShadow::ccw(double ax, double ay, double bx, double by, 189 double cx, double cy) { 190 return (bx - ax) * (cy - ay) - (by - ay) * (cx - ax) > EPSILON; 191} 192 193/** 194 * Calculates the intersection of poly1 with poly2 and put in poly2. 195 * 196 * 197 * @param poly1 The 1st polygon, as a Vector2 array. 198 * @param poly1Length The number of vertices of 1st polygon. 199 * @param poly2 The 2nd and output polygon, as a Vector2 array. 200 * @param poly2Length The number of vertices of 2nd polygon. 201 * @return number of vertices in output polygon as poly2. 202 */ 203int SpotShadow::intersection(Vector2* poly1, int poly1Length, 204 Vector2* poly2, int poly2Length) { 205 makeClockwise(poly1, poly1Length); 206 makeClockwise(poly2, poly2Length); 207 208 Vector2 poly[poly1Length * poly2Length + 2]; 209 int count = 0; 210 int pcount = 0; 211 212 // If one vertex from one polygon sits inside another polygon, add it and 213 // count them. 214 for (int i = 0; i < poly1Length; i++) { 215 if (testPointInsidePolygon(poly1[i], poly2, poly2Length)) { 216 poly[count] = poly1[i]; 217 count++; 218 pcount++; 219 220 } 221 } 222 223 int insidePoly2 = pcount; 224 for (int i = 0; i < poly2Length; i++) { 225 if (testPointInsidePolygon(poly2[i], poly1, poly1Length)) { 226 poly[count] = poly2[i]; 227 count++; 228 } 229 } 230 231 int insidePoly1 = count - insidePoly2; 232 // If all vertices from poly1 are inside poly2, then just return poly1. 233 if (insidePoly2 == poly1Length) { 234 memcpy(poly2, poly1, poly1Length * sizeof(Vector2)); 235 return poly1Length; 236 } 237 238 // If all vertices from poly2 are inside poly1, then just return poly2. 239 if (insidePoly1 == poly2Length) { 240 return poly2Length; 241 } 242 243 // Since neither polygon fully contain the other one, we need to add all the 244 // intersection points. 245 Vector2 intersection; 246 for (int i = 0; i < poly2Length; i++) { 247 for (int j = 0; j < poly1Length; j++) { 248 int poly2LineStart = i; 249 int poly2LineEnd = ((i + 1) % poly2Length); 250 int poly1LineStart = j; 251 int poly1LineEnd = ((j + 1) % poly1Length); 252 bool found = lineIntersection( 253 poly2[poly2LineStart].x, poly2[poly2LineStart].y, 254 poly2[poly2LineEnd].x, poly2[poly2LineEnd].y, 255 poly1[poly1LineStart].x, poly1[poly1LineStart].y, 256 poly1[poly1LineEnd].x, poly1[poly1LineEnd].y, 257 intersection); 258 if (found) { 259 poly[count].x = intersection.x; 260 poly[count].y = intersection.y; 261 count++; 262 } else { 263 Vector2 delta = poly2[i] - poly1[j]; 264 if (delta.lengthSquared() < EPSILON) { 265 poly[count] = poly2[i]; 266 count++; 267 } 268 } 269 } 270 } 271 272 if (count == 0) { 273 return 0; 274 } 275 276 // Sort the result polygon around the center. 277 Vector2 center(0.0f, 0.0f); 278 for (int i = 0; i < count; i++) { 279 center += poly[i]; 280 } 281 center /= count; 282 sort(poly, count, center); 283 284#if DEBUG_SHADOW 285 // Since poly2 is overwritten as the result, we need to save a copy to do 286 // our verification. 287 Vector2 oldPoly2[poly2Length]; 288 int oldPoly2Length = poly2Length; 289 memcpy(oldPoly2, poly2, sizeof(Vector2) * poly2Length); 290#endif 291 292 // Filter the result out from poly and put it into poly2. 293 poly2[0] = poly[0]; 294 int lastOutputIndex = 0; 295 for (int i = 1; i < count; i++) { 296 Vector2 delta = poly[i] - poly2[lastOutputIndex]; 297 if (delta.lengthSquared() >= EPSILON) { 298 poly2[++lastOutputIndex] = poly[i]; 299 } else { 300 // If the vertices are too close, pick the inner one, because the 301 // inner one is more likely to be an intersection point. 302 Vector2 delta1 = poly[i] - center; 303 Vector2 delta2 = poly2[lastOutputIndex] - center; 304 if (delta1.lengthSquared() < delta2.lengthSquared()) { 305 poly2[lastOutputIndex] = poly[i]; 306 } 307 } 308 } 309 int resultLength = lastOutputIndex + 1; 310 311#if DEBUG_SHADOW 312 testConvex(poly2, resultLength, "intersection"); 313 testConvex(poly1, poly1Length, "input poly1"); 314 testConvex(oldPoly2, oldPoly2Length, "input poly2"); 315 316 testIntersection(poly1, poly1Length, oldPoly2, oldPoly2Length, poly2, resultLength); 317#endif 318 319 return resultLength; 320} 321 322/** 323 * Sort points about a center point 324 * 325 * @param poly The in and out polyogon as a Vector2 array. 326 * @param polyLength The number of vertices of the polygon. 327 * @param center the center ctr[0] = x , ctr[1] = y to sort around. 328 */ 329void SpotShadow::sort(Vector2* poly, int polyLength, const Vector2& center) { 330 quicksortCirc(poly, 0, polyLength - 1, center); 331} 332 333/** 334 * Calculate the angle between and x and a y coordinate. 335 * The atan2 range from -PI to PI, if we want to sort the vertices as clockwise, 336 * we just negate the return angle. 337 */ 338float SpotShadow::angle(const Vector2& point, const Vector2& center) { 339 return -(float)atan2(point.y - center.y, point.x - center.x); 340} 341 342/** 343 * Swap points pointed to by i and j 344 */ 345void SpotShadow::swap(Vector2* points, int i, int j) { 346 Vector2 temp = points[i]; 347 points[i] = points[j]; 348 points[j] = temp; 349} 350 351/** 352 * quick sort implementation about the center. 353 */ 354void SpotShadow::quicksortCirc(Vector2* points, int low, int high, 355 const Vector2& center) { 356 int i = low, j = high; 357 int p = low + (high - low) / 2; 358 float pivot = angle(points[p], center); 359 while (i <= j) { 360 while (angle(points[i], center) < pivot) { 361 i++; 362 } 363 while (angle(points[j], center) > pivot) { 364 j--; 365 } 366 367 if (i <= j) { 368 swap(points, i, j); 369 i++; 370 j--; 371 } 372 } 373 if (low < j) quicksortCirc(points, low, j, center); 374 if (i < high) quicksortCirc(points, i, high, center); 375} 376 377/** 378 * Sort points by x axis 379 * 380 * @param points points to sort 381 * @param low start index 382 * @param high end index 383 */ 384void SpotShadow::quicksortX(Vector2* points, int low, int high) { 385 int i = low, j = high; 386 int p = low + (high - low) / 2; 387 float pivot = points[p].x; 388 while (i <= j) { 389 while (points[i].x < pivot) { 390 i++; 391 } 392 while (points[j].x > pivot) { 393 j--; 394 } 395 396 if (i <= j) { 397 swap(points, i, j); 398 i++; 399 j--; 400 } 401 } 402 if (low < j) quicksortX(points, low, j); 403 if (i < high) quicksortX(points, i, high); 404} 405 406/** 407 * Test whether a point is inside the polygon. 408 * 409 * @param testPoint the point to test 410 * @param poly the polygon 411 * @return true if the testPoint is inside the poly. 412 */ 413bool SpotShadow::testPointInsidePolygon(const Vector2 testPoint, 414 const Vector2* poly, int len) { 415 bool c = false; 416 double testx = testPoint.x; 417 double testy = testPoint.y; 418 for (int i = 0, j = len - 1; i < len; j = i++) { 419 double startX = poly[j].x; 420 double startY = poly[j].y; 421 double endX = poly[i].x; 422 double endY = poly[i].y; 423 424 if (((endY > testy) != (startY > testy)) && 425 (testx < (startX - endX) * (testy - endY) 426 / (startY - endY) + endX)) { 427 c = !c; 428 } 429 } 430 return c; 431} 432 433/** 434 * Make the polygon turn clockwise. 435 * 436 * @param polygon the polygon as a Vector2 array. 437 * @param len the number of points of the polygon 438 */ 439void SpotShadow::makeClockwise(Vector2* polygon, int len) { 440 if (polygon == 0 || len == 0) { 441 return; 442 } 443 if (!isClockwise(polygon, len)) { 444 reverse(polygon, len); 445 } 446} 447 448/** 449 * Test whether the polygon is order in clockwise. 450 * 451 * @param polygon the polygon as a Vector2 array 452 * @param len the number of points of the polygon 453 */ 454bool SpotShadow::isClockwise(Vector2* polygon, int len) { 455 double sum = 0; 456 double p1x = polygon[len - 1].x; 457 double p1y = polygon[len - 1].y; 458 for (int i = 0; i < len; i++) { 459 460 double p2x = polygon[i].x; 461 double p2y = polygon[i].y; 462 sum += p1x * p2y - p2x * p1y; 463 p1x = p2x; 464 p1y = p2y; 465 } 466 return sum < 0; 467} 468 469/** 470 * Reverse the polygon 471 * 472 * @param polygon the polygon as a Vector2 array 473 * @param len the number of points of the polygon 474 */ 475void SpotShadow::reverse(Vector2* polygon, int len) { 476 int n = len / 2; 477 for (int i = 0; i < n; i++) { 478 Vector2 tmp = polygon[i]; 479 int k = len - 1 - i; 480 polygon[i] = polygon[k]; 481 polygon[k] = tmp; 482 } 483} 484 485/** 486 * Intersects two lines in parametric form. This function is called in a tight 487 * loop, and we need double precision to get things right. 488 * 489 * @param x1 the x coordinate point 1 of line 1 490 * @param y1 the y coordinate point 1 of line 1 491 * @param x2 the x coordinate point 2 of line 1 492 * @param y2 the y coordinate point 2 of line 1 493 * @param x3 the x coordinate point 1 of line 2 494 * @param y3 the y coordinate point 1 of line 2 495 * @param x4 the x coordinate point 2 of line 2 496 * @param y4 the y coordinate point 2 of line 2 497 * @param ret the x,y location of the intersection 498 * @return true if it found an intersection 499 */ 500inline bool SpotShadow::lineIntersection(double x1, double y1, double x2, double y2, 501 double x3, double y3, double x4, double y4, Vector2& ret) { 502 double d = (x1 - x2) * (y3 - y4) - (y1 - y2) * (x3 - x4); 503 if (d == 0.0) return false; 504 505 double dx = (x1 * y2 - y1 * x2); 506 double dy = (x3 * y4 - y3 * x4); 507 double x = (dx * (x3 - x4) - (x1 - x2) * dy) / d; 508 double y = (dx * (y3 - y4) - (y1 - y2) * dy) / d; 509 510 // The intersection should be in the middle of the point 1 and point 2, 511 // likewise point 3 and point 4. 512 if (((x - x1) * (x - x2) > EPSILON) 513 || ((x - x3) * (x - x4) > EPSILON) 514 || ((y - y1) * (y - y2) > EPSILON) 515 || ((y - y3) * (y - y4) > EPSILON)) { 516 // Not interesected 517 return false; 518 } 519 ret.x = x; 520 ret.y = y; 521 return true; 522 523} 524 525/** 526 * Compute a horizontal circular polygon about point (x , y , height) of radius 527 * (size) 528 * 529 * @param points number of the points of the output polygon. 530 * @param lightCenter the center of the light. 531 * @param size the light size. 532 * @param ret result polygon. 533 */ 534void SpotShadow::computeLightPolygon(int points, const Vector3& lightCenter, 535 float size, Vector3* ret) { 536 // TODO: Caching all the sin / cos values and store them in a look up table. 537 for (int i = 0; i < points; i++) { 538 double angle = 2 * i * M_PI / points; 539 ret[i].x = sinf(angle) * size + lightCenter.x; 540 ret[i].y = cosf(angle) * size + lightCenter.y; 541 ret[i].z = lightCenter.z; 542 } 543} 544 545/** 546* Generate the shadow from a spot light. 547* 548* @param poly x,y,z vertexes of a convex polygon that occludes the light source 549* @param polyLength number of vertexes of the occluding polygon 550* @param lightCenter the center of the light 551* @param lightSize the radius of the light source 552* @param lightVertexCount the vertex counter for the light polygon 553* @param rays the number of vertexes to create along the edges of the shadow 554* @param layers the number of layers of triangles strips to create 555* @param strength the "darkness" of the shadow 556* @param shadowTriangleStrip return an (x,y,alpha) triangle strip representing the shadow. Return 557* empty strip if error. 558* 559*/ 560void SpotShadow::createSpotShadow(const Vector3* poly, int polyLength, 561 const Vector3& lightCenter, float lightSize, int lightVertexCount, 562 int rays, int layers, float strength, VertexBuffer& retStrips) { 563 Vector3 light[lightVertexCount * 3]; 564 computeLightPolygon(lightVertexCount, lightCenter, lightSize, light); 565 computeSpotShadow(light, lightVertexCount, lightCenter, 566 poly, polyLength, rays, layers, strength, retStrips); 567} 568 569/** 570 * Generate the shadow spot light of shape lightPoly and a object poly 571 * 572 * @param lightPoly x,y,z vertex of a convex polygon that is the light source 573 * @param lightPolyLength number of vertexes of the light source polygon 574 * @param poly x,y,z vertexes of a convex polygon that occludes the light source 575 * @param polyLength number of vertexes of the occluding polygon 576 * @param rays the number of vertexes to create along the edges of the shadow 577 * @param layers the number of layers of triangles strips to create 578 * @param strength the "darkness" of the shadow 579 * @param shadowTriangleStrip return an (x,y,alpha) triangle strip representing the shadow. Return 580 * empty strip if error. 581 */ 582void SpotShadow::computeSpotShadow(const Vector3* lightPoly, int lightPolyLength, 583 const Vector3& lightCenter, const Vector3* poly, int polyLength, 584 int rays, int layers, float strength, VertexBuffer& shadowTriangleStrip) { 585 // Point clouds for all the shadowed vertices 586 Vector2 shadowRegion[lightPolyLength * polyLength]; 587 // Shadow polygon from one point light. 588 Vector2 outline[polyLength]; 589 Vector2 umbraMem[polyLength * lightPolyLength]; 590 Vector2* umbra = umbraMem; 591 592 int umbraLength = 0; 593 594 // Validate input, receiver is always at z = 0 plane. 595 bool inputPolyPositionValid = true; 596 for (int i = 0; i < polyLength; i++) { 597 if (poly[i].z <= 0.00001) { 598 inputPolyPositionValid = false; 599 ALOGE("polygon below the surface"); 600 break; 601 } 602 if (poly[i].z >= lightPoly[0].z) { 603 inputPolyPositionValid = false; 604 ALOGE("polygon above the light"); 605 break; 606 } 607 } 608 609 // If the caster's position is invalid, don't draw anything. 610 if (!inputPolyPositionValid) { 611 return; 612 } 613 614 // Calculate the umbra polygon based on intersections of all outlines 615 int k = 0; 616 for (int j = 0; j < lightPolyLength; j++) { 617 int m = 0; 618 for (int i = 0; i < polyLength; i++) { 619 float t = lightPoly[j].z - poly[i].z; 620 if (t == 0) { 621 return; 622 } 623 t = lightPoly[j].z / t; 624 float x = lightPoly[j].x - t * (lightPoly[j].x - poly[i].x); 625 float y = lightPoly[j].y - t * (lightPoly[j].y - poly[i].y); 626 627 Vector2 newPoint = Vector2(x, y); 628 shadowRegion[k] = newPoint; 629 outline[m] = newPoint; 630 631 k++; 632 m++; 633 } 634 635 // For the first light polygon's vertex, use the outline as the umbra. 636 // Later on, use the intersection of the outline and existing umbra. 637 if (umbraLength == 0) { 638 for (int i = 0; i < polyLength; i++) { 639 umbra[i] = outline[i]; 640 } 641 umbraLength = polyLength; 642 } else { 643 int col = ((j * 255) / lightPolyLength); 644 umbraLength = intersection(outline, polyLength, umbra, umbraLength); 645 if (umbraLength == 0) { 646 break; 647 } 648 } 649 } 650 651 // Generate the penumbra area using the hull of all shadow regions. 652 int shadowRegionLength = k; 653 Vector2 penumbra[k]; 654 int penumbraLength = hull(shadowRegion, shadowRegionLength, penumbra); 655 656 Vector2 fakeUmbra[polyLength]; 657 if (umbraLength < 3) { 658 // If there is no real umbra, make a fake one. 659 for (int i = 0; i < polyLength; i++) { 660 float t = lightCenter.z - poly[i].z; 661 if (t == 0) { 662 return; 663 } 664 t = lightCenter.z / t; 665 float x = lightCenter.x - t * (lightCenter.x - poly[i].x); 666 float y = lightCenter.y - t * (lightCenter.y - poly[i].y); 667 668 fakeUmbra[i].x = x; 669 fakeUmbra[i].y = y; 670 } 671 672 // Shrink the centroid's shadow by 10%. 673 // TODO: Study the magic number of 10%. 674 Vector2 shadowCentroid = centroid2d(fakeUmbra, polyLength); 675 for (int i = 0; i < polyLength; i++) { 676 fakeUmbra[i] = shadowCentroid * (1.0f - SHADOW_SHRINK_SCALE) + 677 fakeUmbra[i] * SHADOW_SHRINK_SCALE; 678 } 679#if DEBUG_SHADOW 680 ALOGD("No real umbra make a fake one, centroid2d = %f , %f", 681 shadowCentroid.x, shadowCentroid.y); 682#endif 683 // Set the fake umbra, whose size is the same as the original polygon. 684 umbra = fakeUmbra; 685 umbraLength = polyLength; 686 } 687 688 generateTriangleStrip(penumbra, penumbraLength, umbra, umbraLength, 689 rays, layers, strength, shadowTriangleStrip); 690} 691 692/** 693 * Generate a triangle strip given two convex polygons 694 * 695 * @param penumbra The outer polygon x,y vertexes 696 * @param penumbraLength The number of vertexes in the outer polygon 697 * @param umbra The inner outer polygon x,y vertexes 698 * @param umbraLength The number of vertexes in the inner polygon 699 * @param rays The number of points along the polygons to create 700 * @param layers The number of layers of triangle strips between the umbra and penumbra 701 * @param strength The max alpha of the umbra 702 * @param shadowTriangleStrip return an (x,y,alpha) triangle strip representing the shadow. Return 703 * empty strip if error. 704**/ 705void SpotShadow::generateTriangleStrip(const Vector2* penumbra, int penumbraLength, 706 const Vector2* umbra, int umbraLength, int rays, int layers, 707 float strength, VertexBuffer& shadowTriangleStrip) { 708 709 int rings = layers + 1; 710 int size = rays * rings; 711 712 float step = M_PI * 2 / rays; 713 // Centroid of the umbra. 714 Vector2 centroid = centroid2d(umbra, umbraLength); 715#if DEBUG_SHADOW 716 ALOGD("centroid2d = %f , %f", centroid.x, centroid.y); 717#endif 718 // Intersection to the penumbra. 719 float penumbraDistPerRay[rays]; 720 // Intersection to the umbra. 721 float umbraDistPerRay[rays]; 722 723 for (int i = 0; i < rays; i++) { 724 // TODO: Setup a lookup table for all the sin/cos. 725 float dx = sinf(step * i); 726 float dy = cosf(step * i); 727 umbraDistPerRay[i] = rayIntersectPoly(umbra, umbraLength, centroid, 728 dx, dy); 729 if (isnan(umbraDistPerRay[i])) { 730 ALOGE("rayIntersectPoly returns NAN"); 731 return; 732 } 733 penumbraDistPerRay[i] = rayIntersectPoly(penumbra, penumbraLength, 734 centroid, dx, dy); 735 if (isnan(umbraDistPerRay[i])) { 736 ALOGE("rayIntersectPoly returns NAN"); 737 return; 738 } 739 } 740 741 int stripSize = getStripSize(rays, layers); 742 AlphaVertex* shadowVertices = shadowTriangleStrip.alloc<AlphaVertex>(stripSize); 743 int currentIndex = 0; 744 int firstInLayer = 0; 745 // Calculate the vertex values in the penumbra area. 746 for (int r = 0; r < layers; r++) { 747 firstInLayer = currentIndex; 748 for (int i = 0; i < rays; i++) { 749 float dx = sinf(step * i); 750 float dy = cosf(step * i); 751 752 for (int j = r; j < (r + 2); j++) { 753 float layerRatio = j / (float)(rings - 1); 754 float deltaDist = layerRatio * (umbraDistPerRay[i] - penumbraDistPerRay[i]); 755 float currentDist = penumbraDistPerRay[i] + deltaDist; 756 float op = calculateOpacity(layerRatio, deltaDist); 757 AlphaVertex::set(&shadowVertices[currentIndex++], 758 dx * currentDist + centroid.x, 759 dy * currentDist + centroid.y, 760 layerRatio * op * strength); 761 } 762 } 763 764 // Duplicate the vertices from one layer to another one to make triangle 765 // strip. 766 shadowVertices[currentIndex++] = shadowVertices[firstInLayer + 0]; 767 shadowVertices[currentIndex++] = shadowVertices[firstInLayer + 1]; 768 } 769 770 int lastInPenumbra = currentIndex - 1; 771 shadowVertices[currentIndex++] = shadowVertices[lastInPenumbra]; 772 773 // Preallocate the vertices (index as [firstInUmbra - 1]) for jumping from 774 // the penumbra to umbra. 775 currentIndex++; 776 int firstInUmbra = currentIndex; 777 778 // traverse the umbra area in a zig zag pattern for strips. 779 const int innerRingStartIndex = firstInLayer + 1; 780 for (int k = 0; k < rays; k++) { 781 int i = k / 2; 782 if ((k & 1) == 1) { 783 i = rays - i - 1; 784 } 785 // copy already computed values for umbra vertices 786 shadowVertices[currentIndex++] = shadowVertices[innerRingStartIndex + i * 2]; 787 } 788 789 // Back fill the one vertex for jumping from penumbra to umbra. 790 shadowVertices[firstInUmbra - 1] = shadowVertices[firstInUmbra]; 791 792#if DEBUG_SHADOW 793 for (int i = 0; i < currentIndex; i++) { 794 ALOGD("shadow value: i %d, (x:%f, y:%f, a:%f)", i, shadowVertices[i].x, 795 shadowVertices[i].y, shadowVertices[i].alpha); 796 } 797#endif 798} 799 800/** 801 * This is only for experimental purpose. 802 * After intersections are calculated, we could smooth the polygon if needed. 803 * So far, we don't think it is more appealing yet. 804 * 805 * @param level The level of smoothness. 806 * @param rays The total number of rays. 807 * @param rayDist (In and Out) The distance for each ray. 808 * 809 */ 810void SpotShadow::smoothPolygon(int level, int rays, float* rayDist) { 811 for (int k = 0; k < level; k++) { 812 for (int i = 0; i < rays; i++) { 813 float p1 = rayDist[(rays - 1 + i) % rays]; 814 float p2 = rayDist[i]; 815 float p3 = rayDist[(i + 1) % rays]; 816 rayDist[i] = (p1 + p2 * 2 + p3) / 4; 817 } 818 } 819} 820 821/** 822 * Calculate the opacity according to the distance and falloff ratio. 823 * 824 * @param distRatio The distance ratio of current sample between umbra and 825 * penumbra area. 826 * @param deltaDist The distance between current sample to the penumbra area. 827 * @return The opacity according to the distance between umbra and penumbra. 828 */ 829float SpotShadow::calculateOpacity(float distRatio, float deltaDist) { 830 // TODO: Experiment on the opacity calculation. 831 float falloffRatio = 1 + deltaDist * deltaDist; 832 return (distRatio + 1 - 1 / falloffRatio) / 2; 833} 834 835/** 836 * Calculate the number of vertex we will create given a number of rays and layers 837 * 838 * @param rays number of points around the polygons you want 839 * @param layers number of layers of triangle strips you need 840 * @return number of vertex (multiply by 3 for number of floats) 841 */ 842int SpotShadow::getStripSize(int rays, int layers) { 843 return (2 + rays + ((layers) * 2 * (rays + 1))); 844} 845 846#if DEBUG_SHADOW 847 848#define TEST_POINT_NUMBER 128 849 850/** 851 * Calculate the bounds for generating random test points. 852 */ 853void SpotShadow::updateBound(const Vector2 inVector, Vector2& lowerBound, 854 Vector2& upperBound ) { 855 if (inVector.x < lowerBound.x) { 856 lowerBound.x = inVector.x; 857 } 858 859 if (inVector.y < lowerBound.y) { 860 lowerBound.y = inVector.y; 861 } 862 863 if (inVector.x > upperBound.x) { 864 upperBound.x = inVector.x; 865 } 866 867 if (inVector.y > upperBound.y) { 868 upperBound.y = inVector.y; 869 } 870} 871 872/** 873 * For debug purpose, when things go wrong, dump the whole polygon data. 874 */ 875static void dumpPolygon(const Vector2* poly, int polyLength, const char* polyName) { 876 for (int i = 0; i < polyLength; i++) { 877 ALOGD("polygon %s i %d x %f y %f", polyName, i, poly[i].x, poly[i].y); 878 } 879} 880 881/** 882 * Test whether the polygon is convex. 883 */ 884bool SpotShadow::testConvex(const Vector2* polygon, int polygonLength, 885 const char* name) { 886 bool isConvex = true; 887 for (int i = 0; i < polygonLength; i++) { 888 Vector2 start = polygon[i]; 889 Vector2 middle = polygon[(i + 1) % polygonLength]; 890 Vector2 end = polygon[(i + 2) % polygonLength]; 891 892 double delta = (double(middle.x) - start.x) * (double(end.y) - start.y) - 893 (double(middle.y) - start.y) * (double(end.x) - start.x); 894 bool isCCWOrCoLinear = (delta >= EPSILON); 895 896 if (isCCWOrCoLinear) { 897 ALOGE("(Error Type 2): polygon (%s) is not a convex b/c start (x %f, y %f)," 898 "middle (x %f, y %f) and end (x %f, y %f) , delta is %f !!!", 899 name, start.x, start.y, middle.x, middle.y, end.x, end.y, delta); 900 isConvex = false; 901 break; 902 } 903 } 904 return isConvex; 905} 906 907/** 908 * Test whether or not the polygon (intersection) is within the 2 input polygons. 909 * Using Marte Carlo method, we generate a random point, and if it is inside the 910 * intersection, then it must be inside both source polygons. 911 */ 912void SpotShadow::testIntersection(const Vector2* poly1, int poly1Length, 913 const Vector2* poly2, int poly2Length, 914 const Vector2* intersection, int intersectionLength) { 915 // Find the min and max of x and y. 916 Vector2 lowerBound(FLT_MAX, FLT_MAX); 917 Vector2 upperBound(-FLT_MAX, -FLT_MAX); 918 for (int i = 0; i < poly1Length; i++) { 919 updateBound(poly1[i], lowerBound, upperBound); 920 } 921 for (int i = 0; i < poly2Length; i++) { 922 updateBound(poly2[i], lowerBound, upperBound); 923 } 924 925 bool dumpPoly = false; 926 for (int k = 0; k < TEST_POINT_NUMBER; k++) { 927 // Generate a random point between minX, minY and maxX, maxY. 928 double randomX = rand() / double(RAND_MAX); 929 double randomY = rand() / double(RAND_MAX); 930 931 Vector2 testPoint; 932 testPoint.x = lowerBound.x + randomX * (upperBound.x - lowerBound.x); 933 testPoint.y = lowerBound.y + randomY * (upperBound.y - lowerBound.y); 934 935 // If the random point is in both poly 1 and 2, then it must be intersection. 936 if (testPointInsidePolygon(testPoint, intersection, intersectionLength)) { 937 if (!testPointInsidePolygon(testPoint, poly1, poly1Length)) { 938 dumpPoly = true; 939 ALOGE("(Error Type 1): one point (%f, %f) in the intersection is" 940 " not in the poly1", 941 testPoint.x, testPoint.y); 942 } 943 944 if (!testPointInsidePolygon(testPoint, poly2, poly2Length)) { 945 dumpPoly = true; 946 ALOGE("(Error Type 1): one point (%f, %f) in the intersection is" 947 " not in the poly2", 948 testPoint.x, testPoint.y); 949 } 950 } 951 } 952 953 if (dumpPoly) { 954 dumpPolygon(intersection, intersectionLength, "intersection"); 955 for (int i = 1; i < intersectionLength; i++) { 956 Vector2 delta = intersection[i] - intersection[i - 1]; 957 ALOGD("Intersetion i, %d Vs i-1 is delta %f", i, delta.lengthSquared()); 958 } 959 960 dumpPolygon(poly1, poly1Length, "poly 1"); 961 dumpPolygon(poly2, poly2Length, "poly 2"); 962 } 963} 964#endif 965 966}; // namespace uirenderer 967}; // namespace android 968 969 970 971 972