/* * Copyright (C) 2014 The Android Open Source Project * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ #define LOG_TAG "OpenGLRenderer" // The highest z value can't be higher than (CASTER_Z_CAP_RATIO * light.z) #define CASTER_Z_CAP_RATIO 0.95f // When there is no umbra, then just fake the umbra using // centroid * (1 - FAKE_UMBRA_SIZE_RATIO) + outline * FAKE_UMBRA_SIZE_RATIO #define FAKE_UMBRA_SIZE_RATIO 0.05f // When the polygon is about 90 vertices, the penumbra + umbra can reach 270 rays. // That is consider pretty fine tessllated polygon so far. // This is just to prevent using too much some memory when edge slicing is not // needed any more. #define FINE_TESSELLATED_POLYGON_RAY_NUMBER 270 /** * Extra vertices for the corner for smoother corner. * Only for outer loop. * Note that we use such extra memory to avoid an extra loop. */ // For half circle, we could add EXTRA_VERTEX_PER_PI vertices. // Set to 1 if we don't want to have any. #define SPOT_EXTRA_CORNER_VERTEX_PER_PI 18 // For the whole polygon, the sum of all the deltas b/t normals is 2 * M_PI, // therefore, the maximum number of extra vertices will be twice bigger. #define SPOT_MAX_EXTRA_CORNER_VERTEX_NUMBER (2 * SPOT_EXTRA_CORNER_VERTEX_PER_PI) // For each RADIANS_DIVISOR, we would allocate one more vertex b/t the normals. #define SPOT_CORNER_RADIANS_DIVISOR (M_PI / SPOT_EXTRA_CORNER_VERTEX_PER_PI) #include #include #include #include "ShadowTessellator.h" #include "SpotShadow.h" #include "Vertex.h" #include "utils/MathUtils.h" // TODO: After we settle down the new algorithm, we can remove the old one and // its utility functions. // Right now, we still need to keep it for comparison purpose and future expansion. namespace android { namespace uirenderer { static const double EPSILON = 1e-7; /** * For each polygon's vertex, the light center will project it to the receiver * as one of the outline vertex. * For each outline vertex, we need to store the position and normal. * Normal here is defined against the edge by the current vertex and the next vertex. */ struct OutlineData { Vector2 position; Vector2 normal; float radius; }; /** * For each vertex, we need to keep track of its angle, whether it is penumbra or * umbra, and its corresponding vertex index. */ struct SpotShadow::VertexAngleData { // The angle to the vertex from the centroid. float mAngle; // True is the vertex comes from penumbra, otherwise it comes from umbra. bool mIsPenumbra; // The index of the vertex described by this data. int mVertexIndex; void set(float angle, bool isPenumbra, int index) { mAngle = angle; mIsPenumbra = isPenumbra; mVertexIndex = index; } }; /** * Calculate the angle between and x and a y coordinate. * The atan2 range from -PI to PI. */ static float angle(const Vector2& point, const Vector2& center) { return atan2(point.y - center.y, point.x - center.x); } /** * Calculate the intersection of a ray with the line segment defined by two points. * * Returns a negative value in error conditions. * @param rayOrigin The start of the ray * @param dx The x vector of the ray * @param dy The y vector of the ray * @param p1 The first point defining the line segment * @param p2 The second point defining the line segment * @return The distance along the ray if it intersects with the line segment, negative if otherwise */ static float rayIntersectPoints(const Vector2& rayOrigin, float dx, float dy, const Vector2& p1, const Vector2& p2) { // The math below is derived from solving this formula, basically the // intersection point should stay on both the ray and the edge of (p1, p2). // solve([p1x+t*(p2x-p1x)=dx*t2+px,p1y+t*(p2y-p1y)=dy*t2+py],[t,t2]); double divisor = (dx * (p1.y - p2.y) + dy * p2.x - dy * p1.x); if (divisor == 0) return -1.0f; // error, invalid divisor #if DEBUG_SHADOW double interpVal = (dx * (p1.y - rayOrigin.y) + dy * rayOrigin.x - dy * p1.x) / divisor; if (interpVal < 0 || interpVal > 1) { ALOGW("rayIntersectPoints is hitting outside the segment %f", interpVal); } #endif double distance = (p1.x * (rayOrigin.y - p2.y) + p2.x * (p1.y - rayOrigin.y) + rayOrigin.x * (p2.y - p1.y)) / divisor; return distance; // may be negative in error cases } /** * Sort points by their X coordinates * * @param points the points as a Vector2 array. * @param pointsLength the number of vertices of the polygon. */ void SpotShadow::xsort(Vector2* points, int pointsLength) { quicksortX(points, 0, pointsLength - 1); } /** * compute the convex hull of a collection of Points * * @param points the points as a Vector2 array. * @param pointsLength the number of vertices of the polygon. * @param retPoly pre allocated array of floats to put the vertices * @return the number of points in the polygon 0 if no intersection */ int SpotShadow::hull(Vector2* points, int pointsLength, Vector2* retPoly) { xsort(points, pointsLength); int n = pointsLength; Vector2 lUpper[n]; lUpper[0] = points[0]; lUpper[1] = points[1]; int lUpperSize = 2; for (int i = 2; i < n; i++) { lUpper[lUpperSize] = points[i]; lUpperSize++; while (lUpperSize > 2 && !ccw( lUpper[lUpperSize - 3].x, lUpper[lUpperSize - 3].y, lUpper[lUpperSize - 2].x, lUpper[lUpperSize - 2].y, lUpper[lUpperSize - 1].x, lUpper[lUpperSize - 1].y)) { // Remove the middle point of the three last lUpper[lUpperSize - 2].x = lUpper[lUpperSize - 1].x; lUpper[lUpperSize - 2].y = lUpper[lUpperSize - 1].y; lUpperSize--; } } Vector2 lLower[n]; lLower[0] = points[n - 1]; lLower[1] = points[n - 2]; int lLowerSize = 2; for (int i = n - 3; i >= 0; i--) { lLower[lLowerSize] = points[i]; lLowerSize++; while (lLowerSize > 2 && !ccw( lLower[lLowerSize - 3].x, lLower[lLowerSize - 3].y, lLower[lLowerSize - 2].x, lLower[lLowerSize - 2].y, lLower[lLowerSize - 1].x, lLower[lLowerSize - 1].y)) { // Remove the middle point of the three last lLower[lLowerSize - 2] = lLower[lLowerSize - 1]; lLowerSize--; } } // output points in CW ordering const int total = lUpperSize + lLowerSize - 2; int outIndex = total - 1; for (int i = 0; i < lUpperSize; i++) { retPoly[outIndex] = lUpper[i]; outIndex--; } for (int i = 1; i < lLowerSize - 1; i++) { retPoly[outIndex] = lLower[i]; outIndex--; } // TODO: Add test harness which verify that all the points are inside the hull. return total; } /** * Test whether the 3 points form a counter clockwise turn. * * @return true if a right hand turn */ bool SpotShadow::ccw(double ax, double ay, double bx, double by, double cx, double cy) { return (bx - ax) * (cy - ay) - (by - ay) * (cx - ax) > EPSILON; } /** * Calculates the intersection of poly1 with poly2 and put in poly2. * Note that both poly1 and poly2 must be in CW order already! * * @param poly1 The 1st polygon, as a Vector2 array. * @param poly1Length The number of vertices of 1st polygon. * @param poly2 The 2nd and output polygon, as a Vector2 array. * @param poly2Length The number of vertices of 2nd polygon. * @return number of vertices in output polygon as poly2. */ int SpotShadow::intersection(const Vector2* poly1, int poly1Length, Vector2* poly2, int poly2Length) { #if DEBUG_SHADOW if (!ShadowTessellator::isClockwise(poly1, poly1Length)) { ALOGW("Poly1 is not clockwise! Intersection is wrong!"); } if (!ShadowTessellator::isClockwise(poly2, poly2Length)) { ALOGW("Poly2 is not clockwise! Intersection is wrong!"); } #endif Vector2 poly[poly1Length * poly2Length + 2]; int count = 0; int pcount = 0; // If one vertex from one polygon sits inside another polygon, add it and // count them. for (int i = 0; i < poly1Length; i++) { if (testPointInsidePolygon(poly1[i], poly2, poly2Length)) { poly[count] = poly1[i]; count++; pcount++; } } int insidePoly2 = pcount; for (int i = 0; i < poly2Length; i++) { if (testPointInsidePolygon(poly2[i], poly1, poly1Length)) { poly[count] = poly2[i]; count++; } } int insidePoly1 = count - insidePoly2; // If all vertices from poly1 are inside poly2, then just return poly1. if (insidePoly2 == poly1Length) { memcpy(poly2, poly1, poly1Length * sizeof(Vector2)); return poly1Length; } // If all vertices from poly2 are inside poly1, then just return poly2. if (insidePoly1 == poly2Length) { return poly2Length; } // Since neither polygon fully contain the other one, we need to add all the // intersection points. Vector2 intersection = {0, 0}; for (int i = 0; i < poly2Length; i++) { for (int j = 0; j < poly1Length; j++) { int poly2LineStart = i; int poly2LineEnd = ((i + 1) % poly2Length); int poly1LineStart = j; int poly1LineEnd = ((j + 1) % poly1Length); bool found = lineIntersection( poly2[poly2LineStart].x, poly2[poly2LineStart].y, poly2[poly2LineEnd].x, poly2[poly2LineEnd].y, poly1[poly1LineStart].x, poly1[poly1LineStart].y, poly1[poly1LineEnd].x, poly1[poly1LineEnd].y, intersection); if (found) { poly[count].x = intersection.x; poly[count].y = intersection.y; count++; } else { Vector2 delta = poly2[i] - poly1[j]; if (delta.lengthSquared() < EPSILON) { poly[count] = poly2[i]; count++; } } } } if (count == 0) { return 0; } // Sort the result polygon around the center. Vector2 center = {0.0f, 0.0f}; for (int i = 0; i < count; i++) { center += poly[i]; } center /= count; sort(poly, count, center); #if DEBUG_SHADOW // Since poly2 is overwritten as the result, we need to save a copy to do // our verification. Vector2 oldPoly2[poly2Length]; int oldPoly2Length = poly2Length; memcpy(oldPoly2, poly2, sizeof(Vector2) * poly2Length); #endif // Filter the result out from poly and put it into poly2. poly2[0] = poly[0]; int lastOutputIndex = 0; for (int i = 1; i < count; i++) { Vector2 delta = poly[i] - poly2[lastOutputIndex]; if (delta.lengthSquared() >= EPSILON) { poly2[++lastOutputIndex] = poly[i]; } else { // If the vertices are too close, pick the inner one, because the // inner one is more likely to be an intersection point. Vector2 delta1 = poly[i] - center; Vector2 delta2 = poly2[lastOutputIndex] - center; if (delta1.lengthSquared() < delta2.lengthSquared()) { poly2[lastOutputIndex] = poly[i]; } } } int resultLength = lastOutputIndex + 1; #if DEBUG_SHADOW testConvex(poly2, resultLength, "intersection"); testConvex(poly1, poly1Length, "input poly1"); testConvex(oldPoly2, oldPoly2Length, "input poly2"); testIntersection(poly1, poly1Length, oldPoly2, oldPoly2Length, poly2, resultLength); #endif return resultLength; } /** * Sort points about a center point * * @param poly The in and out polyogon as a Vector2 array. * @param polyLength The number of vertices of the polygon. * @param center the center ctr[0] = x , ctr[1] = y to sort around. */ void SpotShadow::sort(Vector2* poly, int polyLength, const Vector2& center) { quicksortCirc(poly, 0, polyLength - 1, center); } /** * Swap points pointed to by i and j */ void SpotShadow::swap(Vector2* points, int i, int j) { Vector2 temp = points[i]; points[i] = points[j]; points[j] = temp; } /** * quick sort implementation about the center. */ void SpotShadow::quicksortCirc(Vector2* points, int low, int high, const Vector2& center) { int i = low, j = high; int p = low + (high - low) / 2; float pivot = angle(points[p], center); while (i <= j) { while (angle(points[i], center) > pivot) { i++; } while (angle(points[j], center) < pivot) { j--; } if (i <= j) { swap(points, i, j); i++; j--; } } if (low < j) quicksortCirc(points, low, j, center); if (i < high) quicksortCirc(points, i, high, center); } /** * Sort points by x axis * * @param points points to sort * @param low start index * @param high end index */ void SpotShadow::quicksortX(Vector2* points, int low, int high) { int i = low, j = high; int p = low + (high - low) / 2; float pivot = points[p].x; while (i <= j) { while (points[i].x < pivot) { i++; } while (points[j].x > pivot) { j--; } if (i <= j) { swap(points, i, j); i++; j--; } } if (low < j) quicksortX(points, low, j); if (i < high) quicksortX(points, i, high); } /** * Test whether a point is inside the polygon. * * @param testPoint the point to test * @param poly the polygon * @return true if the testPoint is inside the poly. */ bool SpotShadow::testPointInsidePolygon(const Vector2 testPoint, const Vector2* poly, int len) { bool c = false; double testx = testPoint.x; double testy = testPoint.y; for (int i = 0, j = len - 1; i < len; j = i++) { double startX = poly[j].x; double startY = poly[j].y; double endX = poly[i].x; double endY = poly[i].y; if (((endY > testy) != (startY > testy)) && (testx < (startX - endX) * (testy - endY) / (startY - endY) + endX)) { c = !c; } } return c; } /** * Make the polygon turn clockwise. * * @param polygon the polygon as a Vector2 array. * @param len the number of points of the polygon */ void SpotShadow::makeClockwise(Vector2* polygon, int len) { if (polygon == 0 || len == 0) { return; } if (!ShadowTessellator::isClockwise(polygon, len)) { reverse(polygon, len); } } /** * Reverse the polygon * * @param polygon the polygon as a Vector2 array * @param len the number of points of the polygon */ void SpotShadow::reverse(Vector2* polygon, int len) { int n = len / 2; for (int i = 0; i < n; i++) { Vector2 tmp = polygon[i]; int k = len - 1 - i; polygon[i] = polygon[k]; polygon[k] = tmp; } } /** * Intersects two lines in parametric form. This function is called in a tight * loop, and we need double precision to get things right. * * @param x1 the x coordinate point 1 of line 1 * @param y1 the y coordinate point 1 of line 1 * @param x2 the x coordinate point 2 of line 1 * @param y2 the y coordinate point 2 of line 1 * @param x3 the x coordinate point 1 of line 2 * @param y3 the y coordinate point 1 of line 2 * @param x4 the x coordinate point 2 of line 2 * @param y4 the y coordinate point 2 of line 2 * @param ret the x,y location of the intersection * @return true if it found an intersection */ inline bool SpotShadow::lineIntersection(double x1, double y1, double x2, double y2, double x3, double y3, double x4, double y4, Vector2& ret) { double d = (x1 - x2) * (y3 - y4) - (y1 - y2) * (x3 - x4); if (d == 0.0) return false; double dx = (x1 * y2 - y1 * x2); double dy = (x3 * y4 - y3 * x4); double x = (dx * (x3 - x4) - (x1 - x2) * dy) / d; double y = (dx * (y3 - y4) - (y1 - y2) * dy) / d; // The intersection should be in the middle of the point 1 and point 2, // likewise point 3 and point 4. if (((x - x1) * (x - x2) > EPSILON) || ((x - x3) * (x - x4) > EPSILON) || ((y - y1) * (y - y2) > EPSILON) || ((y - y3) * (y - y4) > EPSILON)) { // Not interesected return false; } ret.x = x; ret.y = y; return true; } /** * Compute a horizontal circular polygon about point (x , y , height) of radius * (size) * * @param points number of the points of the output polygon. * @param lightCenter the center of the light. * @param size the light size. * @param ret result polygon. */ void SpotShadow::computeLightPolygon(int points, const Vector3& lightCenter, float size, Vector3* ret) { // TODO: Caching all the sin / cos values and store them in a look up table. for (int i = 0; i < points; i++) { double angle = 2 * i * M_PI / points; ret[i].x = cosf(angle) * size + lightCenter.x; ret[i].y = sinf(angle) * size + lightCenter.y; ret[i].z = lightCenter.z; } } /** * From light center, project one vertex to the z=0 surface and get the outline. * * @param outline The result which is the outline position. * @param lightCenter The center of light. * @param polyVertex The input polygon's vertex. * * @return float The ratio of (polygon.z / light.z - polygon.z) */ float SpotShadow::projectCasterToOutline(Vector2& outline, const Vector3& lightCenter, const Vector3& polyVertex) { float lightToPolyZ = lightCenter.z - polyVertex.z; float ratioZ = CASTER_Z_CAP_RATIO; if (lightToPolyZ != 0) { // If any caster's vertex is almost above the light, we just keep it as 95% // of the height of the light. ratioZ = MathUtils::clamp(polyVertex.z / lightToPolyZ, 0.0f, CASTER_Z_CAP_RATIO); } outline.x = polyVertex.x - ratioZ * (lightCenter.x - polyVertex.x); outline.y = polyVertex.y - ratioZ * (lightCenter.y - polyVertex.y); return ratioZ; } /** * Generate the shadow spot light of shape lightPoly and a object poly * * @param isCasterOpaque whether the caster is opaque * @param lightCenter the center of the light * @param lightSize the radius of the light * @param poly x,y,z vertexes of a convex polygon that occludes the light source * @param polyLength number of vertexes of the occluding polygon * @param shadowTriangleStrip return an (x,y,alpha) triangle strip representing the shadow. Return * empty strip if error. */ void SpotShadow::createSpotShadow(bool isCasterOpaque, const Vector3& lightCenter, float lightSize, const Vector3* poly, int polyLength, const Vector3& polyCentroid, VertexBuffer& shadowTriangleStrip) { if (CC_UNLIKELY(lightCenter.z <= 0)) { ALOGW("Relative Light Z is not positive. No spot shadow!"); return; } if (CC_UNLIKELY(polyLength < 3)) { #if DEBUG_SHADOW ALOGW("Invalid polygon length. No spot shadow!"); #endif return; } OutlineData outlineData[polyLength]; Vector2 outlineCentroid; // Calculate the projected outline for each polygon's vertices from the light center. // // O Light // / // / // . Polygon vertex // / // / // O Outline vertices // // Ratio = (Poly - Outline) / (Light - Poly) // Outline.x = Poly.x - Ratio * (Light.x - Poly.x) // Outline's radius / Light's radius = Ratio // Compute the last outline vertex to make sure we can get the normal and outline // in one single loop. projectCasterToOutline(outlineData[polyLength - 1].position, lightCenter, poly[polyLength - 1]); // Take the outline's polygon, calculate the normal for each outline edge. int currentNormalIndex = polyLength - 1; int nextNormalIndex = 0; for (int i = 0; i < polyLength; i++) { float ratioZ = projectCasterToOutline(outlineData[i].position, lightCenter, poly[i]); outlineData[i].radius = ratioZ * lightSize; outlineData[currentNormalIndex].normal = ShadowTessellator::calculateNormal( outlineData[currentNormalIndex].position, outlineData[nextNormalIndex].position); currentNormalIndex = (currentNormalIndex + 1) % polyLength; nextNormalIndex++; } projectCasterToOutline(outlineCentroid, lightCenter, polyCentroid); int penumbraIndex = 0; // Then each polygon's vertex produce at minmal 2 penumbra vertices. // Since the size can be dynamic here, we keep track of the size and update // the real size at the end. int allocatedPenumbraLength = 2 * polyLength + SPOT_MAX_EXTRA_CORNER_VERTEX_NUMBER; Vector2 penumbra[allocatedPenumbraLength]; int totalExtraCornerSliceNumber = 0; Vector2 umbra[polyLength]; // When centroid is covered by all circles from outline, then we consider // the umbra is invalid, and we will tune down the shadow strength. bool hasValidUmbra = true; // We need the minimal of RaitoVI to decrease the spot shadow strength accordingly. float minRaitoVI = FLT_MAX; for (int i = 0; i < polyLength; i++) { // Generate all the penumbra's vertices only using the (outline vertex + normal * radius) // There is no guarantee that the penumbra is still convex, but for // each outline vertex, it will connect to all its corresponding penumbra vertices as // triangle fans. And for neighber penumbra vertex, it will be a trapezoid. // // Penumbra Vertices marked as Pi // Outline Vertices marked as Vi // (P3) // (P2) | ' (P4) // (P1)' | | ' // ' | | ' // (P0) ------------------------------------------------(P5) // | (V0) |(V1) // | | // | | // | | // | | // | | // | | // | | // | | // (V3)-----------------------------------(V2) int preNormalIndex = (i + polyLength - 1) % polyLength; const Vector2& previousNormal = outlineData[preNormalIndex].normal; const Vector2& currentNormal = outlineData[i].normal; // Depending on how roundness we want for each corner, we can subdivide // further here and/or introduce some heuristic to decide how much the // subdivision should be. int currentExtraSliceNumber = ShadowTessellator::getExtraVertexNumber( previousNormal, currentNormal, SPOT_CORNER_RADIANS_DIVISOR); int currentCornerSliceNumber = 1 + currentExtraSliceNumber; totalExtraCornerSliceNumber += currentExtraSliceNumber; #if DEBUG_SHADOW ALOGD("currentExtraSliceNumber should be %d", currentExtraSliceNumber); ALOGD("currentCornerSliceNumber should be %d", currentCornerSliceNumber); ALOGD("totalCornerSliceNumber is %d", totalExtraCornerSliceNumber); #endif if (CC_UNLIKELY(totalExtraCornerSliceNumber > SPOT_MAX_EXTRA_CORNER_VERTEX_NUMBER)) { currentCornerSliceNumber = 1; } for (int k = 0; k <= currentCornerSliceNumber; k++) { Vector2 avgNormal = (previousNormal * (currentCornerSliceNumber - k) + currentNormal * k) / currentCornerSliceNumber; avgNormal.normalize(); penumbra[penumbraIndex++] = outlineData[i].position + avgNormal * outlineData[i].radius; } // Compute the umbra by the intersection from the outline's centroid! // // (V) ------------------------------------ // | ' | // | ' | // | ' (I) | // | ' | // | ' (C) | // | | // | | // | | // | | // ------------------------------------ // // Connect a line b/t the outline vertex (V) and the centroid (C), it will // intersect with the outline vertex's circle at point (I). // Now, ratioVI = VI / VC, ratioIC = IC / VC // Then the intersetion point can be computed as Ixy = Vxy * ratioIC + Cxy * ratioVI; // // When all of the outline circles cover the the outline centroid, (like I is // on the other side of C), there is no real umbra any more, so we just fake // a small area around the centroid as the umbra, and tune down the spot // shadow's umbra strength to simulate the effect the whole shadow will // become lighter in this case. // The ratio can be simulated by using the inverse of maximum of ratioVI for // all (V). float distOutline = (outlineData[i].position - outlineCentroid).length(); if (CC_UNLIKELY(distOutline == 0)) { // If the outline has 0 area, then there is no spot shadow anyway. ALOGW("Outline has 0 area, no spot shadow!"); return; } float ratioVI = outlineData[i].radius / distOutline; minRaitoVI = MathUtils::min(minRaitoVI, ratioVI); if (ratioVI >= (1 - FAKE_UMBRA_SIZE_RATIO)) { ratioVI = (1 - FAKE_UMBRA_SIZE_RATIO); } // When we know we don't have valid umbra, don't bother to compute the // values below. But we can't skip the loop yet since we want to know the // maximum ratio. float ratioIC = 1 - ratioVI; umbra[i] = outlineData[i].position * ratioIC + outlineCentroid * ratioVI; } hasValidUmbra = (minRaitoVI <= 1.0); float shadowStrengthScale = 1.0; if (!hasValidUmbra) { #if DEBUG_SHADOW ALOGW("The object is too close to the light or too small, no real umbra!"); #endif for (int i = 0; i < polyLength; i++) { umbra[i] = outlineData[i].position * FAKE_UMBRA_SIZE_RATIO + outlineCentroid * (1 - FAKE_UMBRA_SIZE_RATIO); } shadowStrengthScale = 1.0 / minRaitoVI; } int penumbraLength = penumbraIndex; int umbraLength = polyLength; #if DEBUG_SHADOW ALOGD("penumbraLength is %d , allocatedPenumbraLength %d", penumbraLength, allocatedPenumbraLength); dumpPolygon(poly, polyLength, "input poly"); dumpPolygon(penumbra, penumbraLength, "penumbra"); dumpPolygon(umbra, umbraLength, "umbra"); ALOGD("hasValidUmbra is %d and shadowStrengthScale is %f", hasValidUmbra, shadowStrengthScale); #endif // The penumbra and umbra needs to be in convex shape to keep consistency // and quality. // Since we are still shooting rays to penumbra, it needs to be convex. // Umbra can be represented as a fan from the centroid, but visually umbra // looks nicer when it is convex. Vector2 finalUmbra[umbraLength]; Vector2 finalPenumbra[penumbraLength]; int finalUmbraLength = hull(umbra, umbraLength, finalUmbra); int finalPenumbraLength = hull(penumbra, penumbraLength, finalPenumbra); generateTriangleStrip(isCasterOpaque, shadowStrengthScale, finalPenumbra, finalPenumbraLength, finalUmbra, finalUmbraLength, poly, polyLength, shadowTriangleStrip, outlineCentroid); } /** * Converts a polygon specified with CW vertices into an array of distance-from-centroid values. * * Returns false in error conditions * * @param poly Array of vertices. Note that these *must* be CW. * @param polyLength The number of vertices in the polygon. * @param polyCentroid The centroid of the polygon, from which rays will be cast * @param rayDist The output array for the calculated distances, must be SHADOW_RAY_COUNT in size */ bool convertPolyToRayDist(const Vector2* poly, int polyLength, const Vector2& polyCentroid, float* rayDist) { const int rays = SHADOW_RAY_COUNT; const float step = M_PI * 2 / rays; const Vector2* lastVertex = &(poly[polyLength - 1]); float startAngle = angle(*lastVertex, polyCentroid); // Start with the ray that's closest to and less than startAngle int rayIndex = floor((startAngle - EPSILON) / step); rayIndex = (rayIndex + rays) % rays; // ensure positive for (int polyIndex = 0; polyIndex < polyLength; polyIndex++) { /* * For a given pair of vertices on the polygon, poly[i-1] and poly[i], the rays that * intersect these will be those that are between the two angles from the centroid that the * vertices define. * * Because the polygon vertices are stored clockwise, the closest ray with an angle * *smaller* than that defined by angle(poly[i], centroid) will be the first ray that does * not intersect with poly[i-1], poly[i]. */ float currentAngle = angle(poly[polyIndex], polyCentroid); // find first ray that will not intersect the line segment poly[i-1] & poly[i] int firstRayIndexOnNextSegment = floor((currentAngle - EPSILON) / step); firstRayIndexOnNextSegment = (firstRayIndexOnNextSegment + rays) % rays; // ensure positive // Iterate through all rays that intersect with poly[i-1], poly[i] line segment. // This may be 0 rays. while (rayIndex != firstRayIndexOnNextSegment) { float distanceToIntersect = rayIntersectPoints(polyCentroid, cos(rayIndex * step), sin(rayIndex * step), *lastVertex, poly[polyIndex]); if (distanceToIntersect < 0) { #if DEBUG_SHADOW ALOGW("ERROR: convertPolyToRayDist failed"); #endif return false; // error case, abort } rayDist[rayIndex] = distanceToIntersect; rayIndex = (rayIndex - 1 + rays) % rays; } lastVertex = &poly[polyIndex]; } return true; } int SpotShadow::calculateOccludedUmbra(const Vector2* umbra, int umbraLength, const Vector3* poly, int polyLength, Vector2* occludedUmbra) { // Occluded umbra area is computed as the intersection of the projected 2D // poly and umbra. for (int i = 0; i < polyLength; i++) { occludedUmbra[i].x = poly[i].x; occludedUmbra[i].y = poly[i].y; } // Both umbra and incoming polygon are guaranteed to be CW, so we can call // intersection() directly. return intersection(umbra, umbraLength, occludedUmbra, polyLength); } /** * This is only for experimental purpose. * After intersections are calculated, we could smooth the polygon if needed. * So far, we don't think it is more appealing yet. * * @param level The level of smoothness. * @param rays The total number of rays. * @param rayDist (In and Out) The distance for each ray. * */ void SpotShadow::smoothPolygon(int level, int rays, float* rayDist) { for (int k = 0; k < level; k++) { for (int i = 0; i < rays; i++) { float p1 = rayDist[(rays - 1 + i) % rays]; float p2 = rayDist[i]; float p3 = rayDist[(i + 1) % rays]; rayDist[i] = (p1 + p2 * 2 + p3) / 4; } } } /** * Generate a array of the angleData for either umbra or penumbra vertices. * * This array will be merged and used to guide where to shoot the rays, in clockwise order. * * @param angleDataList The result array of angle data. * * @return int The maximum angle's index in the array. */ int SpotShadow::setupAngleList(VertexAngleData* angleDataList, int polyLength, const Vector2* polygon, const Vector2& centroid, bool isPenumbra, const char* name) { float maxAngle = FLT_MIN; int maxAngleIndex = 0; for (int i = 0; i < polyLength; i++) { float currentAngle = angle(polygon[i], centroid); if (currentAngle > maxAngle) { maxAngle = currentAngle; maxAngleIndex = i; } angleDataList[i].set(currentAngle, isPenumbra, i); #if DEBUG_SHADOW ALOGD("%s AngleList i %d %f", name, i, currentAngle); #endif } return maxAngleIndex; } /** * Make sure the polygons are indeed in clockwise order. * * Possible reasons to return false: 1. The input polygon is not setup properly. 2. The hull * algorithm is not able to generate it properly. * * Anyway, since the algorithm depends on the clockwise, when these kind of unexpected error * situation is found, we need to detect it and early return without corrupting the memory. * * @return bool True if the angle list is actually from big to small. */ bool SpotShadow::checkClockwise(int indexOfMaxAngle, int listLength, VertexAngleData* angleList, const char* name) { int currentIndex = indexOfMaxAngle; #if DEBUG_SHADOW ALOGD("max index %d", currentIndex); #endif for (int i = 0; i < listLength - 1; i++) { // TODO: Cache the last angle. float currentAngle = angleList[currentIndex].mAngle; float nextAngle = angleList[(currentIndex + 1) % listLength].mAngle; if (currentAngle < nextAngle) { #if DEBUG_SHADOW ALOGE("%s, is not CW, at index %d", name, currentIndex); #endif return false; } currentIndex = (currentIndex + 1) % listLength; } return true; } /** * Check the polygon is clockwise. * * @return bool True is the polygon is clockwise. */ bool SpotShadow::checkPolyClockwise(int polyAngleLength, int maxPolyAngleIndex, const float* polyAngleList) { bool isPolyCW = true; // Starting from maxPolyAngleIndex , check around to make sure angle decrease. for (int i = 0; i < polyAngleLength - 1; i++) { float currentAngle = polyAngleList[(i + maxPolyAngleIndex) % polyAngleLength]; float nextAngle = polyAngleList[(i + maxPolyAngleIndex + 1) % polyAngleLength]; if (currentAngle < nextAngle) { isPolyCW = false; } } return isPolyCW; } /** * Given the sorted array of all the vertices angle data, calculate for each * vertices, the offset value to array element which represent the start edge * of the polygon we need to shoot the ray at. * * TODO: Calculate this for umbra and penumbra in one loop using one single array. * * @param distances The result of the array distance counter. */ void SpotShadow::calculateDistanceCounter(bool needsOffsetToUmbra, int angleLength, const VertexAngleData* allVerticesAngleData, int* distances) { bool firstVertexIsPenumbra = allVerticesAngleData[0].mIsPenumbra; // If we want distance to inner, then we just set to 0 when we see inner. bool needsSearch = needsOffsetToUmbra ? firstVertexIsPenumbra : !firstVertexIsPenumbra; int distanceCounter = 0; if (needsSearch) { int foundIndex = -1; for (int i = (angleLength - 1); i >= 0; i--) { bool currentIsOuter = allVerticesAngleData[i].mIsPenumbra; // If we need distance to inner, then we need to find a inner vertex. if (currentIsOuter != firstVertexIsPenumbra) { foundIndex = i; break; } } LOG_ALWAYS_FATAL_IF(foundIndex == -1, "Wrong index found, means either" " umbra or penumbra's length is 0"); distanceCounter = angleLength - foundIndex; } #if DEBUG_SHADOW ALOGD("distances[0] is %d", distanceCounter); #endif distances[0] = distanceCounter; // means never see a target poly for (int i = 1; i < angleLength; i++) { bool firstVertexIsPenumbra = allVerticesAngleData[i].mIsPenumbra; // When we needs for distance for each outer vertex to inner, then we // increase the distance when seeing outer vertices. Otherwise, we clear // to 0. bool needsIncrement = needsOffsetToUmbra ? firstVertexIsPenumbra : !firstVertexIsPenumbra; // If counter is not -1, that means we have seen an other polygon's vertex. if (needsIncrement && distanceCounter != -1) { distanceCounter++; } else { distanceCounter = 0; } distances[i] = distanceCounter; } } /** * Given umbra and penumbra angle data list, merge them by sorting the angle * from the biggest to smallest. * * @param allVerticesAngleData The result array of merged angle data. */ void SpotShadow::mergeAngleList(int maxUmbraAngleIndex, int maxPenumbraAngleIndex, const VertexAngleData* umbraAngleList, int umbraLength, const VertexAngleData* penumbraAngleList, int penumbraLength, VertexAngleData* allVerticesAngleData) { int totalRayNumber = umbraLength + penumbraLength; int umbraIndex = maxUmbraAngleIndex; int penumbraIndex = maxPenumbraAngleIndex; float currentUmbraAngle = umbraAngleList[umbraIndex].mAngle; float currentPenumbraAngle = penumbraAngleList[penumbraIndex].mAngle; // TODO: Clean this up using a while loop with 2 iterators. for (int i = 0; i < totalRayNumber; i++) { if (currentUmbraAngle > currentPenumbraAngle) { allVerticesAngleData[i] = umbraAngleList[umbraIndex]; umbraIndex = (umbraIndex + 1) % umbraLength; // If umbraIndex round back, that means we are running out of // umbra vertices to merge, so just copy all the penumbra leftover. // Otherwise, we update the currentUmbraAngle. if (umbraIndex != maxUmbraAngleIndex) { currentUmbraAngle = umbraAngleList[umbraIndex].mAngle; } else { for (int j = i + 1; j < totalRayNumber; j++) { allVerticesAngleData[j] = penumbraAngleList[penumbraIndex]; penumbraIndex = (penumbraIndex + 1) % penumbraLength; } break; } } else { allVerticesAngleData[i] = penumbraAngleList[penumbraIndex]; penumbraIndex = (penumbraIndex + 1) % penumbraLength; // If penumbraIndex round back, that means we are running out of // penumbra vertices to merge, so just copy all the umbra leftover. // Otherwise, we update the currentPenumbraAngle. if (penumbraIndex != maxPenumbraAngleIndex) { currentPenumbraAngle = penumbraAngleList[penumbraIndex].mAngle; } else { for (int j = i + 1; j < totalRayNumber; j++) { allVerticesAngleData[j] = umbraAngleList[umbraIndex]; umbraIndex = (umbraIndex + 1) % umbraLength; } break; } } } } #if DEBUG_SHADOW /** * DEBUG ONLY: Verify all the offset compuation is correctly done by examining * each vertex and its neighbor. */ static void verifyDistanceCounter(const VertexAngleData* allVerticesAngleData, const int* distances, int angleLength, const char* name) { int currentDistance = distances[0]; for (int i = 1; i < angleLength; i++) { if (distances[i] != INT_MIN) { if (!((currentDistance + 1) == distances[i] || distances[i] == 0)) { ALOGE("Wrong distance found at i %d name %s", i, name); } currentDistance = distances[i]; if (currentDistance != 0) { bool currentOuter = allVerticesAngleData[i].mIsPenumbra; for (int j = 1; j <= (currentDistance - 1); j++) { bool neigborOuter = allVerticesAngleData[(i + angleLength - j) % angleLength].mIsPenumbra; if (neigborOuter != currentOuter) { ALOGE("Wrong distance found at i %d name %s", i, name); } } bool oppositeOuter = allVerticesAngleData[(i + angleLength - currentDistance) % angleLength].mIsPenumbra; if (oppositeOuter == currentOuter) { ALOGE("Wrong distance found at i %d name %s", i, name); } } } } } /** * DEBUG ONLY: Verify all the angle data compuated are is correctly done */ static void verifyAngleData(int totalRayNumber, const VertexAngleData* allVerticesAngleData, const int* distancesToInner, const int* distancesToOuter, const VertexAngleData* umbraAngleList, int maxUmbraAngleIndex, int umbraLength, const VertexAngleData* penumbraAngleList, int maxPenumbraAngleIndex, int penumbraLength) { for (int i = 0; i < totalRayNumber; i++) { ALOGD("currentAngleList i %d, angle %f, isInner %d, index %d distancesToInner" " %d distancesToOuter %d", i, allVerticesAngleData[i].mAngle, !allVerticesAngleData[i].mIsPenumbra, allVerticesAngleData[i].mVertexIndex, distancesToInner[i], distancesToOuter[i]); } verifyDistanceCounter(allVerticesAngleData, distancesToInner, totalRayNumber, "distancesToInner"); verifyDistanceCounter(allVerticesAngleData, distancesToOuter, totalRayNumber, "distancesToOuter"); for (int i = 0; i < totalRayNumber; i++) { if ((distancesToInner[i] * distancesToOuter[i]) != 0) { ALOGE("distancesToInner wrong at index %d distancesToInner[i] %d," " distancesToOuter[i] %d", i, distancesToInner[i], distancesToOuter[i]); } } int currentUmbraVertexIndex = umbraAngleList[maxUmbraAngleIndex].mVertexIndex; int currentPenumbraVertexIndex = penumbraAngleList[maxPenumbraAngleIndex].mVertexIndex; for (int i = 0; i < totalRayNumber; i++) { if (allVerticesAngleData[i].mIsPenumbra == true) { if (allVerticesAngleData[i].mVertexIndex != currentPenumbraVertexIndex) { ALOGW("wrong penumbra indexing i %d allVerticesAngleData[i].mVertexIndex %d " "currentpenumbraVertexIndex %d", i, allVerticesAngleData[i].mVertexIndex, currentPenumbraVertexIndex); } currentPenumbraVertexIndex = (currentPenumbraVertexIndex + 1) % penumbraLength; } else { if (allVerticesAngleData[i].mVertexIndex != currentUmbraVertexIndex) { ALOGW("wrong umbra indexing i %d allVerticesAngleData[i].mVertexIndex %d " "currentUmbraVertexIndex %d", i, allVerticesAngleData[i].mVertexIndex, currentUmbraVertexIndex); } currentUmbraVertexIndex = (currentUmbraVertexIndex + 1) % umbraLength; } } for (int i = 0; i < totalRayNumber - 1; i++) { float currentAngle = allVerticesAngleData[i].mAngle; float nextAngle = allVerticesAngleData[(i + 1) % totalRayNumber].mAngle; if (currentAngle < nextAngle) { ALOGE("Unexpected angle values!, currentAngle nextAngle %f %f", currentAngle, nextAngle); } } } #endif /** * In order to compute the occluded umbra, we need to setup the angle data list * for the polygon data. Since we only store one poly vertex per polygon vertex, * this array only needs to be a float array which are the angles for each vertex. * * @param polyAngleList The result list * * @return int The index for the maximum angle in this array. */ int SpotShadow::setupPolyAngleList(float* polyAngleList, int polyAngleLength, const Vector2* poly2d, const Vector2& centroid) { int maxPolyAngleIndex = -1; float maxPolyAngle = -FLT_MAX; for (int i = 0; i < polyAngleLength; i++) { polyAngleList[i] = angle(poly2d[i], centroid); if (polyAngleList[i] > maxPolyAngle) { maxPolyAngle = polyAngleList[i]; maxPolyAngleIndex = i; } } return maxPolyAngleIndex; } /** * For umbra and penumbra, given the offset info and the current ray number, * find the right edge index (the (starting vertex) for the ray to shoot at. * * @return int The index of the starting vertex of the edge. */ inline int SpotShadow::getEdgeStartIndex(const int* offsets, int rayIndex, int totalRayNumber, const VertexAngleData* allVerticesAngleData) { int tempOffset = offsets[rayIndex]; int targetRayIndex = (rayIndex - tempOffset + totalRayNumber) % totalRayNumber; return allVerticesAngleData[targetRayIndex].mVertexIndex; } /** * For the occluded umbra, given the array of angles, find the index of the * starting vertex of the edge, for the ray to shoo at. * * TODO: Save the last result to shorten the search distance. * * @return int The index of the starting vertex of the edge. */ inline int SpotShadow::getPolyEdgeStartIndex(int maxPolyAngleIndex, int polyLength, const float* polyAngleList, float rayAngle) { int minPolyAngleIndex = (maxPolyAngleIndex + polyLength - 1) % polyLength; int resultIndex = -1; if (rayAngle > polyAngleList[maxPolyAngleIndex] || rayAngle <= polyAngleList[minPolyAngleIndex]) { resultIndex = minPolyAngleIndex; } else { for (int i = 0; i < polyLength - 1; i++) { int currentIndex = (maxPolyAngleIndex + i) % polyLength; int nextIndex = (maxPolyAngleIndex + i + 1) % polyLength; if (rayAngle <= polyAngleList[currentIndex] && rayAngle > polyAngleList[nextIndex]) { resultIndex = currentIndex; } } } if (CC_UNLIKELY(resultIndex == -1)) { // TODO: Add more error handling here. ALOGE("Wrong index found, means no edge can't be found for rayAngle %f", rayAngle); } return resultIndex; } /** * Convert the incoming polygons into arrays of vertices, for each ray. * Ray only shoots when there is one vertex either on penumbra on umbra. * * Finally, it will generate vertices per ray for umbra, penumbra and optionally * occludedUmbra. * * Return true (success) when all vertices are generated */ int SpotShadow::convertPolysToVerticesPerRay( bool hasOccludedUmbraArea, const Vector2* poly2d, int polyLength, const Vector2* umbra, int umbraLength, const Vector2* penumbra, int penumbraLength, const Vector2& centroid, Vector2* umbraVerticesPerRay, Vector2* penumbraVerticesPerRay, Vector2* occludedUmbraVerticesPerRay) { int totalRayNumber = umbraLength + penumbraLength; // For incoming umbra / penumbra polygons, we will build an intermediate data // structure to help us sort all the vertices according to the vertices. // Using this data structure, we can tell where (the angle) to shoot the ray, // whether we shoot at penumbra edge or umbra edge, and which edge to shoot at. // // We first parse each vertices and generate a table of VertexAngleData. // Based on that, we create 2 arrays telling us which edge to shoot at. VertexAngleData allVerticesAngleData[totalRayNumber]; VertexAngleData umbraAngleList[umbraLength]; VertexAngleData penumbraAngleList[penumbraLength]; int polyAngleLength = hasOccludedUmbraArea ? polyLength : 0; float polyAngleList[polyAngleLength]; const int maxUmbraAngleIndex = setupAngleList(umbraAngleList, umbraLength, umbra, centroid, false, "umbra"); const int maxPenumbraAngleIndex = setupAngleList(penumbraAngleList, penumbraLength, penumbra, centroid, true, "penumbra"); const int maxPolyAngleIndex = setupPolyAngleList(polyAngleList, polyAngleLength, poly2d, centroid); // Check all the polygons here are CW. bool isPolyCW = checkPolyClockwise(polyAngleLength, maxPolyAngleIndex, polyAngleList); bool isUmbraCW = checkClockwise(maxUmbraAngleIndex, umbraLength, umbraAngleList, "umbra"); bool isPenumbraCW = checkClockwise(maxPenumbraAngleIndex, penumbraLength, penumbraAngleList, "penumbra"); if (!isUmbraCW || !isPenumbraCW || !isPolyCW) { #if DEBUG_SHADOW ALOGE("One polygon is not CW isUmbraCW %d isPenumbraCW %d isPolyCW %d", isUmbraCW, isPenumbraCW, isPolyCW); #endif return false; } mergeAngleList(maxUmbraAngleIndex, maxPenumbraAngleIndex, umbraAngleList, umbraLength, penumbraAngleList, penumbraLength, allVerticesAngleData); // Calculate the offset to the left most Inner vertex for each outerVertex. // Then the offset to the left most Outer vertex for each innerVertex. int offsetToInner[totalRayNumber]; int offsetToOuter[totalRayNumber]; calculateDistanceCounter(true, totalRayNumber, allVerticesAngleData, offsetToInner); calculateDistanceCounter(false, totalRayNumber, allVerticesAngleData, offsetToOuter); // Generate both umbraVerticesPerRay and penumbraVerticesPerRay for (int i = 0; i < totalRayNumber; i++) { float rayAngle = allVerticesAngleData[i].mAngle; bool isUmbraVertex = !allVerticesAngleData[i].mIsPenumbra; float dx = cosf(rayAngle); float dy = sinf(rayAngle); float distanceToIntersectUmbra = -1; if (isUmbraVertex) { // We can just copy umbra easily, and calculate the distance for the // occluded umbra computation. int startUmbraIndex = allVerticesAngleData[i].mVertexIndex; umbraVerticesPerRay[i] = umbra[startUmbraIndex]; if (hasOccludedUmbraArea) { distanceToIntersectUmbra = (umbraVerticesPerRay[i] - centroid).length(); } //shoot ray to penumbra only int startPenumbraIndex = getEdgeStartIndex(offsetToOuter, i, totalRayNumber, allVerticesAngleData); float distanceToIntersectPenumbra = rayIntersectPoints(centroid, dx, dy, penumbra[startPenumbraIndex], penumbra[(startPenumbraIndex + 1) % penumbraLength]); if (distanceToIntersectPenumbra < 0) { #if DEBUG_SHADOW ALOGW("convertPolyToRayDist for penumbra failed rayAngle %f dx %f dy %f", rayAngle, dx, dy); #endif distanceToIntersectPenumbra = 0; } penumbraVerticesPerRay[i].x = centroid.x + dx * distanceToIntersectPenumbra; penumbraVerticesPerRay[i].y = centroid.y + dy * distanceToIntersectPenumbra; } else { // We can just copy the penumbra int startPenumbraIndex = allVerticesAngleData[i].mVertexIndex; penumbraVerticesPerRay[i] = penumbra[startPenumbraIndex]; // And shoot ray to umbra only int startUmbraIndex = getEdgeStartIndex(offsetToInner, i, totalRayNumber, allVerticesAngleData); distanceToIntersectUmbra = rayIntersectPoints(centroid, dx, dy, umbra[startUmbraIndex], umbra[(startUmbraIndex + 1) % umbraLength]); if (distanceToIntersectUmbra < 0) { #if DEBUG_SHADOW ALOGW("convertPolyToRayDist for umbra failed rayAngle %f dx %f dy %f", rayAngle, dx, dy); #endif distanceToIntersectUmbra = 0; } umbraVerticesPerRay[i].x = centroid.x + dx * distanceToIntersectUmbra; umbraVerticesPerRay[i].y = centroid.y + dy * distanceToIntersectUmbra; } if (hasOccludedUmbraArea) { // Shoot the same ray to the poly2d, and get the distance. int startPolyIndex = getPolyEdgeStartIndex(maxPolyAngleIndex, polyLength, polyAngleList, rayAngle); float distanceToIntersectPoly = rayIntersectPoints(centroid, dx, dy, poly2d[startPolyIndex], poly2d[(startPolyIndex + 1) % polyLength]); if (distanceToIntersectPoly < 0) { distanceToIntersectPoly = 0; } distanceToIntersectPoly = MathUtils::min(distanceToIntersectUmbra, distanceToIntersectPoly); occludedUmbraVerticesPerRay[i].x = centroid.x + dx * distanceToIntersectPoly; occludedUmbraVerticesPerRay[i].y = centroid.y + dy * distanceToIntersectPoly; } } #if DEBUG_SHADOW verifyAngleData(totalRayNumber, allVerticesAngleData, offsetToInner, offsetToOuter, umbraAngleList, maxUmbraAngleIndex, umbraLength, penumbraAngleList, maxPenumbraAngleIndex, penumbraLength); #endif return true; // success } /** * Generate a triangle strip given two convex polygon **/ void SpotShadow::generateTriangleStrip(bool isCasterOpaque, float shadowStrengthScale, Vector2* penumbra, int penumbraLength, Vector2* umbra, int umbraLength, const Vector3* poly, int polyLength, VertexBuffer& shadowTriangleStrip, const Vector2& centroid) { bool hasOccludedUmbraArea = false; Vector2 poly2d[polyLength]; if (isCasterOpaque) { for (int i = 0; i < polyLength; i++) { poly2d[i].x = poly[i].x; poly2d[i].y = poly[i].y; } // Make sure the centroid is inside the umbra, otherwise, fall back to the // approach as if there is no occluded umbra area. if (testPointInsidePolygon(centroid, poly2d, polyLength)) { hasOccludedUmbraArea = true; } } int totalRayNum = umbraLength + penumbraLength; Vector2 umbraVertices[totalRayNum]; Vector2 penumbraVertices[totalRayNum]; Vector2 occludedUmbraVertices[totalRayNum]; bool convertSuccess = convertPolysToVerticesPerRay(hasOccludedUmbraArea, poly2d, polyLength, umbra, umbraLength, penumbra, penumbraLength, centroid, umbraVertices, penumbraVertices, occludedUmbraVertices); if (!convertSuccess) { return; } // Minimal value is 1, for each vertex show up once. // The bigger this value is , the smoother the look is, but more memory // is consumed. // When the ray number is high, that means the polygon has been fine // tessellated, we don't need this extra slice, just keep it as 1. int sliceNumberPerEdge = (totalRayNum > FINE_TESSELLATED_POLYGON_RAY_NUMBER) ? 1 : 2; // For each polygon, we at most add (totalRayNum * sliceNumberPerEdge) vertices. int slicedVertexCountPerPolygon = totalRayNum * sliceNumberPerEdge; int totalVertexCount = slicedVertexCountPerPolygon * 2 + totalRayNum; int totalIndexCount = 2 * (slicedVertexCountPerPolygon * 2 + 2); AlphaVertex* shadowVertices = shadowTriangleStrip.alloc(totalVertexCount); uint16_t* indexBuffer = shadowTriangleStrip.allocIndices(totalIndexCount); int indexBufferIndex = 0; int vertexBufferIndex = 0; uint16_t slicedUmbraVertexIndex[totalRayNum * sliceNumberPerEdge]; // Should be something like 0 0 0 1 1 1 2 3 3 3... int rayNumberPerSlicedUmbra[totalRayNum * sliceNumberPerEdge]; int realUmbraVertexCount = 0; for (int i = 0; i < totalRayNum; i++) { Vector2 currentPenumbra = penumbraVertices[i]; Vector2 currentUmbra = umbraVertices[i]; Vector2 nextPenumbra = penumbraVertices[(i + 1) % totalRayNum]; Vector2 nextUmbra = umbraVertices[(i + 1) % totalRayNum]; // NextUmbra/Penumbra will be done in the next loop!! for (int weight = 0; weight < sliceNumberPerEdge; weight++) { const Vector2& slicedPenumbra = (currentPenumbra * (sliceNumberPerEdge - weight) + nextPenumbra * weight) / sliceNumberPerEdge; const Vector2& slicedUmbra = (currentUmbra * (sliceNumberPerEdge - weight) + nextUmbra * weight) / sliceNumberPerEdge; // In the vertex buffer, we fill the Penumbra first, then umbra. indexBuffer[indexBufferIndex++] = vertexBufferIndex; AlphaVertex::set(&shadowVertices[vertexBufferIndex++], slicedPenumbra.x, slicedPenumbra.y, 0.0f); // When we add umbra vertex, we need to remember its current ray number. // And its own vertexBufferIndex. This is for occluded umbra usage. indexBuffer[indexBufferIndex++] = vertexBufferIndex; rayNumberPerSlicedUmbra[realUmbraVertexCount] = i; slicedUmbraVertexIndex[realUmbraVertexCount] = vertexBufferIndex; realUmbraVertexCount++; AlphaVertex::set(&shadowVertices[vertexBufferIndex++], slicedUmbra.x, slicedUmbra.y, M_PI); } } indexBuffer[indexBufferIndex++] = 0; //RealUmbraVertexIndex[0] must be 1, so we connect back well at the //beginning of occluded area. indexBuffer[indexBufferIndex++] = 1; float occludedUmbraAlpha = M_PI; if (hasOccludedUmbraArea) { // Now the occludedUmbra area; int currentRayNumber = -1; int firstOccludedUmbraIndex = -1; for (int i = 0; i < realUmbraVertexCount; i++) { indexBuffer[indexBufferIndex++] = slicedUmbraVertexIndex[i]; // If the occludedUmbra vertex has not been added yet, then add it. // Otherwise, just use the previously added occludedUmbra vertices. if (rayNumberPerSlicedUmbra[i] != currentRayNumber) { currentRayNumber++; indexBuffer[indexBufferIndex++] = vertexBufferIndex; // We need to remember the begining of the occludedUmbra vertices // to close this loop. if (currentRayNumber == 0) { firstOccludedUmbraIndex = vertexBufferIndex; } AlphaVertex::set(&shadowVertices[vertexBufferIndex++], occludedUmbraVertices[currentRayNumber].x, occludedUmbraVertices[currentRayNumber].y, occludedUmbraAlpha); } else { indexBuffer[indexBufferIndex++] = (vertexBufferIndex - 1); } } // Close the loop here! indexBuffer[indexBufferIndex++] = slicedUmbraVertexIndex[0]; indexBuffer[indexBufferIndex++] = firstOccludedUmbraIndex; } else { int lastCentroidIndex = vertexBufferIndex; AlphaVertex::set(&shadowVertices[vertexBufferIndex++], centroid.x, centroid.y, occludedUmbraAlpha); for (int i = 0; i < realUmbraVertexCount; i++) { indexBuffer[indexBufferIndex++] = slicedUmbraVertexIndex[i]; indexBuffer[indexBufferIndex++] = lastCentroidIndex; } // Close the loop here! indexBuffer[indexBufferIndex++] = slicedUmbraVertexIndex[0]; indexBuffer[indexBufferIndex++] = lastCentroidIndex; } #if DEBUG_SHADOW ALOGD("allocated IB %d allocated VB is %d", totalIndexCount, totalVertexCount); ALOGD("IB index %d VB index is %d", indexBufferIndex, vertexBufferIndex); for (int i = 0; i < vertexBufferIndex; i++) { ALOGD("vertexBuffer i %d, (%f, %f %f)", i, shadowVertices[i].x, shadowVertices[i].y, shadowVertices[i].alpha); } for (int i = 0; i < indexBufferIndex; i++) { ALOGD("indexBuffer i %d, indexBuffer[i] %d", i, indexBuffer[i]); } #endif // At the end, update the real index and vertex buffer size. shadowTriangleStrip.updateVertexCount(vertexBufferIndex); shadowTriangleStrip.updateIndexCount(indexBufferIndex); ShadowTessellator::checkOverflow(vertexBufferIndex, totalVertexCount, "Spot Vertex Buffer"); ShadowTessellator::checkOverflow(indexBufferIndex, totalIndexCount, "Spot Index Buffer"); shadowTriangleStrip.setMode(VertexBuffer::kIndices); shadowTriangleStrip.computeBounds(); } #if DEBUG_SHADOW #define TEST_POINT_NUMBER 128 /** * Calculate the bounds for generating random test points. */ void SpotShadow::updateBound(const Vector2 inVector, Vector2& lowerBound, Vector2& upperBound) { if (inVector.x < lowerBound.x) { lowerBound.x = inVector.x; } if (inVector.y < lowerBound.y) { lowerBound.y = inVector.y; } if (inVector.x > upperBound.x) { upperBound.x = inVector.x; } if (inVector.y > upperBound.y) { upperBound.y = inVector.y; } } /** * For debug purpose, when things go wrong, dump the whole polygon data. */ void SpotShadow::dumpPolygon(const Vector2* poly, int polyLength, const char* polyName) { for (int i = 0; i < polyLength; i++) { ALOGD("polygon %s i %d x %f y %f", polyName, i, poly[i].x, poly[i].y); } } /** * For debug purpose, when things go wrong, dump the whole polygon data. */ void SpotShadow::dumpPolygon(const Vector3* poly, int polyLength, const char* polyName) { for (int i = 0; i < polyLength; i++) { ALOGD("polygon %s i %d x %f y %f", polyName, i, poly[i].x, poly[i].y); } } /** * Test whether the polygon is convex. */ bool SpotShadow::testConvex(const Vector2* polygon, int polygonLength, const char* name) { bool isConvex = true; for (int i = 0; i < polygonLength; i++) { Vector2 start = polygon[i]; Vector2 middle = polygon[(i + 1) % polygonLength]; Vector2 end = polygon[(i + 2) % polygonLength]; double delta = (double(middle.x) - start.x) * (double(end.y) - start.y) - (double(middle.y) - start.y) * (double(end.x) - start.x); bool isCCWOrCoLinear = (delta >= EPSILON); if (isCCWOrCoLinear) { ALOGW("(Error Type 2): polygon (%s) is not a convex b/c start (x %f, y %f)," "middle (x %f, y %f) and end (x %f, y %f) , delta is %f !!!", name, start.x, start.y, middle.x, middle.y, end.x, end.y, delta); isConvex = false; break; } } return isConvex; } /** * Test whether or not the polygon (intersection) is within the 2 input polygons. * Using Marte Carlo method, we generate a random point, and if it is inside the * intersection, then it must be inside both source polygons. */ void SpotShadow::testIntersection(const Vector2* poly1, int poly1Length, const Vector2* poly2, int poly2Length, const Vector2* intersection, int intersectionLength) { // Find the min and max of x and y. Vector2 lowerBound = {FLT_MAX, FLT_MAX}; Vector2 upperBound = {-FLT_MAX, -FLT_MAX}; for (int i = 0; i < poly1Length; i++) { updateBound(poly1[i], lowerBound, upperBound); } for (int i = 0; i < poly2Length; i++) { updateBound(poly2[i], lowerBound, upperBound); } bool dumpPoly = false; for (int k = 0; k < TEST_POINT_NUMBER; k++) { // Generate a random point between minX, minY and maxX, maxY. double randomX = rand() / double(RAND_MAX); double randomY = rand() / double(RAND_MAX); Vector2 testPoint; testPoint.x = lowerBound.x + randomX * (upperBound.x - lowerBound.x); testPoint.y = lowerBound.y + randomY * (upperBound.y - lowerBound.y); // If the random point is in both poly 1 and 2, then it must be intersection. if (testPointInsidePolygon(testPoint, intersection, intersectionLength)) { if (!testPointInsidePolygon(testPoint, poly1, poly1Length)) { dumpPoly = true; ALOGW("(Error Type 1): one point (%f, %f) in the intersection is" " not in the poly1", testPoint.x, testPoint.y); } if (!testPointInsidePolygon(testPoint, poly2, poly2Length)) { dumpPoly = true; ALOGW("(Error Type 1): one point (%f, %f) in the intersection is" " not in the poly2", testPoint.x, testPoint.y); } } } if (dumpPoly) { dumpPolygon(intersection, intersectionLength, "intersection"); for (int i = 1; i < intersectionLength; i++) { Vector2 delta = intersection[i] - intersection[i - 1]; ALOGD("Intersetion i, %d Vs i-1 is delta %f", i, delta.lengthSquared()); } dumpPolygon(poly1, poly1Length, "poly 1"); dumpPolygon(poly2, poly2Length, "poly 2"); } } #endif }; // namespace uirenderer }; // namespace android