/*
* 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.
*/
// 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)
#define PENUMBRA_ALPHA 0.0f
#define UMBRA_ALPHA 1.0f
#include "SpotShadow.h"
#include "ShadowTessellator.h"
#include "Vertex.h"
#include "VertexBuffer.h"
#include "utils/MathUtils.h"
#include <algorithm>
#include <math.h>
#include <stdlib.h>
#include <utils/Log.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 float 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]);
float divisor = (dx * (p1.y - p2.y) + dy * p2.x - dy * p1.x);
if (divisor == 0) return -1.0f; // error, invalid divisor
#if DEBUG_SHADOW
float 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
float 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) {
auto cmp = [](const Vector2& a, const Vector2& b) -> bool {
return a.x < b.x;
};
std::sort(points, points + pointsLength, cmp);
}
/**
* 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(float ax, float ay, float bx, float by,
float cx, float cy) {
return (bx - ax) * (cy - ay) - (by - ay) * (cx - ax) > EPSILON;
}
/**
* 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);
}
/**
* 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;
float testx = testPoint.x;
float testy = testPoint.y;
for (int i = 0, j = len - 1; i < len; j = i++) {
float startX = poly[j].x;
float startY = poly[j].y;
float endX = poly[i].x;
float 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 == nullptr || 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;
}
}
/**
* 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++) {
float 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 = std::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);
}
/**
* 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;
}
}
}
// Index pair is meant for storing the tessellation information for the penumbra
// area. One index must come from exterior tangent of the circles, the other one
// must come from the interior tangent of the circles.
struct IndexPair {
int outerIndex;
int innerIndex;
};
// For one penumbra vertex, find the cloest umbra vertex and return its index.
inline int getClosestUmbraIndex(const Vector2& pivot, const Vector2* polygon, int polygonLength) {
float minLengthSquared = FLT_MAX;
int resultIndex = -1;
bool hasDecreased = false;
// Starting with some negative offset, assuming both umbra and penumbra are starting
// at the same angle, this can help to find the result faster.
// Normally, loop 3 times, we can find the closest point.
int offset = polygonLength - 2;
for (int i = 0; i < polygonLength; i++) {
int currentIndex = (i + offset) % polygonLength;
float currentLengthSquared = (pivot - polygon[currentIndex]).lengthSquared();
if (currentLengthSquared < minLengthSquared) {
if (minLengthSquared != FLT_MAX) {
hasDecreased = true;
}
minLengthSquared = currentLengthSquared;
resultIndex = currentIndex;
} else if (currentLengthSquared > minLengthSquared && hasDecreased) {
// Early break b/c we have found the closet one and now the length
// is increasing again.
break;
}
}
if(resultIndex == -1) {
ALOGE("resultIndex is -1, the polygon must be invalid!");
resultIndex = 0;
}
return resultIndex;
}
// Allow some epsilon here since the later ray intersection did allow for some small
// floating point error, when the intersection point is slightly outside the segment.
inline bool sameDirections(bool isPositiveCross, float a, float b) {
if (isPositiveCross) {
return a >= -EPSILON && b >= -EPSILON;
} else {
return a <= EPSILON && b <= EPSILON;
}
}
// Find the right polygon edge to shoot the ray at.
inline int findPolyIndex(bool isPositiveCross, int startPolyIndex, const Vector2& umbraDir,
const Vector2* polyToCentroid, int polyLength) {
// Make sure we loop with a bound.
for (int i = 0; i < polyLength; i++) {
int currentIndex = (i + startPolyIndex) % polyLength;
const Vector2& currentToCentroid = polyToCentroid[currentIndex];
const Vector2& nextToCentroid = polyToCentroid[(currentIndex + 1) % polyLength];
float currentCrossUmbra = currentToCentroid.cross(umbraDir);
float umbraCrossNext = umbraDir.cross(nextToCentroid);
if (sameDirections(isPositiveCross, currentCrossUmbra, umbraCrossNext)) {
#if DEBUG_SHADOW
ALOGD("findPolyIndex loop %d times , index %d", i, currentIndex );
#endif
return currentIndex;
}
}
LOG_ALWAYS_FATAL("Can't find the right polygon's edge from startPolyIndex %d", startPolyIndex);
return -1;
}
// Generate the index pair for penumbra / umbra vertices, and more penumbra vertices
// if needed.
inline void genNewPenumbraAndPairWithUmbra(const Vector2* penumbra, int penumbraLength,
const Vector2* umbra, int umbraLength, Vector2* newPenumbra, int& newPenumbraIndex,
IndexPair* verticesPair, int& verticesPairIndex) {
// In order to keep everything in just one loop, we need to pre-compute the
// closest umbra vertex for the last penumbra vertex.
int previousClosestUmbraIndex = getClosestUmbraIndex(penumbra[penumbraLength - 1],
umbra, umbraLength);
for (int i = 0; i < penumbraLength; i++) {
const Vector2& currentPenumbraVertex = penumbra[i];
// For current penumbra vertex, starting from previousClosestUmbraIndex,
// then check the next one until the distance increase.
// The last one before the increase is the umbra vertex we need to pair with.
float currentLengthSquared =
(currentPenumbraVertex - umbra[previousClosestUmbraIndex]).lengthSquared();
int currentClosestUmbraIndex = previousClosestUmbraIndex;
int indexDelta = 0;
for (int j = 1; j < umbraLength; j++) {
int newUmbraIndex = (previousClosestUmbraIndex + j) % umbraLength;
float newLengthSquared = (currentPenumbraVertex - umbra[newUmbraIndex]).lengthSquared();
if (newLengthSquared > currentLengthSquared) {
// currentClosestUmbraIndex is the umbra vertex's index which has
// currently found smallest distance, so we can simply break here.
break;
} else {
currentLengthSquared = newLengthSquared;
indexDelta++;
currentClosestUmbraIndex = newUmbraIndex;
}
}
if (indexDelta > 1) {
// For those umbra don't have penumbra, generate new penumbra vertices by interpolation.
//
// Assuming Pi for penumbra vertices, and Ui for umbra vertices.
// In the case like below P1 paired with U1 and P2 paired with U5.
// U2 to U4 are unpaired umbra vertices.
//
// P1 P2
// | |
// U1 U2 U3 U4 U5
//
// We will need to generate 3 more penumbra vertices P1.1, P1.2, P1.3
// to pair with U2 to U4.
//
// P1 P1.1 P1.2 P1.3 P2
// | | | | |
// U1 U2 U3 U4 U5
//
// That distance ratio b/t Ui to U1 and Ui to U5 decides its paired penumbra
// vertex's location.
int newPenumbraNumber = indexDelta - 1;
float accumulatedDeltaLength[indexDelta];
float totalDeltaLength = 0;
// To save time, cache the previous umbra vertex info outside the loop
// and update each loop.
Vector2 previousClosestUmbra = umbra[previousClosestUmbraIndex];
Vector2 skippedUmbra;
// Use umbra data to precompute the length b/t unpaired umbra vertices,
// and its ratio against the total length.
for (int k = 0; k < indexDelta; k++) {
int skippedUmbraIndex = (previousClosestUmbraIndex + k + 1) % umbraLength;
skippedUmbra = umbra[skippedUmbraIndex];
float currentDeltaLength = (skippedUmbra - previousClosestUmbra).length();
totalDeltaLength += currentDeltaLength;
accumulatedDeltaLength[k] = totalDeltaLength;
previousClosestUmbra = skippedUmbra;
}
const Vector2& previousPenumbra = penumbra[(i + penumbraLength - 1) % penumbraLength];
// Then for each unpaired umbra vertex, create a new penumbra by the ratio,
// and pair them togehter.
for (int k = 0; k < newPenumbraNumber; k++) {
float weightForCurrentPenumbra = 1.0f;
if (totalDeltaLength != 0.0f) {
weightForCurrentPenumbra = accumulatedDeltaLength[k] / totalDeltaLength;
}
float weightForPreviousPenumbra = 1.0f - weightForCurrentPenumbra;
Vector2 interpolatedPenumbra = currentPenumbraVertex * weightForCurrentPenumbra +
previousPenumbra * weightForPreviousPenumbra;
int skippedUmbraIndex = (previousClosestUmbraIndex + k + 1) % umbraLength;
verticesPair[verticesPairIndex].outerIndex = newPenumbraIndex;
verticesPair[verticesPairIndex].innerIndex = skippedUmbraIndex;
verticesPairIndex++;
newPenumbra[newPenumbraIndex++] = interpolatedPenumbra;
}
}
verticesPair[verticesPairIndex].outerIndex = newPenumbraIndex;
verticesPair[verticesPairIndex].innerIndex = currentClosestUmbraIndex;
verticesPairIndex++;
newPenumbra[newPenumbraIndex++] = currentPenumbraVertex;
previousClosestUmbraIndex = currentClosestUmbraIndex;
}
}
// Precompute all the polygon's vector, return true if the reference cross product is positive.
inline bool genPolyToCentroid(const Vector2* poly2d, int polyLength,
const Vector2& centroid, Vector2* polyToCentroid) {
for (int j = 0; j < polyLength; j++) {
polyToCentroid[j] = poly2d[j] - centroid;
// Normalize these vectors such that we can use epsilon comparison after
// computing their cross products with another normalized vector.
polyToCentroid[j].normalize();
}
float refCrossProduct = 0;
for (int j = 0; j < polyLength; j++) {
refCrossProduct = polyToCentroid[j].cross(polyToCentroid[(j + 1) % polyLength]);
if (refCrossProduct != 0) {
break;
}
}
return refCrossProduct > 0;
}
// For one umbra vertex, shoot an ray from centroid to it.
// If the ray hit the polygon first, then return the intersection point as the
// closer vertex.
inline Vector2 getCloserVertex(const Vector2& umbraVertex, const Vector2& centroid,
const Vector2* poly2d, int polyLength, const Vector2* polyToCentroid,
bool isPositiveCross, int& previousPolyIndex) {
Vector2 umbraToCentroid = umbraVertex - centroid;
float distanceToUmbra = umbraToCentroid.length();
umbraToCentroid = umbraToCentroid / distanceToUmbra;
// previousPolyIndex is updated for each item such that we can minimize the
// looping inside findPolyIndex();
previousPolyIndex = findPolyIndex(isPositiveCross, previousPolyIndex,
umbraToCentroid, polyToCentroid, polyLength);
float dx = umbraToCentroid.x;
float dy = umbraToCentroid.y;
float distanceToIntersectPoly = rayIntersectPoints(centroid, dx, dy,
poly2d[previousPolyIndex], poly2d[(previousPolyIndex + 1) % polyLength]);
if (distanceToIntersectPoly < 0) {
distanceToIntersectPoly = 0;
}
// Pick the closer one as the occluded area vertex.
Vector2 closerVertex;
if (distanceToIntersectPoly < distanceToUmbra) {
closerVertex.x = centroid.x + dx * distanceToIntersectPoly;
closerVertex.y = centroid.y + dy * distanceToIntersectPoly;
} else {
closerVertex = umbraVertex;
}
return closerVertex;
}
/**
* 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;
}
}
// For each penumbra vertex, find its corresponding closest umbra vertex index.
//
// Penumbra Vertices marked as Pi
// Umbra Vertices marked as Ui
// (P3)
// (P2) | ' (P4)
// (P1)' | | '
// ' | | '
// (P0) ------------------------------------------------(P5)
// | (U0) |(U1)
// | |
// | |(U2) (P5.1)
// | |
// | |
// | |
// | |
// | |
// | |
// (U4)-----------------------------------(U3) (P6)
//
// At least, like P0, P1, P2, they will find the matching umbra as U0.
// If we jump over some umbra vertex without matching penumbra vertex, then
// we will generate some new penumbra vertex by interpolation. Like P6 is
// matching U3, but U2 is not matched with any penumbra vertex.
// So interpolate P5.1 out and match U2.
// In this way, every umbra vertex will have a matching penumbra vertex.
//
// The total pair number can be as high as umbraLength + penumbraLength.
const int maxNewPenumbraLength = umbraLength + penumbraLength;
IndexPair verticesPair[maxNewPenumbraLength];
int verticesPairIndex = 0;
// Cache all the existing penumbra vertices and newly interpolated vertices into a
// a new array.
Vector2 newPenumbra[maxNewPenumbraLength];
int newPenumbraIndex = 0;
// For each penumbra vertex, find its closet umbra vertex by comparing the
// neighbor umbra vertices.
genNewPenumbraAndPairWithUmbra(penumbra, penumbraLength, umbra, umbraLength, newPenumbra,
newPenumbraIndex, verticesPair, verticesPairIndex);
ShadowTessellator::checkOverflow(verticesPairIndex, maxNewPenumbraLength, "Spot pair");
ShadowTessellator::checkOverflow(newPenumbraIndex, maxNewPenumbraLength, "Spot new penumbra");
#if DEBUG_SHADOW
for (int i = 0; i < umbraLength; i++) {
ALOGD("umbra i %d, [%f, %f]", i, umbra[i].x, umbra[i].y);
}
for (int i = 0; i < newPenumbraIndex; i++) {
ALOGD("new penumbra i %d, [%f, %f]", i, newPenumbra[i].x, newPenumbra[i].y);
}
for (int i = 0; i < verticesPairIndex; i++) {
ALOGD("index i %d, [%d, %d]", i, verticesPair[i].outerIndex, verticesPair[i].innerIndex);
}
#endif
// For the size of vertex buffer, we need 3 rings, one has newPenumbraSize,
// one has umbraLength, the last one has at most umbraLength.
//
// For the size of index buffer, the umbra area needs (2 * umbraLength + 2).
// The penumbra one can vary a bit, but it is bounded by (2 * verticesPairIndex + 2).
// And 2 more for jumping between penumbra to umbra.
const int newPenumbraLength = newPenumbraIndex;
const int totalVertexCount = newPenumbraLength + umbraLength * 2;
const int totalIndexCount = 2 * umbraLength + 2 * verticesPairIndex + 6;
AlphaVertex* shadowVertices =
shadowTriangleStrip.alloc<AlphaVertex>(totalVertexCount);
uint16_t* indexBuffer =
shadowTriangleStrip.allocIndices<uint16_t>(totalIndexCount);
int vertexBufferIndex = 0;
int indexBufferIndex = 0;
// Fill the IB and VB for the penumbra area.
for (int i = 0; i < newPenumbraLength; i++) {
AlphaVertex::set(&shadowVertices[vertexBufferIndex++], newPenumbra[i].x,
newPenumbra[i].y, PENUMBRA_ALPHA);
}
// Since the umbra can be a faked one when the occluder is too high, the umbra should be lighter
// in this case.
float scaledUmbraAlpha = UMBRA_ALPHA * shadowStrengthScale;
for (int i = 0; i < umbraLength; i++) {
AlphaVertex::set(&shadowVertices[vertexBufferIndex++], umbra[i].x, umbra[i].y,
scaledUmbraAlpha);
}
for (int i = 0; i < verticesPairIndex; i++) {
indexBuffer[indexBufferIndex++] = verticesPair[i].outerIndex;
// All umbra index need to be offseted by newPenumbraSize.
indexBuffer[indexBufferIndex++] = verticesPair[i].innerIndex + newPenumbraLength;
}
indexBuffer[indexBufferIndex++] = verticesPair[0].outerIndex;
indexBuffer[indexBufferIndex++] = verticesPair[0].innerIndex + newPenumbraLength;
// Now fill the IB and VB for the umbra area.
// First duplicated the index from previous strip and the first one for the
// degenerated triangles.
indexBuffer[indexBufferIndex] = indexBuffer[indexBufferIndex - 1];
indexBufferIndex++;
indexBuffer[indexBufferIndex++] = newPenumbraLength + 0;
// Save the first VB index for umbra area in order to close the loop.
int savedStartIndex = vertexBufferIndex;
if (hasOccludedUmbraArea) {
// Precompute all the polygon's vector, and the reference cross product,
// in order to find the right polygon edge for the ray to intersect.
Vector2 polyToCentroid[polyLength];
bool isPositiveCross = genPolyToCentroid(poly2d, polyLength, centroid, polyToCentroid);
// Because both the umbra and polygon are going in the same direction,
// we can save the previous polygon index to make sure we have less polygon
// vertex to compute for each ray.
int previousPolyIndex = 0;
for (int i = 0; i < umbraLength; i++) {
// Shoot a ray from centroid to each umbra vertices and pick the one with
// shorter distance to the centroid, b/t the umbra vertex or the intersection point.
Vector2 closerVertex = getCloserVertex(umbra[i], centroid, poly2d, polyLength,
polyToCentroid, isPositiveCross, previousPolyIndex);
// We already stored the umbra vertices, just need to add the occlued umbra's ones.
indexBuffer[indexBufferIndex++] = newPenumbraLength + i;
indexBuffer[indexBufferIndex++] = vertexBufferIndex;
AlphaVertex::set(&shadowVertices[vertexBufferIndex++],
closerVertex.x, closerVertex.y, scaledUmbraAlpha);
}
} else {
// If there is no occluded umbra at all, then draw the triangle fan
// starting from the centroid to all umbra vertices.
int lastCentroidIndex = vertexBufferIndex;
AlphaVertex::set(&shadowVertices[vertexBufferIndex++], centroid.x,
centroid.y, scaledUmbraAlpha);
for (int i = 0; i < umbraLength; i++) {
indexBuffer[indexBufferIndex++] = newPenumbraLength + i;
indexBuffer[indexBufferIndex++] = lastCentroidIndex;
}
}
// Closing the umbra area triangle's loop here.
indexBuffer[indexBufferIndex++] = newPenumbraLength;
indexBuffer[indexBufferIndex++] = savedStartIndex;
// 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.setMeshFeatureFlags(VertexBuffer::kAlpha | VertexBuffer::kIndices);
shadowTriangleStrip.computeBounds<AlphaVertex>();
}
#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 z %f", polyName, i, poly[i].x, poly[i].y, poly[i].z);
}
}
/**
* 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];
float delta = (float(middle.x) - start.x) * (float(end.y) - start.y) -
(float(middle.y) - start.y) * (float(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.
float randomX = rand() / float(RAND_MAX);
float randomY = rand() / float(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