libs/hwui/AmbientShadow.cpp - platform/frameworks/base - Gitiles

 /*
  * Copyright (C) 2013 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"

 /**
  * Extra vertices for the corner for smoother corner.
  * Only for outer vertices.
  * 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 EXTRA_CORNER_VERTEX_PER_PI 12

 // 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 MAX_EXTRA_CORNER_VERTEX_NUMBER  (2 * EXTRA_CORNER_VERTEX_PER_PI)

 // For each RADIANS_DIVISOR, we would allocate one more vertex b/t the normals.
 #define CORNER_RADIANS_DIVISOR (M_PI / EXTRA_CORNER_VERTEX_PER_PI)

 /**
  * Extra vertices for the Edge for interpolation artifacts.
  * Same value for both inner and outer vertices.
  */
 #define EXTRA_EDGE_VERTEX_PER_PI 50

 #define MAX_EXTRA_EDGE_VERTEX_NUMBER  (2 * EXTRA_EDGE_VERTEX_PER_PI)

 #define EDGE_RADIANS_DIVISOR  (M_PI / EXTRA_EDGE_VERTEX_PER_PI)

 /**
  * Other constants:
  */
 // For the edge of the penumbra, the opacity is 0.
 #define OUTER_OPACITY (0.0f)

 // Once the alpha difference is greater than this threshold, we will allocate extra
 // edge vertices.
 // If this is set to negative value, then all the edge will be tessellated.
 #define ALPHA_THRESHOLD (0.1f / 255.0f)

 #include <math.h>
 #include <utils/Log.h>
 #include <utils/Vector.h>

 #include "AmbientShadow.h"
 #include "ShadowTessellator.h"
 #include "Vertex.h"
 #include "utils/MathUtils.h"

 namespace android {
 namespace uirenderer {

 /**
  *  Local utility functions.
  */
 inline Vector2 getNormalFromVertices(const Vector3* vertices, int current, int next) {
     // Convert from Vector3 to Vector2 first.
     Vector2 currentVertex = { vertices[current].x, vertices[current].y };
     Vector2 nextVertex = { vertices[next].x, vertices[next].y };

     return ShadowTessellator::calculateNormal(currentVertex, nextVertex);
 }

 // The input z value will be converted to be non-negative inside.
 // The output must be ranged from 0 to 1.
 inline float getAlphaFromFactoredZ(float factoredZ) {
     return 1.0 / (1 + MathUtils::max(factoredZ, 0.0f));
 }

 inline float getTransformedAlphaFromAlpha(float alpha) {
     return acosf(1.0f - 2.0f * alpha);
 }

 // The output is ranged from 0 to M_PI.
 inline float getTransformedAlphaFromFactoredZ(float factoredZ) {
     return getTransformedAlphaFromAlpha(getAlphaFromFactoredZ(factoredZ));
 }

 inline int getExtraVertexNumber(const Vector2& vector1, const Vector2& vector2,
         float divisor) {
     // When there is no distance difference, there is no need for extra vertices.
     if (vector1.lengthSquared() == 0 || vector2.lengthSquared() == 0) {
         return 0;
     }
     // The formula is :
     // extraNumber = floor(acos(dot(n1, n2)) / (M_PI / EXTRA_VERTEX_PER_PI))
     // The value ranges for each step are:
     // dot( ) --- [-1, 1]
     // acos( )     --- [0, M_PI]
     // floor(...)  --- [0, EXTRA_VERTEX_PER_PI]
     float dotProduct = vector1.dot(vector2);
     // TODO: Use look up table for the dotProduct to extraVerticesNumber
     // computation, if needed.
     float angle = acosf(dotProduct);
     return (int) floor(angle / divisor);
 }

 inline void checkOverflow(int used, int total, const char* bufferName) {
     LOG_ALWAYS_FATAL_IF(used > total, "Error: %s overflow!!! used %d, total %d",
             bufferName, used, total);
 }

 inline int getEdgeExtraAndUpdateSpike(Vector2* currentSpike,
         const Vector3& secondVertex, const Vector3& centroid) {
     Vector2 secondSpike  = {secondVertex.x - centroid.x, secondVertex.y - centroid.y};
     secondSpike.normalize();

     int result = getExtraVertexNumber(secondSpike, *currentSpike, EDGE_RADIANS_DIVISOR);
     *currentSpike = secondSpike;
     return result;
 }

 // Given the caster's vertex count, compute all the buffers size depending on
 // whether or not the caster is opaque.
 inline void computeBufferSize(int* totalVertexCount, int* totalIndexCount,
         int* totalUmbraCount, int casterVertexCount, bool isCasterOpaque) {
     // Compute the size of the vertex buffer.
     int outerVertexCount = casterVertexCount * 2 + MAX_EXTRA_CORNER_VERTEX_NUMBER +
         MAX_EXTRA_EDGE_VERTEX_NUMBER;
     int innerVertexCount = casterVertexCount + MAX_EXTRA_EDGE_VERTEX_NUMBER;
     *totalVertexCount = outerVertexCount + innerVertexCount;

     // Compute the size of the index buffer.
     *totalIndexCount = 2 * outerVertexCount + 2;

     // Compute the size of the umber buffer.
     // For translucent object, keep track of the umbra(inner) vertex in order to draw
     // inside. We only need to store the index information.
     *totalUmbraCount = 0;
     if (!isCasterOpaque) {
         // Add the centroid if occluder is translucent.
         *totalVertexCount++;
         *totalIndexCount += 2 * innerVertexCount + 1;
         *totalUmbraCount = innerVertexCount;
     }
 }

 inline bool needsExtraForEdge(float firstAlpha, float secondAlpha) {
     return abs(firstAlpha - secondAlpha) > ALPHA_THRESHOLD;
 }

 /**
  * Calculate the shadows as a triangle strips while alpha value as the
  * shadow values.
  *
  * @param isCasterOpaque Whether the caster is opaque.
  * @param vertices The shadow caster's polygon, which is represented in a Vector3
  *                  array.
  * @param vertexCount The length of caster's polygon in terms of number of
  *                    vertices.
  * @param centroid3d The centroid of the shadow caster.
  * @param heightFactor The factor showing the higher the object, the lighter the
  *                     shadow.
  * @param geomFactor The factor scaling the geometry expansion along the normal.
  *
  * @param shadowVertexBuffer Return an floating point array of (x, y, a)
  *               triangle strips mode.
  *
  * An simple illustration:
  * For now let's mark the outer vertex as Pi, the inner as Vi, the centroid as C.
  *
  * First project the occluder to the Z=0 surface.
  * Then we got all the inner vertices. And we compute the normal for each edge.
  * According to the normal, we generate outer vertices. E.g: We generate P1 / P4
  * as extra corner vertices to make the corner looks round and smoother.
  *
  * Due to the fact that the alpha is not linear interpolated along the inner
  * edge, when the alpha is different, we may add extra vertices such as P2.1, P2.2,
  * V0.1, V0.2 to avoid the visual artifacts.
  *
  *                                            (P3)
  *          (P2)     (P2.1)     (P2.2)         |     ' (P4)
  *   (P1)'   |        |           |            |   '
  *         ' |        |           |            | '
  * (P0)  ------------------------------------------------(P5)
  *           | (V0)   (V0.1)    (V0.2)         |(V1)
  *           |                                 |
  *           |                                 |
  *           |               (C)               |
  *           |                                 |
  *           |                                 |
  *           |                                 |
  *           |                                 |
  *        (V3)-----------------------------------(V2)
  */
 void AmbientShadow::createAmbientShadow(bool isCasterOpaque,
         const Vector3* casterVertices, int casterVertexCount, const Vector3& centroid3d,
         float heightFactor, float geomFactor, VertexBuffer& shadowVertexBuffer) {
     shadowVertexBuffer.setMode(VertexBuffer::kIndices);

     // In order to computer the outer vertices in one loop, we need pre-compute
     // the normal by the vertex (n - 1) to vertex 0, and the spike and alpha value
     // for vertex 0.
     Vector2 previousNormal = getNormalFromVertices(casterVertices,
             casterVertexCount - 1 , 0);
     Vector2 currentSpike = {casterVertices[0].x - centroid3d.x,
         casterVertices[0].y - centroid3d.y};
     currentSpike.normalize();
     float currentAlpha = getAlphaFromFactoredZ(casterVertices[0].z * heightFactor);

     // Preparing all the output data.
     int totalVertexCount, totalIndexCount, totalUmbraCount;
     computeBufferSize(&totalVertexCount, &totalIndexCount, &totalUmbraCount,
             casterVertexCount, isCasterOpaque);
     AlphaVertex* shadowVertices =
             shadowVertexBuffer.alloc<AlphaVertex>(totalVertexCount);
     int vertexBufferIndex = 0;
     uint16_t* indexBuffer = shadowVertexBuffer.allocIndices<uint16_t>(totalIndexCount);
     int indexBufferIndex = 0;
     uint16_t umbraVertices[totalUmbraCount];
     int umbraIndex = 0;

     for (int i = 0; i < casterVertexCount; i++)  {
         // Corner: first figure out the extra vertices we need for the corner.
         const Vector3& innerVertex = casterVertices[i];
         Vector2 currentNormal = getNormalFromVertices(casterVertices, i,
                 (i + 1) % casterVertexCount);

         int extraVerticesNumber = getExtraVertexNumber(currentNormal, previousNormal,
                 CORNER_RADIANS_DIVISOR);

         float expansionDist = innerVertex.z * heightFactor * geomFactor;
         const int cornerSlicesNumber = extraVerticesNumber + 1; // Minimal as 1.
 #if DEBUG_SHADOW
         ALOGD("cornerSlicesNumber is %d", cornerSlicesNumber);
 #endif

         // Corner: fill the corner Vertex Buffer(VB) and Index Buffer(IB).
         // We fill the inner vertex first, such that we can fill the index buffer
         // inside the loop.
         int currentInnerVertexIndex = vertexBufferIndex;
         if (!isCasterOpaque) {
             umbraVertices[umbraIndex++] = vertexBufferIndex;
         }
         AlphaVertex::set(&shadowVertices[vertexBufferIndex++], casterVertices[i].x,
                 casterVertices[i].y,
                 getTransformedAlphaFromAlpha(currentAlpha));

         const Vector3& innerStart = casterVertices[i];

         // outerStart is the first outer vertex for this inner vertex.
         // outerLast is the last outer vertex for this inner vertex.
         Vector2 outerStart = {0, 0};
         Vector2 outerLast = {0, 0};
         // This will create vertices from [0, cornerSlicesNumber] inclusively,
         // which means minimally 2 vertices even without the extra ones.
         for (int j = 0; j <= cornerSlicesNumber; j++) {
             Vector2 averageNormal =
                 previousNormal * (cornerSlicesNumber - j) + currentNormal * j;
             averageNormal /= cornerSlicesNumber;
             averageNormal.normalize();
             Vector2 outerVertex;
             outerVertex.x = innerVertex.x + averageNormal.x * expansionDist;
             outerVertex.y = innerVertex.y + averageNormal.y * expansionDist;

             indexBuffer[indexBufferIndex++] = vertexBufferIndex;
             indexBuffer[indexBufferIndex++] = currentInnerVertexIndex;
             AlphaVertex::set(&shadowVertices[vertexBufferIndex++], outerVertex.x,
                     outerVertex.y, OUTER_OPACITY);

             if (j == 0) {
                 outerStart = outerVertex;
             } else if (j == cornerSlicesNumber) {
                 outerLast = outerVertex;
             }
         }
         previousNormal = currentNormal;

         // Edge: first figure out the extra vertices needed for the edge.
         const Vector3& innerNext = casterVertices[(i + 1) % casterVertexCount];
         float nextAlpha = getAlphaFromFactoredZ(innerNext.z * heightFactor);
         if (needsExtraForEdge(currentAlpha, nextAlpha)) {
             // TODO: See if we can / should cache this outer vertex across the loop.
             Vector2 outerNext;
             float expansionDist = innerNext.z * heightFactor * geomFactor;
             outerNext.x = innerNext.x + currentNormal.x * expansionDist;
             outerNext.y = innerNext.y + currentNormal.y * expansionDist;

             // Compute the angle and see how many extra points we need.
             int extraVerticesNumber = getEdgeExtraAndUpdateSpike(&currentSpike,
                     innerNext, centroid3d);
 #if DEBUG_SHADOW
             ALOGD("extraVerticesNumber %d for edge %d", extraVerticesNumber, i);
 #endif
             // Edge: fill the edge's VB and IB.
             // This will create vertices pair from [1, extraVerticesNumber - 1].
             // If there is no extra vertices created here, the edge will be drawn
             // as just 2 triangles.
             for (int k = 1; k < extraVerticesNumber; k++) {
                 int startWeight = extraVerticesNumber - k;
                 Vector2 currentOuter =
                     (outerLast * startWeight + outerNext * k) / extraVerticesNumber;
                 indexBuffer[indexBufferIndex++] = vertexBufferIndex;
                 AlphaVertex::set(&shadowVertices[vertexBufferIndex++], currentOuter.x,
                         currentOuter.y, OUTER_OPACITY);

                 if (!isCasterOpaque) {
                     umbraVertices[umbraIndex++] = vertexBufferIndex;
                 }
                 Vector3 currentInner =
                     (innerStart * startWeight + innerNext * k) / extraVerticesNumber;
                 indexBuffer[indexBufferIndex++] = vertexBufferIndex;
                 AlphaVertex::set(&shadowVertices[vertexBufferIndex++], currentInner.x,
                         currentInner.y,
                         getTransformedAlphaFromFactoredZ(currentInner.z * heightFactor));
             }
         }
         currentAlpha = nextAlpha;
     }

     indexBuffer[indexBufferIndex++] = 1;
     indexBuffer[indexBufferIndex++] = 0;

     if (!isCasterOpaque) {
         // Add the centroid as the last one in the vertex buffer.
         float centroidOpacity =
             getTransformedAlphaFromFactoredZ(centroid3d.z * heightFactor);
         int centroidIndex = vertexBufferIndex;
         AlphaVertex::set(&shadowVertices[vertexBufferIndex++], centroid3d.x,
                 centroid3d.y, centroidOpacity);

         for (int i = 0; i < umbraIndex; i++) {
             // Note that umbraVertices[0] is always 0.
             // So the start and the end of the umbra are using the "0".
             // And penumbra ended with 0, so a degenerated triangle is formed b/t
             // the umbra and penumbra.
             indexBuffer[indexBufferIndex++] = umbraVertices[i];
             indexBuffer[indexBufferIndex++] = centroidIndex;
         }
         indexBuffer[indexBufferIndex++] = 0;
     }

     // At the end, update the real index and vertex buffer size.
     shadowVertexBuffer.updateVertexCount(vertexBufferIndex);
     shadowVertexBuffer.updateIndexCount(indexBufferIndex);

     checkOverflow(vertexBufferIndex, totalVertexCount, "Vertex Buffer");
     checkOverflow(indexBufferIndex, totalIndexCount, "Index Buffer");
     checkOverflow(umbraIndex, totalUmbraCount, "Umbra Buffer");

 #if DEBUG_SHADOW
     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
 }

 }; // namespace uirenderer
 }; // namespace android
	/*
	* Copyright (C) 2013 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"

	/**
	* Extra vertices for the corner for smoother corner.
	* Only for outer vertices.
	* 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 EXTRA_CORNER_VERTEX_PER_PI 12

	// 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 MAX_EXTRA_CORNER_VERTEX_NUMBER (2 * EXTRA_CORNER_VERTEX_PER_PI)

	// For each RADIANS_DIVISOR, we would allocate one more vertex b/t the normals.
	#define CORNER_RADIANS_DIVISOR (M_PI / EXTRA_CORNER_VERTEX_PER_PI)

	/**
	* Extra vertices for the Edge for interpolation artifacts.
	* Same value for both inner and outer vertices.
	*/
	#define EXTRA_EDGE_VERTEX_PER_PI 50

	#define MAX_EXTRA_EDGE_VERTEX_NUMBER (2 * EXTRA_EDGE_VERTEX_PER_PI)

	#define EDGE_RADIANS_DIVISOR (M_PI / EXTRA_EDGE_VERTEX_PER_PI)

	/**
	* Other constants:
	*/
	// For the edge of the penumbra, the opacity is 0.
	#define OUTER_OPACITY (0.0f)

	// Once the alpha difference is greater than this threshold, we will allocate extra
	// edge vertices.
	// If this is set to negative value, then all the edge will be tessellated.
	#define ALPHA_THRESHOLD (0.1f / 255.0f)

	#include <math.h>
	#include <utils/Log.h>
	#include <utils/Vector.h>

	#include "AmbientShadow.h"
	#include "ShadowTessellator.h"
	#include "Vertex.h"
	#include "utils/MathUtils.h"

	namespace android {
	namespace uirenderer {

	/**
	* Local utility functions.
	*/
	inline Vector2 getNormalFromVertices(const Vector3* vertices, int current, int next) {
	// Convert from Vector3 to Vector2 first.
	Vector2 currentVertex = { vertices[current].x, vertices[current].y };
	Vector2 nextVertex = { vertices[next].x, vertices[next].y };

	return ShadowTessellator::calculateNormal(currentVertex, nextVertex);
	}

	// The input z value will be converted to be non-negative inside.
	// The output must be ranged from 0 to 1.
	inline float getAlphaFromFactoredZ(float factoredZ) {
	return 1.0 / (1 + MathUtils::max(factoredZ, 0.0f));
	}

	inline float getTransformedAlphaFromAlpha(float alpha) {
	return acosf(1.0f - 2.0f * alpha);
	}

	// The output is ranged from 0 to M_PI.
	inline float getTransformedAlphaFromFactoredZ(float factoredZ) {
	return getTransformedAlphaFromAlpha(getAlphaFromFactoredZ(factoredZ));
	}

	inline int getExtraVertexNumber(const Vector2& vector1, const Vector2& vector2,
	float divisor) {
	// When there is no distance difference, there is no need for extra vertices.
	if (vector1.lengthSquared() == 0 \|\| vector2.lengthSquared() == 0) {
	return 0;
	}
	// The formula is :
	// extraNumber = floor(acos(dot(n1, n2)) / (M_PI / EXTRA_VERTEX_PER_PI))
	// The value ranges for each step are:
	// dot( ) --- [-1, 1]
	// acos( ) --- [0, M_PI]
	// floor(...) --- [0, EXTRA_VERTEX_PER_PI]
	float dotProduct = vector1.dot(vector2);
	// TODO: Use look up table for the dotProduct to extraVerticesNumber
	// computation, if needed.
	float angle = acosf(dotProduct);
	return (int) floor(angle / divisor);
	}

	inline void checkOverflow(int used, int total, const char* bufferName) {
	LOG_ALWAYS_FATAL_IF(used > total, "Error: %s overflow!!! used %d, total %d",
	bufferName, used, total);
	}

	inline int getEdgeExtraAndUpdateSpike(Vector2* currentSpike,
	const Vector3& secondVertex, const Vector3& centroid) {
	Vector2 secondSpike = {secondVertex.x - centroid.x, secondVertex.y - centroid.y};
	secondSpike.normalize();

	int result = getExtraVertexNumber(secondSpike, *currentSpike, EDGE_RADIANS_DIVISOR);
	*currentSpike = secondSpike;
	return result;
	}

	// Given the caster's vertex count, compute all the buffers size depending on
	// whether or not the caster is opaque.
	inline void computeBufferSize(int* totalVertexCount, int* totalIndexCount,
	int* totalUmbraCount, int casterVertexCount, bool isCasterOpaque) {
	// Compute the size of the vertex buffer.
	int outerVertexCount = casterVertexCount * 2 + MAX_EXTRA_CORNER_VERTEX_NUMBER +
	MAX_EXTRA_EDGE_VERTEX_NUMBER;
	int innerVertexCount = casterVertexCount + MAX_EXTRA_EDGE_VERTEX_NUMBER;
	*totalVertexCount = outerVertexCount + innerVertexCount;

	// Compute the size of the index buffer.
	totalIndexCount = 2 outerVertexCount + 2;

	// Compute the size of the umber buffer.
	// For translucent object, keep track of the umbra(inner) vertex in order to draw
	// inside. We only need to store the index information.
	*totalUmbraCount = 0;
	if (!isCasterOpaque) {
	// Add the centroid if occluder is translucent.
	*totalVertexCount++;
	totalIndexCount += 2 innerVertexCount + 1;
	*totalUmbraCount = innerVertexCount;
	}
	}

	inline bool needsExtraForEdge(float firstAlpha, float secondAlpha) {
	return abs(firstAlpha - secondAlpha) > ALPHA_THRESHOLD;
	}

	/**
	* Calculate the shadows as a triangle strips while alpha value as the
	* shadow values.
	*
	* @param isCasterOpaque Whether the caster is opaque.
	* @param vertices The shadow caster's polygon, which is represented in a Vector3
	* array.
	* @param vertexCount The length of caster's polygon in terms of number of
	* vertices.
	* @param centroid3d The centroid of the shadow caster.
	* @param heightFactor The factor showing the higher the object, the lighter the
	* shadow.
	* @param geomFactor The factor scaling the geometry expansion along the normal.
	*
	* @param shadowVertexBuffer Return an floating point array of (x, y, a)
	* triangle strips mode.
	*
	* An simple illustration:
	* For now let's mark the outer vertex as Pi, the inner as Vi, the centroid as C.
	*
	* First project the occluder to the Z=0 surface.
	* Then we got all the inner vertices. And we compute the normal for each edge.
	* According to the normal, we generate outer vertices. E.g: We generate P1 / P4
	* as extra corner vertices to make the corner looks round and smoother.
	*
	* Due to the fact that the alpha is not linear interpolated along the inner
	* edge, when the alpha is different, we may add extra vertices such as P2.1, P2.2,
	* V0.1, V0.2 to avoid the visual artifacts.
	*
	* (P3)
	* (P2) (P2.1) (P2.2) \| ' (P4)
	* (P1)' \| \| \| \| '
	* ' \| \| \| \| '
	* (P0) ------------------------------------------------(P5)
	* \| (V0) (V0.1) (V0.2) \|(V1)
	* \| \|
	* \| \|
	* \| (C) \|
	* \| \|
	* \| \|
	* \| \|
	* \| \|
	* (V3)-----------------------------------(V2)
	*/
	void AmbientShadow::createAmbientShadow(bool isCasterOpaque,
	const Vector3* casterVertices, int casterVertexCount, const Vector3& centroid3d,
	float heightFactor, float geomFactor, VertexBuffer& shadowVertexBuffer) {
	shadowVertexBuffer.setMode(VertexBuffer::kIndices);

	// In order to computer the outer vertices in one loop, we need pre-compute
	// the normal by the vertex (n - 1) to vertex 0, and the spike and alpha value
	// for vertex 0.
	Vector2 previousNormal = getNormalFromVertices(casterVertices,
	casterVertexCount - 1 , 0);
	Vector2 currentSpike = {casterVertices[0].x - centroid3d.x,
	casterVertices[0].y - centroid3d.y};
	currentSpike.normalize();
	float currentAlpha = getAlphaFromFactoredZ(casterVertices[0].z * heightFactor);

	// Preparing all the output data.
	int totalVertexCount, totalIndexCount, totalUmbraCount;
	computeBufferSize(&totalVertexCount, &totalIndexCount, &totalUmbraCount,
	casterVertexCount, isCasterOpaque);
	AlphaVertex* shadowVertices =
	shadowVertexBuffer.alloc<AlphaVertex>(totalVertexCount);
	int vertexBufferIndex = 0;
	uint16_t* indexBuffer = shadowVertexBuffer.allocIndices<uint16_t>(totalIndexCount);
	int indexBufferIndex = 0;
	uint16_t umbraVertices[totalUmbraCount];
	int umbraIndex = 0;

	for (int i = 0; i < casterVertexCount; i++) {
	// Corner: first figure out the extra vertices we need for the corner.
	const Vector3& innerVertex = casterVertices[i];
	Vector2 currentNormal = getNormalFromVertices(casterVertices, i,
	(i + 1) % casterVertexCount);

	int extraVerticesNumber = getExtraVertexNumber(currentNormal, previousNormal,
	CORNER_RADIANS_DIVISOR);

	float expansionDist = innerVertex.z * heightFactor * geomFactor;
	const int cornerSlicesNumber = extraVerticesNumber + 1; // Minimal as 1.
	#if DEBUG_SHADOW
	ALOGD("cornerSlicesNumber is %d", cornerSlicesNumber);
	#endif

	// Corner: fill the corner Vertex Buffer(VB) and Index Buffer(IB).
	// We fill the inner vertex first, such that we can fill the index buffer
	// inside the loop.
	int currentInnerVertexIndex = vertexBufferIndex;
	if (!isCasterOpaque) {
	umbraVertices[umbraIndex++] = vertexBufferIndex;
	}
	AlphaVertex::set(&shadowVertices[vertexBufferIndex++], casterVertices[i].x,
	casterVertices[i].y,
	getTransformedAlphaFromAlpha(currentAlpha));

	const Vector3& innerStart = casterVertices[i];

	// outerStart is the first outer vertex for this inner vertex.
	// outerLast is the last outer vertex for this inner vertex.
	Vector2 outerStart = {0, 0};
	Vector2 outerLast = {0, 0};
	// This will create vertices from [0, cornerSlicesNumber] inclusively,
	// which means minimally 2 vertices even without the extra ones.
	for (int j = 0; j <= cornerSlicesNumber; j++) {
	Vector2 averageNormal =
	previousNormal * (cornerSlicesNumber - j) + currentNormal * j;
	averageNormal /= cornerSlicesNumber;
	averageNormal.normalize();
	Vector2 outerVertex;
	outerVertex.x = innerVertex.x + averageNormal.x * expansionDist;
	outerVertex.y = innerVertex.y + averageNormal.y * expansionDist;

	indexBuffer[indexBufferIndex++] = vertexBufferIndex;
	indexBuffer[indexBufferIndex++] = currentInnerVertexIndex;
	AlphaVertex::set(&shadowVertices[vertexBufferIndex++], outerVertex.x,
	outerVertex.y, OUTER_OPACITY);

	if (j == 0) {
	outerStart = outerVertex;
	} else if (j == cornerSlicesNumber) {
	outerLast = outerVertex;
	}
	}
	previousNormal = currentNormal;

	// Edge: first figure out the extra vertices needed for the edge.
	const Vector3& innerNext = casterVertices[(i + 1) % casterVertexCount];
	float nextAlpha = getAlphaFromFactoredZ(innerNext.z * heightFactor);
	if (needsExtraForEdge(currentAlpha, nextAlpha)) {
	// TODO: See if we can / should cache this outer vertex across the loop.
	Vector2 outerNext;
	float expansionDist = innerNext.z * heightFactor * geomFactor;
	outerNext.x = innerNext.x + currentNormal.x * expansionDist;
	outerNext.y = innerNext.y + currentNormal.y * expansionDist;

	// Compute the angle and see how many extra points we need.
	int extraVerticesNumber = getEdgeExtraAndUpdateSpike(&currentSpike,
	innerNext, centroid3d);
	#if DEBUG_SHADOW
	ALOGD("extraVerticesNumber %d for edge %d", extraVerticesNumber, i);
	#endif
	// Edge: fill the edge's VB and IB.
	// This will create vertices pair from [1, extraVerticesNumber - 1].
	// If there is no extra vertices created here, the edge will be drawn
	// as just 2 triangles.
	for (int k = 1; k < extraVerticesNumber; k++) {
	int startWeight = extraVerticesNumber - k;
	Vector2 currentOuter =
	(outerLast * startWeight + outerNext * k) / extraVerticesNumber;
	indexBuffer[indexBufferIndex++] = vertexBufferIndex;
	AlphaVertex::set(&shadowVertices[vertexBufferIndex++], currentOuter.x,
	currentOuter.y, OUTER_OPACITY);

	if (!isCasterOpaque) {
	umbraVertices[umbraIndex++] = vertexBufferIndex;
	}
	Vector3 currentInner =
	(innerStart * startWeight + innerNext * k) / extraVerticesNumber;
	indexBuffer[indexBufferIndex++] = vertexBufferIndex;
	AlphaVertex::set(&shadowVertices[vertexBufferIndex++], currentInner.x,
	currentInner.y,
	getTransformedAlphaFromFactoredZ(currentInner.z * heightFactor));
	}
	}
	currentAlpha = nextAlpha;
	}

	indexBuffer[indexBufferIndex++] = 1;
	indexBuffer[indexBufferIndex++] = 0;

	if (!isCasterOpaque) {
	// Add the centroid as the last one in the vertex buffer.
	float centroidOpacity =
	getTransformedAlphaFromFactoredZ(centroid3d.z * heightFactor);
	int centroidIndex = vertexBufferIndex;
	AlphaVertex::set(&shadowVertices[vertexBufferIndex++], centroid3d.x,
	centroid3d.y, centroidOpacity);

	for (int i = 0; i < umbraIndex; i++) {
	// Note that umbraVertices[0] is always 0.
	// So the start and the end of the umbra are using the "0".
	// And penumbra ended with 0, so a degenerated triangle is formed b/t
	// the umbra and penumbra.
	indexBuffer[indexBufferIndex++] = umbraVertices[i];
	indexBuffer[indexBufferIndex++] = centroidIndex;
	}
	indexBuffer[indexBufferIndex++] = 0;
	}

	// At the end, update the real index and vertex buffer size.
	shadowVertexBuffer.updateVertexCount(vertexBufferIndex);
	shadowVertexBuffer.updateIndexCount(indexBufferIndex);

	checkOverflow(vertexBufferIndex, totalVertexCount, "Vertex Buffer");
	checkOverflow(indexBufferIndex, totalIndexCount, "Index Buffer");
	checkOverflow(umbraIndex, totalUmbraCount, "Umbra Buffer");

	#if DEBUG_SHADOW
	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
	}

	}; // namespace uirenderer
	}; // namespace android