Update the shadow fall off function from cosine to gaussian.

Also tune the parameters to match a better look designed by UX team.
For ambient part, the acos transformed alpha is not needed any more.

b/19370798

Change-Id: I20d2615d1be502eb900942ed756aecd1660dee48
diff --git a/libs/hwui/AmbientShadow.cpp b/libs/hwui/AmbientShadow.cpp
index 0a210d6..a4100a2 100644
--- a/libs/hwui/AmbientShadow.cpp
+++ b/libs/hwui/AmbientShadow.cpp
@@ -45,8 +45,9 @@
 /**
  * Other constants:
  */
-// For the edge of the penumbra, the opacity is 0.
-#define OUTER_OPACITY (0.0f)
+// For the edge of the penumbra, the opacity is 0. After transform (1 - alpha),
+// it is 1.
+#define TRANSFORMED_OUTER_OPACITY (1.0f)
 
 // Once the alpha difference is greater than this threshold, we will allocate extra
 // edge vertices.
@@ -83,11 +84,13 @@
     return 1.0 / (1 + MathUtils::max(factoredZ, 0.0f));
 }
 
+// The shader is using gaussian function e^-(1-x)*(1-x)*4, therefore, we transform
+// the alpha value to (1 - alpha)
 inline float getTransformedAlphaFromAlpha(float alpha) {
-    return acosf(1.0f - 2.0f * alpha);
+    return 1.0f - alpha;
 }
 
-// The output is ranged from 0 to M_PI.
+// The output is ranged from 0 to 1.
 inline float getTransformedAlphaFromFactoredZ(float factoredZ) {
     return getTransformedAlphaFromAlpha(getAlphaFromFactoredZ(factoredZ));
 }
@@ -249,7 +252,7 @@
             indexBuffer[indexBufferIndex++] = vertexBufferIndex;
             indexBuffer[indexBufferIndex++] = currentInnerVertexIndex;
             AlphaVertex::set(&shadowVertices[vertexBufferIndex++], outerVertex.x,
-                    outerVertex.y, OUTER_OPACITY);
+                    outerVertex.y, TRANSFORMED_OUTER_OPACITY);
 
             if (j == 0) {
                 outerStart = outerVertex;
@@ -285,7 +288,7 @@
                     (outerLast * startWeight + outerNext * k) / extraVerticesNumber;
                 indexBuffer[indexBufferIndex++] = vertexBufferIndex;
                 AlphaVertex::set(&shadowVertices[vertexBufferIndex++], currentOuter.x,
-                        currentOuter.y, OUTER_OPACITY);
+                        currentOuter.y, TRANSFORMED_OUTER_OPACITY);
 
                 if (!isCasterOpaque) {
                     umbraVertices[umbraIndex++] = vertexBufferIndex;
diff --git a/libs/hwui/ProgramCache.cpp b/libs/hwui/ProgramCache.cpp
index e9b22e2..41adda1 100644
--- a/libs/hwui/ProgramCache.cpp
+++ b/libs/hwui/ProgramCache.cpp
@@ -240,8 +240,9 @@
 const char* gFS_Main_ApplyVertexAlphaLinearInterp =
         "    fragColor *= alpha;\n";
 const char* gFS_Main_ApplyVertexAlphaShadowInterp =
-        "    fragColor *= (1.0 - cos(alpha)) / 2.0;\n";
-
+        // Use a gaussian function for the shadow fall off. Note that alpha here
+        // is actually (1.0 - alpha) for saving computation.
+        "    fragColor *= exp(- alpha * alpha * 4.0) - 0.018;\n";
 const char* gFS_Main_FetchTexture[2] = {
         // Don't modulate
         "    fragColor = texture2D(baseSampler, outTexCoords);\n",
diff --git a/libs/hwui/SpotShadow.cpp b/libs/hwui/SpotShadow.cpp
index b3b06d6..db3c2d9 100644
--- a/libs/hwui/SpotShadow.cpp
+++ b/libs/hwui/SpotShadow.cpp
@@ -44,6 +44,9 @@
 // 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)
 
+// For performance, we use (1 - alpha) value for the shader input.
+#define TRANSFORMED_PENUMBRA_ALPHA 1.0f
+#define TRANSFORMED_UMBRA_ALPHA 0.0f
 
 #include <math.h>
 #include <stdlib.h>
@@ -964,11 +967,11 @@
     // 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, 0.0f);
+                newPenumbra[i].y, TRANSFORMED_PENUMBRA_ALPHA);
     }
     for (int i = 0; i < umbraLength; i++) {
         AlphaVertex::set(&shadowVertices[vertexBufferIndex++], umbra[i].x, umbra[i].y,
-                M_PI);
+                TRANSFORMED_UMBRA_ALPHA);
     }
 
     for (int i = 0; i < verticesPairIndex; i++) {
@@ -1008,14 +1011,14 @@
             indexBuffer[indexBufferIndex++] = newPenumbraLength + i;
             indexBuffer[indexBufferIndex++] = vertexBufferIndex;
             AlphaVertex::set(&shadowVertices[vertexBufferIndex++],
-                    closerVertex.x, closerVertex.y, M_PI);
+                    closerVertex.x, closerVertex.y, TRANSFORMED_UMBRA_ALPHA);
         }
     } 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, M_PI);
+                centroid.y, TRANSFORMED_UMBRA_ALPHA);
         for (int i = 0; i < umbraLength; i++) {
             indexBuffer[indexBufferIndex++] = newPenumbraLength + i;
             indexBuffer[indexBufferIndex++] = lastCentroidIndex;