Add cap tessellation support

bug:7117155
bug:8114304

Currently used for lines (with and without AA) and arcs with useCenter=false

Also removes 0.375, 0.375 offset for AA lines

Change-Id: Ic8ace418739344db1e2814edf65253fe7448b0b0
diff --git a/libs/hwui/PathTessellator.cpp b/libs/hwui/PathTessellator.cpp
new file mode 100644
index 0000000..69ccdfa
--- /dev/null
+++ b/libs/hwui/PathTessellator.cpp
@@ -0,0 +1,970 @@
+/*
+ * Copyright (C) 2012 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 "PathTessellator"
+#define LOG_NDEBUG 1
+#define ATRACE_TAG ATRACE_TAG_GRAPHICS
+
+#define VERTEX_DEBUG 0
+
+#if VERTEX_DEBUG
+#define DEBUG_DUMP_ALPHA_BUFFER() \
+    for (unsigned int i = 0; i < vertexBuffer.getSize(); i++) { \
+        ALOGD("point %d at %f %f, alpha %f", \
+        i, buffer[i].position[0], buffer[i].position[1], buffer[i].alpha); \
+    }
+#define DEBUG_DUMP_BUFFER() \
+    for (unsigned int i = 0; i < vertexBuffer.getSize(); i++) { \
+        ALOGD("point %d at %f %f", i, buffer[i].position[0], buffer[i].position[1]); \
+    }
+#else
+#define DEBUG_DUMP_ALPHA_BUFFER()
+#define DEBUG_DUMP_BUFFER()
+#endif
+
+#include <SkPath.h>
+#include <SkPaint.h>
+
+#include <stdlib.h>
+#include <stdint.h>
+#include <sys/types.h>
+
+#include <utils/Log.h>
+#include <utils/Trace.h>
+
+#include "PathTessellator.h"
+#include "Matrix.h"
+#include "Vector.h"
+#include "Vertex.h"
+
+namespace android {
+namespace uirenderer {
+
+#define THRESHOLD 0.5f
+#define ROUND_CAP_THRESH 0.25f
+#define PI 3.1415926535897932f
+
+void PathTessellator::expandBoundsForStroke(SkRect& bounds, const SkPaint* paint,
+        bool forceExpand) {
+    if (forceExpand || paint->getStyle() != SkPaint::kFill_Style) {
+        float outset = paint->getStrokeWidth() * 0.5f;
+        bounds.outset(outset, outset);
+    }
+}
+
+inline void copyVertex(Vertex* destPtr, const Vertex* srcPtr) {
+    Vertex::set(destPtr, srcPtr->position[0], srcPtr->position[1]);
+}
+
+inline void copyAlphaVertex(AlphaVertex* destPtr, const AlphaVertex* srcPtr) {
+    AlphaVertex::set(destPtr, srcPtr->position[0], srcPtr->position[1], srcPtr->alpha);
+}
+
+/**
+ * Produces a pseudo-normal for a vertex, given the normals of the two incoming lines. If the offset
+ * from each vertex in a perimeter is calculated, the resultant lines connecting the offset vertices
+ * will be offset by 1.0
+ *
+ * Note that we can't add and normalize the two vectors, that would result in a rectangle having an
+ * offset of (sqrt(2)/2, sqrt(2)/2) at each corner, instead of (1, 1)
+ *
+ * NOTE: assumes angles between normals 90 degrees or less
+ */
+inline vec2 totalOffsetFromNormals(const vec2& normalA, const vec2& normalB) {
+    return (normalA + normalB) / (1 + fabs(normalA.dot(normalB)));
+}
+
+/**
+ * Structure used for storing useful information about the SkPaint and scale used for tessellating
+ */
+struct PaintInfo {
+public:
+    PaintInfo(const SkPaint* paint, const mat4 *transform) :
+            style(paint->getStyle()), cap(paint->getStrokeCap()), isAA(paint->isAntiAlias()),
+            inverseScaleX(1.0f), inverseScaleY(1.0f),
+            halfStrokeWidth(paint->getStrokeWidth() * 0.5f), maxAlpha(1.0f) {
+        // compute inverse scales
+        if (CC_UNLIKELY(!transform->isPureTranslate())) {
+            float m00 = transform->data[Matrix4::kScaleX];
+            float m01 = transform->data[Matrix4::kSkewY];
+            float m10 = transform->data[Matrix4::kSkewX];
+            float m11 = transform->data[Matrix4::kScaleY];
+            float scaleX = sqrt(m00 * m00 + m01 * m01);
+            float scaleY = sqrt(m10 * m10 + m11 * m11);
+            inverseScaleX = (scaleX != 0) ? (1.0f / scaleX) : 1.0f;
+            inverseScaleY = (scaleY != 0) ? (1.0f / scaleY) : 1.0f;
+        }
+
+        if (isAA && halfStrokeWidth != 0 && inverseScaleX == inverseScaleY &&
+                halfStrokeWidth * inverseScaleX < 0.5f) {
+            maxAlpha *= (2 * halfStrokeWidth) / inverseScaleX;
+            halfStrokeWidth = 0.0f;
+        }
+    }
+
+    SkPaint::Style style;
+    SkPaint::Cap cap;
+    bool isAA;
+    float inverseScaleX;
+    float inverseScaleY;
+    float halfStrokeWidth;
+    float maxAlpha;
+
+    inline void scaleOffsetForStrokeWidth(vec2& offset) const {
+        if (halfStrokeWidth == 0.0f) {
+            // hairline - compensate for scale
+            offset.x *= 0.5f * inverseScaleX;
+            offset.y *= 0.5f * inverseScaleY;
+        } else {
+            offset *= halfStrokeWidth;
+        }
+    }
+
+    /**
+     * NOTE: the input will not always be a normal, especially for sharp edges - it should be the
+     * result of totalOffsetFromNormals (see documentation there)
+     */
+    inline vec2 deriveAAOffset(const vec2& offset) const {
+        return vec2(offset.x * 0.5f * inverseScaleX,
+            offset.y * 0.5f * inverseScaleY);
+    }
+
+    /**
+     * Returns the number of cap divisions beyond the minimum 2 (kButt_Cap/kSquareCap will return 0)
+     * Should only be used when stroking and drawing caps
+     */
+    inline int capExtraDivisions() const {
+        if (cap == SkPaint::kRound_Cap) {
+            if (halfStrokeWidth == 0.0f) return 2;
+
+            // ROUND_CAP_THRESH is the maximum error for polygonal approximation of the round cap
+            const float errConst = (-ROUND_CAP_THRESH / halfStrokeWidth + 1);
+            const float targetCosVal = 2 * errConst * errConst - 1;
+            int neededDivisions = (int)(ceilf(PI / acos(targetCosVal)/2)) * 2;
+            return neededDivisions;
+        }
+        return 0;
+    }
+};
+
+void getFillVerticesFromPerimeter(const Vector<Vertex>& perimeter, VertexBuffer& vertexBuffer) {
+    Vertex* buffer = vertexBuffer.alloc<Vertex>(perimeter.size());
+
+    int currentIndex = 0;
+    // zig zag between all previous points on the inside of the hull to create a
+    // triangle strip that fills the hull
+    int srcAindex = 0;
+    int srcBindex = perimeter.size() - 1;
+    while (srcAindex <= srcBindex) {
+        copyVertex(&buffer[currentIndex++], &perimeter[srcAindex]);
+        if (srcAindex == srcBindex) break;
+        copyVertex(&buffer[currentIndex++], &perimeter[srcBindex]);
+        srcAindex++;
+        srcBindex--;
+    }
+}
+
+/*
+ * Fills a vertexBuffer with non-alpha vertices, zig-zagging at each perimeter point to create a
+ * tri-strip as wide as the stroke.
+ *
+ * Uses an additional 2 vertices at the end to wrap around, closing the tri-strip
+ * (for a total of perimeter.size() * 2 + 2 vertices)
+ */
+void getStrokeVerticesFromPerimeter(const PaintInfo& paintInfo, const Vector<Vertex>& perimeter,
+        VertexBuffer& vertexBuffer) {
+    Vertex* buffer = vertexBuffer.alloc<Vertex>(perimeter.size() * 2 + 2);
+
+    int currentIndex = 0;
+    const Vertex* last = &(perimeter[perimeter.size() - 1]);
+    const Vertex* current = &(perimeter[0]);
+    vec2 lastNormal(current->position[1] - last->position[1],
+            last->position[0] - current->position[0]);
+    lastNormal.normalize();
+    for (unsigned int i = 0; i < perimeter.size(); i++) {
+        const Vertex* next = &(perimeter[i + 1 >= perimeter.size() ? 0 : i + 1]);
+        vec2 nextNormal(next->position[1] - current->position[1],
+                current->position[0] - next->position[0]);
+        nextNormal.normalize();
+
+        vec2 totalOffset = totalOffsetFromNormals(lastNormal, nextNormal);
+        paintInfo.scaleOffsetForStrokeWidth(totalOffset);
+
+        Vertex::set(&buffer[currentIndex++],
+                current->position[0] + totalOffset.x,
+                current->position[1] + totalOffset.y);
+
+        Vertex::set(&buffer[currentIndex++],
+                current->position[0] - totalOffset.x,
+                current->position[1] - totalOffset.y);
+
+        last = current;
+        current = next;
+        lastNormal = nextNormal;
+    }
+
+    // wrap around to beginning
+    copyVertex(&buffer[currentIndex++], &buffer[0]);
+    copyVertex(&buffer[currentIndex++], &buffer[1]);
+
+    DEBUG_DUMP_BUFFER();
+}
+
+/**
+ * Fills a vertexBuffer with non-alpha vertices similar to getStrokeVerticesFromPerimeter, except:
+ *
+ * 1 - Doesn't need to wrap around, since the input vertices are unclosed
+ *
+ * 2 - can zig-zag across 'extra' vertices at either end, to create round caps
+ */
+void getStrokeVerticesFromUnclosedVertices(const PaintInfo& paintInfo,
+        const Vector<Vertex>& vertices, VertexBuffer& vertexBuffer) {
+    const int extra = paintInfo.capExtraDivisions();
+    const int allocSize = (vertices.size() + extra) * 2;
+
+    Vertex* buffer = vertexBuffer.alloc<Vertex>(allocSize);
+
+    if (extra > 0) {
+        // tessellate both round caps
+        const int last = vertices.size() - 1;
+        float beginTheta = atan2(
+                - (vertices[0].position[0] - vertices[1].position[0]),
+                vertices[0].position[1] - vertices[1].position[1]);
+        float endTheta = atan2(
+                - (vertices[last].position[0] - vertices[last - 1].position[0]),
+                vertices[last].position[1] - vertices[last - 1].position[1]);
+
+        const float dTheta = PI / (extra + 1);
+        const float radialScale = 2.0f / (1 + cos(dTheta));
+
+        int capOffset;
+        for (int i = 0; i < extra; i++) {
+            if (i < extra / 2) {
+                capOffset = extra - 2 * i - 1;
+            } else {
+                capOffset = 2 * i - extra;
+            }
+
+            beginTheta += dTheta;
+            vec2 beginRadialOffset(cos(beginTheta), sin(beginTheta));
+            paintInfo.scaleOffsetForStrokeWidth(beginRadialOffset);
+            Vertex::set(&buffer[capOffset],
+                    vertices[0].position[0] + beginRadialOffset.x,
+                    vertices[0].position[1] + beginRadialOffset.y);
+
+            endTheta += dTheta;
+            vec2 endRadialOffset(cos(endTheta), sin(endTheta));
+            paintInfo.scaleOffsetForStrokeWidth(endRadialOffset);
+            Vertex::set(&buffer[allocSize - 1 - capOffset],
+                    vertices[last].position[0] + endRadialOffset.x,
+                    vertices[last].position[1] + endRadialOffset.y);
+        }
+    }
+
+    int currentIndex = extra;
+    const Vertex* current = &(vertices[0]);
+    vec2 lastNormal;
+    for (unsigned int i = 0; i < vertices.size() - 1; i++) {
+        const Vertex* next = &(vertices[i + 1]);
+        vec2 nextNormal(next->position[1] - current->position[1],
+                current->position[0] - next->position[0]);
+        nextNormal.normalize();
+
+        vec2 totalOffset;
+        if (i == 0) {
+            totalOffset = nextNormal;
+        } else {
+            totalOffset = totalOffsetFromNormals(lastNormal, nextNormal);
+        }
+        paintInfo.scaleOffsetForStrokeWidth(totalOffset);
+
+        Vertex::set(&buffer[currentIndex++],
+                current->position[0] + totalOffset.x,
+                current->position[1] + totalOffset.y);
+
+        Vertex::set(&buffer[currentIndex++],
+                current->position[0] - totalOffset.x,
+                current->position[1] - totalOffset.y);
+
+        current = next;
+        lastNormal = nextNormal;
+    }
+
+    vec2 totalOffset = lastNormal;
+    paintInfo.scaleOffsetForStrokeWidth(totalOffset);
+
+    Vertex::set(&buffer[currentIndex++],
+            current->position[0] + totalOffset.x,
+            current->position[1] + totalOffset.y);
+    Vertex::set(&buffer[currentIndex++],
+            current->position[0] - totalOffset.x,
+            current->position[1] - totalOffset.y);
+
+    DEBUG_DUMP_BUFFER();
+}
+
+/**
+ * Populates a vertexBuffer with AlphaVertices to create an anti-aliased fill shape tessellation
+ * 
+ * 1 - create the AA perimeter of unit width, by zig-zagging at each point around the perimeter of
+ * the shape (using 2 * perimeter.size() vertices)
+ *
+ * 2 - wrap around to the beginning to complete the perimeter (2 vertices)
+ *
+ * 3 - zig zag back and forth inside the shape to fill it (using perimeter.size() vertices)
+ */
+void getFillVerticesFromPerimeterAA(const PaintInfo& paintInfo, const Vector<Vertex>& perimeter,
+        VertexBuffer& vertexBuffer) {
+    AlphaVertex* buffer = vertexBuffer.alloc<AlphaVertex>(perimeter.size() * 3 + 2);
+
+    // generate alpha points - fill Alpha vertex gaps in between each point with
+    // alpha 0 vertex, offset by a scaled normal.
+    int currentIndex = 0;
+    const Vertex* last = &(perimeter[perimeter.size() - 1]);
+    const Vertex* current = &(perimeter[0]);
+    vec2 lastNormal(current->position[1] - last->position[1],
+            last->position[0] - current->position[0]);
+    lastNormal.normalize();
+    for (unsigned int i = 0; i < perimeter.size(); i++) {
+        const Vertex* next = &(perimeter[i + 1 >= perimeter.size() ? 0 : i + 1]);
+        vec2 nextNormal(next->position[1] - current->position[1],
+                current->position[0] - next->position[0]);
+        nextNormal.normalize();
+
+        // AA point offset from original point is that point's normal, such that each side is offset
+        // by .5 pixels
+        vec2 totalOffset = paintInfo.deriveAAOffset(totalOffsetFromNormals(lastNormal, nextNormal));
+
+        AlphaVertex::set(&buffer[currentIndex++],
+                current->position[0] + totalOffset.x,
+                current->position[1] + totalOffset.y,
+                0.0f);
+        AlphaVertex::set(&buffer[currentIndex++],
+                current->position[0] - totalOffset.x,
+                current->position[1] - totalOffset.y,
+                1.0f);
+
+        last = current;
+        current = next;
+        lastNormal = nextNormal;
+    }
+
+    // wrap around to beginning
+    copyAlphaVertex(&buffer[currentIndex++], &buffer[0]);
+    copyAlphaVertex(&buffer[currentIndex++], &buffer[1]);
+
+    // zig zag between all previous points on the inside of the hull to create a
+    // triangle strip that fills the hull, repeating the first inner point to
+    // create degenerate tris to start inside path
+    int srcAindex = 0;
+    int srcBindex = perimeter.size() - 1;
+    while (srcAindex <= srcBindex) {
+        copyAlphaVertex(&buffer[currentIndex++], &buffer[srcAindex * 2 + 1]);
+        if (srcAindex == srcBindex) break;
+        copyAlphaVertex(&buffer[currentIndex++], &buffer[srcBindex * 2 + 1]);
+        srcAindex++;
+        srcBindex--;
+    }
+
+    DEBUG_DUMP_BUFFER();
+}
+
+/**
+ * Stores geometry for a single, AA-perimeter (potentially rounded) cap
+ *
+ * For explanation of constants and general methodoloyg, see comments for
+ * getStrokeVerticesFromUnclosedVerticesAA() below.
+ */
+inline void storeCapAA(const PaintInfo& paintInfo, const Vector<Vertex>& vertices,
+        AlphaVertex* buffer, bool isFirst, vec2 normal, int offset) {
+    const int extra = paintInfo.capExtraDivisions();
+    const int extraOffset = (extra + 1) / 2;
+    const int capIndex = isFirst
+            ? 2 * offset + 6 + 2 * (extra + extraOffset)
+            : offset + 2 + 2 * extraOffset;
+    if (isFirst) normal *= -1;
+
+    // TODO: this normal should be scaled by radialScale if extra != 0, see totalOffsetFromNormals()
+    vec2 AAOffset = paintInfo.deriveAAOffset(normal);
+
+    vec2 strokeOffset = normal;
+    paintInfo.scaleOffsetForStrokeWidth(strokeOffset);
+    vec2 outerOffset = strokeOffset + AAOffset;
+    vec2 innerOffset = strokeOffset - AAOffset;
+
+    vec2 capAAOffset;
+    if (paintInfo.cap != SkPaint::kRound_Cap) {
+        // if the cap is square or butt, the inside primary cap vertices will be inset in two
+        // directions - both normal to the stroke, and parallel to it.
+        capAAOffset = vec2(-AAOffset.y, AAOffset.x);
+    }
+
+    // determine referencePoint, the center point for the 4 primary cap vertices
+    const Vertex* point = isFirst ? vertices.begin() : (vertices.end() - 1);
+    vec2 referencePoint(point->position[0], point->position[1]);
+    if (paintInfo.cap == SkPaint::kSquare_Cap) {
+        // To account for square cap, move the primary cap vertices (that create the AA edge) by the
+        // stroke offset vector (rotated to be parallel to the stroke)
+        referencePoint += vec2(-strokeOffset.y, strokeOffset.x);
+    }
+
+    AlphaVertex::set(&buffer[capIndex + 0],
+            referencePoint.x + outerOffset.x + capAAOffset.x,
+            referencePoint.y + outerOffset.y + capAAOffset.y,
+            0.0f);
+    AlphaVertex::set(&buffer[capIndex + 1],
+            referencePoint.x + innerOffset.x - capAAOffset.x,
+            referencePoint.y + innerOffset.y - capAAOffset.y,
+            paintInfo.maxAlpha);
+
+    bool isRound = paintInfo.cap == SkPaint::kRound_Cap;
+
+    const int postCapIndex = (isRound && isFirst) ? (2 * extraOffset - 2) : capIndex + (2 * extra);
+    AlphaVertex::set(&buffer[postCapIndex + 2],
+            referencePoint.x - outerOffset.x + capAAOffset.x,
+            referencePoint.y - outerOffset.y + capAAOffset.y,
+            0.0f);
+    AlphaVertex::set(&buffer[postCapIndex + 3],
+            referencePoint.x - innerOffset.x - capAAOffset.x,
+            referencePoint.y - innerOffset.y - capAAOffset.y,
+            paintInfo.maxAlpha);
+
+    if (isRound) {
+        const float dTheta = PI / (extra + 1);
+        const float radialScale = 2.0f / (1 + cos(dTheta));
+        float theta = atan2(normal.y, normal.x);
+        int capPerimIndex = capIndex + 2;
+
+        for (int i = 0; i < extra; i++) {
+            theta += dTheta;
+
+            vec2 radialOffset(cos(theta), sin(theta));
+
+            // scale to compensate for pinching at sharp angles, see totalOffsetFromNormals()
+            radialOffset *= radialScale;
+
+            AAOffset = paintInfo.deriveAAOffset(radialOffset);
+            paintInfo.scaleOffsetForStrokeWidth(radialOffset);
+            AlphaVertex::set(&buffer[capPerimIndex++],
+                    referencePoint.x + radialOffset.x + AAOffset.x,
+                    referencePoint.y + radialOffset.y + AAOffset.y,
+                    0.0f);
+            AlphaVertex::set(&buffer[capPerimIndex++],
+                    referencePoint.x + radialOffset.x - AAOffset.x,
+                    referencePoint.y + radialOffset.y - AAOffset.y,
+                    paintInfo.maxAlpha);
+
+            if (isFirst && i == extra - extraOffset) {
+                //copy most recent two points to first two points
+                copyAlphaVertex(&buffer[0], &buffer[capPerimIndex - 2]);
+                copyAlphaVertex(&buffer[1], &buffer[capPerimIndex - 1]);
+
+                capPerimIndex = 2; // start writing the rest of the round cap at index 2
+            }
+        }
+
+        if (isFirst) {
+            const int startCapFillIndex = capIndex + 2 * (extra - extraOffset) + 4;
+            int capFillIndex = startCapFillIndex;
+            for (int i = 0; i < extra + 2; i += 2) {
+                copyAlphaVertex(&buffer[capFillIndex++], &buffer[1 + i]);
+                // TODO: to support odd numbers of divisions, break here on the last iteration
+                copyAlphaVertex(&buffer[capFillIndex++], &buffer[startCapFillIndex - 3 - i]);
+            }
+        } else {
+            int capFillIndex = 6 * vertices.size() + 2 + 6 * extra - (extra + 2);
+            for (int i = 0; i < extra + 2; i += 2) {
+                copyAlphaVertex(&buffer[capFillIndex++], &buffer[capIndex + 1 + i]);
+                // TODO: to support odd numbers of divisions, break here on the last iteration
+                copyAlphaVertex(&buffer[capFillIndex++], &buffer[capIndex + 3 + 2 * extra - i]);
+            }
+        }
+        return;
+    }
+    if (isFirst) {
+        copyAlphaVertex(&buffer[0], &buffer[postCapIndex + 2]);
+        copyAlphaVertex(&buffer[1], &buffer[postCapIndex + 3]);
+        copyAlphaVertex(&buffer[postCapIndex + 4], &buffer[1]); // degenerate tris (the only two!)
+        copyAlphaVertex(&buffer[postCapIndex + 5], &buffer[postCapIndex + 1]);
+    } else {
+        copyAlphaVertex(&buffer[6 * vertices.size()], &buffer[postCapIndex + 1]);
+        copyAlphaVertex(&buffer[6 * vertices.size() + 1], &buffer[postCapIndex + 3]);
+    }
+}
+
+/*
+the geometry for an aa, capped stroke consists of the following:
+
+       # vertices       |    function
+----------------------------------------------------------------------
+a) 2                    | Start AA perimeter
+b) 2, 2 * roundDivOff   | First half of begin cap's perimeter
+                        |
+   2 * middlePts        | 'Outer' or 'Top' AA perimeter half (between caps)
+                        |
+a) 4                    | End cap's
+b) 2, 2 * roundDivs, 2  |    AA perimeter
+                        |
+   2 * middlePts        | 'Inner' or 'bottom' AA perimeter half
+                        |
+a) 6                    | Begin cap's perimeter
+b) 2, 2*(rD - rDO + 1), | Last half of begin cap's perimeter
+       roundDivs, 2     |
+                        |
+   2 * middlePts        | Stroke's full opacity center strip
+                        |
+a) 2                    | end stroke
+b) 2, roundDivs         |    (and end cap fill, for round)
+
+Notes:
+* rows starting with 'a)' denote the Butt or Square cap vertex use, 'b)' denote Round
+
+* 'middlePts' is (number of points in the unclosed input vertex list, minus 2) times two
+
+* 'roundDivs' or 'rD' is the number of extra vertices (beyond the minimum of 2) that define the
+        round cap's shape, and is at least two. This will increase with cap size to sufficiently
+        define the cap's level of tessellation.
+
+* 'roundDivOffset' or 'rDO' is the point about halfway along the start cap's round perimeter, where
+        the stream of vertices for the AA perimeter starts. By starting and ending the perimeter at
+        this offset, the fill of the stroke is drawn from this point with minimal extra vertices.
+
+This means the outer perimeter starts at:
+    outerIndex = (2) OR (2 + 2 * roundDivOff)
+the inner perimeter (since it is filled in reverse) starts at:
+    innerIndex = outerIndex + (4 * middlePts) + ((4) OR (4 + 2 * roundDivs)) - 1
+the stroke starts at:
+    strokeIndex = innerIndex + 1 + ((6) OR (6 + 3 * roundDivs - 2 * roundDivOffset))
+
+The total needed allocated space is either:
+    2 + 4 + 6 + 2 + 3 * (2 * middlePts) = 14 + 6 * middlePts = 2 + 6 * pts
+or, for rounded caps:
+    (2 + 2 * rDO) + (4 + 2 * rD) + (2 * (rD - rDO + 1)
+            + roundDivs + 4) + (2 + roundDivs) + 3 * (2 * middlePts)
+    = 14 + 6 * middlePts + 6 * roundDivs
+    = 2 + 6 * pts + 6 * roundDivs
+ */
+void getStrokeVerticesFromUnclosedVerticesAA(const PaintInfo& paintInfo,
+        const Vector<Vertex>& vertices, VertexBuffer& vertexBuffer) {
+
+    const int extra = paintInfo.capExtraDivisions();
+    const int allocSize = 6 * vertices.size() + 2 + 6 * extra;
+
+    AlphaVertex* buffer = vertexBuffer.alloc<AlphaVertex>(allocSize);
+
+    const int extraOffset = (extra + 1) / 2;
+    int offset = 2 * (vertices.size() - 2);
+    // there is no outer/inner here, using them for consistency with below approach
+    int currentAAOuterIndex = 2 + 2 * extraOffset;
+    int currentAAInnerIndex = currentAAOuterIndex + (2 * offset) + 3 + (2 * extra);
+    int currentStrokeIndex = currentAAInnerIndex + 7 + (3 * extra - 2 * extraOffset);
+
+    const Vertex* last = &(vertices[0]);
+    const Vertex* current = &(vertices[1]);
+    vec2 lastNormal(current->position[1] - last->position[1],
+            last->position[0] - current->position[0]);
+    lastNormal.normalize();
+
+    // TODO: use normal from bezier traversal for cap, instead of from vertices
+    storeCapAA(paintInfo, vertices, buffer, true, lastNormal, offset);
+
+    for (unsigned int i = 1; i < vertices.size() - 1; i++) {
+        const Vertex* next = &(vertices[i + 1]);
+        vec2 nextNormal(next->position[1] - current->position[1],
+                current->position[0] - next->position[0]);
+        nextNormal.normalize();
+
+        vec2 totalOffset = totalOffsetFromNormals(lastNormal, nextNormal);
+        vec2 AAOffset = paintInfo.deriveAAOffset(totalOffset);
+
+        vec2 innerOffset = totalOffset;
+        paintInfo.scaleOffsetForStrokeWidth(innerOffset);
+        vec2 outerOffset = innerOffset + AAOffset;
+        innerOffset -= AAOffset;
+
+        AlphaVertex::set(&buffer[currentAAOuterIndex++],
+                current->position[0] + outerOffset.x,
+                current->position[1] + outerOffset.y,
+                0.0f);
+        AlphaVertex::set(&buffer[currentAAOuterIndex++],
+                current->position[0] + innerOffset.x,
+                current->position[1] + innerOffset.y,
+                paintInfo.maxAlpha);
+
+        AlphaVertex::set(&buffer[currentStrokeIndex++],
+                current->position[0] + innerOffset.x,
+                current->position[1] + innerOffset.y,
+                paintInfo.maxAlpha);
+        AlphaVertex::set(&buffer[currentStrokeIndex++],
+                current->position[0] - innerOffset.x,
+                current->position[1] - innerOffset.y,
+                paintInfo.maxAlpha);
+
+        AlphaVertex::set(&buffer[currentAAInnerIndex--],
+                current->position[0] - innerOffset.x,
+                current->position[1] - innerOffset.y,
+                paintInfo.maxAlpha);
+        AlphaVertex::set(&buffer[currentAAInnerIndex--],
+                current->position[0] - outerOffset.x,
+                current->position[1] - outerOffset.y,
+                0.0f);
+
+        current = next;
+        lastNormal = nextNormal;
+    }
+
+    // TODO: use normal from bezier traversal for cap, instead of from vertices
+    storeCapAA(paintInfo, vertices, buffer, false, lastNormal, offset);
+
+    DEBUG_DUMP_ALPHA_BUFFER();
+}
+
+
+void getStrokeVerticesFromPerimeterAA(const PaintInfo& paintInfo, const Vector<Vertex>& perimeter,
+        VertexBuffer& vertexBuffer) {
+    AlphaVertex* buffer = vertexBuffer.alloc<AlphaVertex>(6 * perimeter.size() + 8);
+
+    int offset = 2 * perimeter.size() + 3;
+    int currentAAOuterIndex = 0;
+    int currentStrokeIndex = offset;
+    int currentAAInnerIndex = offset * 2;
+
+    const Vertex* last = &(perimeter[perimeter.size() - 1]);
+    const Vertex* current = &(perimeter[0]);
+    vec2 lastNormal(current->position[1] - last->position[1],
+            last->position[0] - current->position[0]);
+    lastNormal.normalize();
+    for (unsigned int i = 0; i < perimeter.size(); i++) {
+        const Vertex* next = &(perimeter[i + 1 >= perimeter.size() ? 0 : i + 1]);
+        vec2 nextNormal(next->position[1] - current->position[1],
+                current->position[0] - next->position[0]);
+        nextNormal.normalize();
+
+        vec2 totalOffset = totalOffsetFromNormals(lastNormal, nextNormal);
+        vec2 AAOffset = paintInfo.deriveAAOffset(totalOffset);
+
+        vec2 innerOffset = totalOffset;
+        paintInfo.scaleOffsetForStrokeWidth(innerOffset);
+        vec2 outerOffset = innerOffset + AAOffset;
+        innerOffset -= AAOffset;
+
+        AlphaVertex::set(&buffer[currentAAOuterIndex++],
+                current->position[0] + outerOffset.x,
+                current->position[1] + outerOffset.y,
+                0.0f);
+        AlphaVertex::set(&buffer[currentAAOuterIndex++],
+                current->position[0] + innerOffset.x,
+                current->position[1] + innerOffset.y,
+                paintInfo.maxAlpha);
+
+        AlphaVertex::set(&buffer[currentStrokeIndex++],
+                current->position[0] + innerOffset.x,
+                current->position[1] + innerOffset.y,
+                paintInfo.maxAlpha);
+        AlphaVertex::set(&buffer[currentStrokeIndex++],
+                current->position[0] - innerOffset.x,
+                current->position[1] - innerOffset.y,
+                paintInfo.maxAlpha);
+
+        AlphaVertex::set(&buffer[currentAAInnerIndex++],
+                current->position[0] - innerOffset.x,
+                current->position[1] - innerOffset.y,
+                paintInfo.maxAlpha);
+        AlphaVertex::set(&buffer[currentAAInnerIndex++],
+                current->position[0] - outerOffset.x,
+                current->position[1] - outerOffset.y,
+                0.0f);
+
+        last = current;
+        current = next;
+        lastNormal = nextNormal;
+    }
+
+    // wrap each strip around to beginning, creating degenerate tris to bridge strips
+    copyAlphaVertex(&buffer[currentAAOuterIndex++], &buffer[0]);
+    copyAlphaVertex(&buffer[currentAAOuterIndex++], &buffer[1]);
+    copyAlphaVertex(&buffer[currentAAOuterIndex++], &buffer[1]);
+
+    copyAlphaVertex(&buffer[currentStrokeIndex++], &buffer[offset]);
+    copyAlphaVertex(&buffer[currentStrokeIndex++], &buffer[offset + 1]);
+    copyAlphaVertex(&buffer[currentStrokeIndex++], &buffer[offset + 1]);
+
+    copyAlphaVertex(&buffer[currentAAInnerIndex++], &buffer[2 * offset]);
+    copyAlphaVertex(&buffer[currentAAInnerIndex++], &buffer[2 * offset + 1]);
+    // don't need to create last degenerate tri
+
+    DEBUG_DUMP_ALPHA_BUFFER();
+}
+
+void PathTessellator::tessellatePath(const SkPath &path, const SkPaint* paint,
+        const mat4 *transform, VertexBuffer& vertexBuffer) {
+    ATRACE_CALL();
+
+    const PaintInfo paintInfo(paint, transform);
+
+    Vector<Vertex> tempVertices;
+    float threshInvScaleX = paintInfo.inverseScaleX;
+    float threshInvScaleY = paintInfo.inverseScaleY;
+    if (paintInfo.style == SkPaint::kStroke_Style) {
+        // alter the bezier recursion threshold values we calculate in order to compensate for
+        // expansion done after the path vertices are found
+        SkRect bounds = path.getBounds();
+        if (!bounds.isEmpty()) {
+            threshInvScaleX *= bounds.width() / (bounds.width() + paint->getStrokeWidth());
+            threshInvScaleY *= bounds.height() / (bounds.height() + paint->getStrokeWidth());
+        }
+    }
+
+    // force close if we're filling the path, since fill path expects closed perimeter.
+    bool forceClose = paintInfo.style != SkPaint::kStroke_Style;
+    bool wasClosed = approximatePathOutlineVertices(path, forceClose,
+            threshInvScaleX * threshInvScaleX, threshInvScaleY * threshInvScaleY, tempVertices);
+
+    if (!tempVertices.size()) {
+        // path was empty, return without allocating vertex buffer
+        return;
+    }
+
+#if VERTEX_DEBUG
+    for (unsigned int i = 0; i < tempVertices.size(); i++) {
+        ALOGD("orig path: point at %f %f",
+                tempVertices[i].position[0], tempVertices[i].position[1]);
+    }
+#endif
+
+    if (paintInfo.style == SkPaint::kStroke_Style) {
+        if (!paintInfo.isAA) {
+            if (wasClosed) {
+                getStrokeVerticesFromPerimeter(paintInfo, tempVertices, vertexBuffer);
+            } else {
+                getStrokeVerticesFromUnclosedVertices(paintInfo, tempVertices, vertexBuffer);
+            }
+
+        } else {
+            if (wasClosed) {
+                getStrokeVerticesFromPerimeterAA(paintInfo, tempVertices, vertexBuffer);
+            } else {
+                getStrokeVerticesFromUnclosedVerticesAA(paintInfo, tempVertices, vertexBuffer);
+            }
+        }
+    } else {
+        // For kStrokeAndFill style, the path should be adjusted externally.
+        // It will be treated as a fill here.
+        if (!paintInfo.isAA) {
+            getFillVerticesFromPerimeter(tempVertices, vertexBuffer);
+        } else {
+            getFillVerticesFromPerimeterAA(paintInfo, tempVertices, vertexBuffer);
+        }
+    }
+}
+
+static void expandRectToCoverVertex(SkRect& rect, const Vertex& vertex) {
+    rect.fLeft = fminf(rect.fLeft, vertex.position[0]);
+    rect.fTop = fminf(rect.fTop, vertex.position[1]);
+    rect.fRight = fmaxf(rect.fRight, vertex.position[0]);
+    rect.fBottom = fmaxf(rect.fBottom, vertex.position[1]);
+}
+
+void PathTessellator::tessellateLines(const float* points, int count, SkPaint* paint,
+        const mat4* transform, SkRect& bounds, VertexBuffer& vertexBuffer) {
+    ATRACE_CALL();
+    const PaintInfo paintInfo(paint, transform);
+
+    const int extra = paintInfo.capExtraDivisions();
+    int numLines = count / 4;
+    int lineAllocSize;
+    // pre-allocate space for lines in the buffer, and degenerate tris in between
+    if (paintInfo.isAA) {
+        lineAllocSize = 6 * (2) + 2 + 6 * extra;
+        vertexBuffer.alloc<AlphaVertex>(numLines * lineAllocSize + (numLines - 1) * 2);
+    } else {
+        lineAllocSize = 2 * ((2) + extra);
+        vertexBuffer.alloc<Vertex>(numLines * lineAllocSize + (numLines - 1) * 2);
+    }
+
+    Vector<Vertex> tempVertices;
+    tempVertices.push();
+    tempVertices.push();
+    Vertex* tempVerticesData = tempVertices.editArray();
+    bounds.set(points[0], points[1], points[0], points[1]);
+    for (int i = 0; i < count; i += 4) {
+        Vertex::set(&(tempVerticesData[0]), points[i + 0], points[i + 1]);
+        Vertex::set(&(tempVerticesData[1]), points[i + 2], points[i + 3]);
+
+        if (paintInfo.isAA) {
+            getStrokeVerticesFromUnclosedVerticesAA(paintInfo, tempVertices, vertexBuffer);
+        } else {
+            getStrokeVerticesFromUnclosedVertices(paintInfo, tempVertices, vertexBuffer);
+        }
+
+        // calculate bounds
+        expandRectToCoverVertex(bounds, tempVerticesData[0]);
+        expandRectToCoverVertex(bounds, tempVerticesData[1]);
+    }
+
+    expandBoundsForStroke(bounds, paint, true); // force-expand bounds to incorporate stroke
+
+    // since multiple objects tessellated into buffer, separate them with degen tris
+    if (paintInfo.isAA) {
+        vertexBuffer.createDegenerateSeparators<AlphaVertex>(lineAllocSize);
+    } else {
+        vertexBuffer.createDegenerateSeparators<Vertex>(lineAllocSize);
+    }
+}
+
+///////////////////////////////////////////////////////////////////////////////
+// Simple path line approximation
+///////////////////////////////////////////////////////////////////////////////
+
+void pushToVector(Vector<Vertex>& vertices, float x, float y) {
+    // TODO: make this not yuck
+    vertices.push();
+    Vertex* newVertex = &(vertices.editArray()[vertices.size() - 1]);
+    Vertex::set(newVertex, x, y);
+}
+
+bool PathTessellator::approximatePathOutlineVertices(const SkPath& path, bool forceClose,
+        float sqrInvScaleX, float sqrInvScaleY, Vector<Vertex>& outputVertices) {
+    ATRACE_CALL();
+
+    // TODO: to support joins other than sharp miter, join vertices should be labelled in the
+    // perimeter, or resolved into more vertices. Reconsider forceClose-ing in that case.
+    SkPath::Iter iter(path, forceClose);
+    SkPoint pts[4];
+    SkPath::Verb v;
+    while (SkPath::kDone_Verb != (v = iter.next(pts))) {
+            switch (v) {
+            case SkPath::kMove_Verb:
+                pushToVector(outputVertices, pts[0].x(), pts[0].y());
+                ALOGV("Move to pos %f %f", pts[0].x(), pts[0].y());
+                break;
+            case SkPath::kClose_Verb:
+                ALOGV("Close at pos %f %f", pts[0].x(), pts[0].y());
+                break;
+            case SkPath::kLine_Verb:
+                ALOGV("kLine_Verb %f %f -> %f %f", pts[0].x(), pts[0].y(), pts[1].x(), pts[1].y());
+                pushToVector(outputVertices, pts[1].x(), pts[1].y());
+                break;
+            case SkPath::kQuad_Verb:
+                ALOGV("kQuad_Verb");
+                recursiveQuadraticBezierVertices(
+                        pts[0].x(), pts[0].y(),
+                        pts[2].x(), pts[2].y(),
+                        pts[1].x(), pts[1].y(),
+                        sqrInvScaleX, sqrInvScaleY, outputVertices);
+                break;
+            case SkPath::kCubic_Verb:
+                ALOGV("kCubic_Verb");
+                recursiveCubicBezierVertices(
+                        pts[0].x(), pts[0].y(),
+                        pts[1].x(), pts[1].y(),
+                        pts[3].x(), pts[3].y(),
+                        pts[2].x(), pts[2].y(),
+                        sqrInvScaleX, sqrInvScaleY, outputVertices);
+                break;
+            default:
+                break;
+            }
+    }
+
+    int size = outputVertices.size();
+    if (size >= 2 && outputVertices[0].position[0] == outputVertices[size - 1].position[0] &&
+            outputVertices[0].position[1] == outputVertices[size - 1].position[1]) {
+        outputVertices.pop();
+        return true;
+    }
+    return false;
+}
+
+///////////////////////////////////////////////////////////////////////////////
+// Bezier approximation
+///////////////////////////////////////////////////////////////////////////////
+
+void PathTessellator::recursiveCubicBezierVertices(
+        float p1x, float p1y, float c1x, float c1y,
+        float p2x, float p2y, float c2x, float c2y,
+        float sqrInvScaleX, float sqrInvScaleY, Vector<Vertex>& outputVertices) {
+    float dx = p2x - p1x;
+    float dy = p2y - p1y;
+    float d1 = fabs((c1x - p2x) * dy - (c1y - p2y) * dx);
+    float d2 = fabs((c2x - p2x) * dy - (c2y - p2y) * dx);
+    float d = d1 + d2;
+
+    // multiplying by sqrInvScaleY/X equivalent to multiplying in dimensional scale factors
+
+    if (d * d < THRESHOLD * THRESHOLD * (dx * dx * sqrInvScaleY + dy * dy * sqrInvScaleX)) {
+        // below thresh, draw line by adding endpoint
+        pushToVector(outputVertices, p2x, p2y);
+    } else {
+        float p1c1x = (p1x + c1x) * 0.5f;
+        float p1c1y = (p1y + c1y) * 0.5f;
+        float p2c2x = (p2x + c2x) * 0.5f;
+        float p2c2y = (p2y + c2y) * 0.5f;
+
+        float c1c2x = (c1x + c2x) * 0.5f;
+        float c1c2y = (c1y + c2y) * 0.5f;
+
+        float p1c1c2x = (p1c1x + c1c2x) * 0.5f;
+        float p1c1c2y = (p1c1y + c1c2y) * 0.5f;
+
+        float p2c1c2x = (p2c2x + c1c2x) * 0.5f;
+        float p2c1c2y = (p2c2y + c1c2y) * 0.5f;
+
+        float mx = (p1c1c2x + p2c1c2x) * 0.5f;
+        float my = (p1c1c2y + p2c1c2y) * 0.5f;
+
+        recursiveCubicBezierVertices(
+                p1x, p1y, p1c1x, p1c1y,
+                mx, my, p1c1c2x, p1c1c2y,
+                sqrInvScaleX, sqrInvScaleY, outputVertices);
+        recursiveCubicBezierVertices(
+                mx, my, p2c1c2x, p2c1c2y,
+                p2x, p2y, p2c2x, p2c2y,
+                sqrInvScaleX, sqrInvScaleY, outputVertices);
+    }
+}
+
+void PathTessellator::recursiveQuadraticBezierVertices(
+        float ax, float ay,
+        float bx, float by,
+        float cx, float cy,
+        float sqrInvScaleX, float sqrInvScaleY, Vector<Vertex>& outputVertices) {
+    float dx = bx - ax;
+    float dy = by - ay;
+    float d = (cx - bx) * dy - (cy - by) * dx;
+
+    if (d * d < THRESHOLD * THRESHOLD * (dx * dx * sqrInvScaleY + dy * dy * sqrInvScaleX)) {
+        // below thresh, draw line by adding endpoint
+        pushToVector(outputVertices, bx, by);
+    } else {
+        float acx = (ax + cx) * 0.5f;
+        float bcx = (bx + cx) * 0.5f;
+        float acy = (ay + cy) * 0.5f;
+        float bcy = (by + cy) * 0.5f;
+
+        // midpoint
+        float mx = (acx + bcx) * 0.5f;
+        float my = (acy + bcy) * 0.5f;
+
+        recursiveQuadraticBezierVertices(ax, ay, mx, my, acx, acy,
+                sqrInvScaleX, sqrInvScaleY, outputVertices);
+        recursiveQuadraticBezierVertices(mx, my, bx, by, bcx, bcy,
+                sqrInvScaleX, sqrInvScaleY, outputVertices);
+    }
+}
+
+}; // namespace uirenderer
+}; // namespace android