SkCanvas::drawPatch param SkPoint[12]

src/utils/SkPatchUtils.cpp

 /*
  * Copyright 2014 Google Inc.
  *
  * Use of this source code is governed by a BSD-style license that can be
  * found in the LICENSE file.
  */
 
 #include "SkPatchUtils.h"
 
+#include "SkColorPriv.h"
+#include "SkGeometry.h"
+
+/**
+ * Evaluator to sample the values of a cubic bezier using forward differences.
+ * Forward differences is a method for evaluating a nth degree polynomial at a uniform step by only
+ * adding precalculated values.
+ * For a linear example we have the function f(t) = m*t+b, then the value of that function at t+h
+ * would be f(t+h) = m*(t+h)+b. If we want to know the uniform step that we must add to the first
+ * evaluation f(t) then we need to substract f(t+h) - f(t) = m*t + m*h + b - m*t + b = mh. After
+ * obtaining this value (mh) we could just add this constant step to our first sampled point
+ * to compute the next one.
+ *
+ * For the cubic case the first difference gives as a result a quadratic polynomial to which we can
+ * apply again forward differences and get linear function to which we can apply again forward
+ * differences to get a constant difference. This is why we keep an array of size 4, the 0th
+ * position keeps the sampled value while the next ones keep the quadratic, linear and constant
+ * difference values.
+ */
+
+class FwDCubicEvaluator {
+    
+public:
+    FwDCubicEvaluator()
+    : fMax(0)
+    , fCurrent(0)
+    , fDivisions(0) {
+        memset(fPoints, 0, 4 * sizeof(SkPoint));
+        memset(fPoints, 0, 4 * sizeof(SkPoint));
+        memset(fPoints, 0, 4 * sizeof(SkPoint));
+    }
+    
+    /**
+     * Receives the 4 control points of the cubic bezier.
+     */
+    FwDCubicEvaluator(SkPoint a, SkPoint b, SkPoint c, SkPoint d) {
+        fPoints[0] = a;
+        fPoints[1] = b;
+        fPoints[2] = c;
+        fPoints[3] = d;
+        
+        SkScalar cx[4], cy[4];
+        SkGetCubicCoeff(fPoints, cx, cy);
+        fCoefs[0].set(cx[0], cy[0]);
+        fCoefs[1].set(cx[1], cy[1]);
+        fCoefs[2].set(cx[2], cy[2]);
+        fCoefs[3].set(cx[3], cy[3]);
+        
+        this->restart(1);
+    }
+    
+    explicit FwDCubicEvaluator(const SkPoint points[4])  {
+        memcpy(fPoints, points, 4 * sizeof(SkPoint));
+        
+        SkScalar cx[4], cy[4];
+        SkGetCubicCoeff(fPoints, cx, cy);
+        fCoefs[0].set(cx[0], cy[0]);
+        fCoefs[1].set(cx[1], cy[1]);
+        fCoefs[2].set(cx[2], cy[2]);
+        fCoefs[3].set(cx[3], cy[3]);
+        
+        this->restart(1);
+    }
+    
+    /**
+     * Restarts the forward differences evaluator to the first value of t = 0.
+     */
+    void restart(int divisions)  {
+        fDivisions = divisions;
+        SkScalar h  = 1.f / fDivisions;
+        fCurrent    = 0;
+        fMax        = fDivisions + 1;
+        fFwDiff[0]  = fCoefs[3];
+        SkScalar h2 = h * h;
+        SkScalar h3 = h2 * h;
+        
+        fFwDiff[3].set(6.f * fCoefs[0].x() * h3, 6.f * fCoefs[0].y() * h3); //6ah^3
+        fFwDiff[2].set(fFwDiff[3].x() + 2.f * fCoefs[1].x() * h2, //6ah^3 + 2bh^2
+                       fFwDiff[3].y() + 2.f * fCoefs[1].y() * h2);
+        fFwDiff[1].set(fCoefs[0].x() * h3 + fCoefs[1].x() * h2 + fCoefs[2].x() * h,//ah^3 + bh^2 +ch
+                       fCoefs[0].y() * h3 + fCoefs[1].y() * h2 + fCoefs[2].y() * h);
+    }
+    
+    /**
+     * Check if the evaluator is still within the range of 0<=t<=1
+     */
+    bool done() const {
+        return fCurrent > fMax;
+    }
+    
+    /**
+     * Call next to obtain the SkPoint sampled and move to the next one.
+     */
+    SkPoint next() {
+        SkPoint point = fFwDiff[0];
+        fFwDiff[0]    += fFwDiff[1];
+        fFwDiff[1]    += fFwDiff[2];
+        fFwDiff[2]    += fFwDiff[3];
+        fCurrent++;
+        return point;
+    }
+    
+    const SkPoint* getCtrlPoints() const {
+        return fPoints;
+    }
+    
+private:
+    int fMax, fCurrent, fDivisions;
+    SkPoint fFwDiff[4], fCoefs[4], fPoints[4];
+};
+
+////////////////////////////////////////////////////////////////////////////////
+
 // size in pixels of each partition per axis, adjust this knob
-static const int kPartitionSize = 15;
+static const int kPartitionSize = 10;
 
 /**
  * Calculate the approximate arc length given a bezier curve's control points.
  */
 static SkScalar approx_arc_length(SkPoint* points, int count) {
     if (count < 2) {
         return 0;
     }
     SkScalar arcLength = 0;
     for (int i = 0; i < count - 1; i++) {
         arcLength += SkPoint::Distance(points[i], points[i + 1]);
     }
     return arcLength;
 }
 
-SkISize SkPatchUtils::GetLevelOfDetail(const SkPatch& patch, const SkMatrix* matrix) {
-    
-    SkPoint mapPts[12];
-    matrix->mapPoints(mapPts, patch.getControlPoints(), 12);
+static SkScalar bilerp(SkScalar tx, SkScalar ty, SkScalar c00, SkScalar c10, SkScalar c01,
+                      SkScalar c11) {
+    SkScalar a = c00 * (1.f - tx) + c10 * tx;
+    SkScalar b = c01 * (1.f - tx) + c11 * tx;
+    return a * (1.f - ty) + b * ty;
+}
+
+SkISize SkPatchUtils::GetLevelOfDetail(const SkPoint cubics[12], const SkMatrix* matrix) {
     
     // Approximate length of each cubic.
-    SkPoint pts[4];
-    patch.getTopPoints(pts);
-    matrix->mapPoints(pts, 4);
-    SkScalar topLength = approx_arc_length(pts, 4);
+    SkPoint pts[kNumPtsCubic];
+    SkPatchUtils::getTopCubic(cubics, pts);
+    matrix->mapPoints(pts, kNumPtsCubic);
+    SkScalar topLength = approx_arc_length(pts, kNumPtsCubic);
     
-    patch.getBottomPoints(pts);
-    matrix->mapPoints(pts, 4);
-    SkScalar bottomLength = approx_arc_length(pts, 4);
+    SkPatchUtils::getBottomCubic(cubics, pts);
+    matrix->mapPoints(pts, kNumPtsCubic);
+    SkScalar bottomLength = approx_arc_length(pts, kNumPtsCubic);
     
-    patch.getLeftPoints(pts);
-    matrix->mapPoints(pts, 4);
-    SkScalar leftLength = approx_arc_length(pts, 4);
+    SkPatchUtils::getLeftCubic(cubics, pts);
+    matrix->mapPoints(pts, kNumPtsCubic);
+    SkScalar leftLength = approx_arc_length(pts, kNumPtsCubic);
     
-    patch.getRightPoints(pts);
-    matrix->mapPoints(pts, 4);
-    SkScalar rightLength = approx_arc_length(pts, 4);
+    SkPatchUtils::getRightCubic(cubics, pts);
+    matrix->mapPoints(pts, kNumPtsCubic);
+    SkScalar rightLength = approx_arc_length(pts, kNumPtsCubic);
     
     // Level of detail per axis, based on the larger side between top and bottom or left and right
     int lodX = static_cast<int>(SkMaxScalar(topLength, bottomLength) / kPartitionSize);
     int lodY = static_cast<int>(SkMaxScalar(leftLength, rightLength) / kPartitionSize);
     
-    return SkISize::Make(SkMax32(4, lodX), SkMax32(4, lodY));
+    return SkISize::Make(SkMax32(8, lodX), SkMax32(8, lodY));
 }
+
+void SkPatchUtils::getTopCubic(const SkPoint cubics[12], SkPoint points[4]) {
+    points[0] = cubics[kTopP0_CubicCtrlPts];
+    points[1] = cubics[kTopP1_CubicCtrlPts];
+    points[2] = cubics[kTopP2_CubicCtrlPts];
+    points[3] = cubics[kTopP3_CubicCtrlPts];
+}
+
+void SkPatchUtils::getBottomCubic(const SkPoint cubics[12], SkPoint points[4]) {
+    points[0] = cubics[kBottomP0_CubicCtrlPts];
+    points[1] = cubics[kBottomP1_CubicCtrlPts];
+    points[2] = cubics[kBottomP2_CubicCtrlPts];
+    points[3] = cubics[kBottomP3_CubicCtrlPts];
+}
+
+void SkPatchUtils::getLeftCubic(const SkPoint cubics[12], SkPoint points[4]) {
+    points[0] = cubics[kLeftP0_CubicCtrlPts];
+    points[1] = cubics[kLeftP1_CubicCtrlPts];
+    points[2] = cubics[kLeftP2_CubicCtrlPts];
+    points[3] = cubics[kLeftP3_CubicCtrlPts];
+}
+
+void SkPatchUtils::getRightCubic(const SkPoint cubics[12], SkPoint points[4]) {
+    points[0] = cubics[kRightP0_CubicCtrlPts];
+    points[1] = cubics[kRightP1_CubicCtrlPts];
+    points[2] = cubics[kRightP2_CubicCtrlPts];
+    points[3] = cubics[kRightP3_CubicCtrlPts];
+}
+
+bool SkPatchUtils::getVertexData(SkPatchUtils::VertexData* data, const SkPoint cubics[12],
+                   const SkColor colors[4], const SkPoint texCoords[4], int lodX, int lodY) {
+    if (lodX < 1 || lodY < 1 || NULL == cubics || NULL == data) {
+        return false;
+    }
+    
+    // number of indices is limited by size of uint16_t, so we clamp it to avoid overflow
+    data->fVertexCount = SkMin32((lodX + 1) * (lodY + 1), 65536);
+    lodX  = SkMin32(lodX, 255);
+    lodY  = SkMin32(lodY, 255);
+    data->fIndexCount = lodX * lodY * 6;
+    
+    data->fPoints = SkNEW_ARRAY(SkPoint, data->fVertexCount);
+    data->fIndices = SkNEW_ARRAY(uint16_t, data->fIndexCount);
+    
+    // if colors is not null then create array for colors
+    SkPMColor colorsPM[kNumCorners];
+    if (NULL != colors) {
+        // premultiply colors to avoid color bleeding.
+        for (int i = 0; i < kNumCorners; i++) {
+            colorsPM[i] = SkPreMultiplyColor(colors[i]);
+        }
+        data->fColors = SkNEW_ARRAY(uint32_t, data->fVertexCount);
+    }
+    
+    // if texture coordinates are not null then create array for them
+    if (NULL != texCoords) {
+        data->fTexCoords = SkNEW_ARRAY(SkPoint, data->fVertexCount);
+    }
+    
+    SkPoint pts[kNumPtsCubic];
+    SkPatchUtils::getBottomCubic(cubics, pts);
+    FwDCubicEvaluator fBottom(pts);
+    SkPatchUtils::getTopCubic(cubics, pts);
+    FwDCubicEvaluator fTop(pts);
+    SkPatchUtils::getLeftCubic(cubics, pts);
+    FwDCubicEvaluator fLeft(pts);
+    SkPatchUtils::getRightCubic(cubics, pts);
+    FwDCubicEvaluator fRight(pts);
+    
+    fBottom.restart(lodX);
+    fTop.restart(lodX);
+    
+    SkScalar u = 0.0f;
+    int stride = lodY + 1;
+    for (int x = 0; x <= lodX; x++) {
+        SkPoint bottom = fBottom.next(), top = fTop.next();
+        fLeft.restart(lodY);
+        fRight.restart(lodY);
+        SkScalar v = 0.f;
+        for (int y = 0; y <= lodY; y++) {
+            int dataIndex = x * (lodY + 1) + y;
+            
+            SkPoint left = fLeft.next(), right = fRight.next();
+            
+            SkPoint s0 = SkPoint::Make((1.0f - v) * top.x() + v * bottom.x(),
+                                       (1.0f - v) * top.y() + v * bottom.y());
+            SkPoint s1 = SkPoint::Make((1.0f - u) * left.x() + u * right.x(),
+                                       (1.0f - u) * left.y() + u * right.y());
+            SkPoint s2 = SkPoint::Make(
+                                       (1.0f - v) * ((1.0f - u) * fTop.getCtrlPoints()[0].x()
+                                                     + u * fTop.getCtrlPoints()[3].x())
+                                       + v * ((1.0f - u) * fBottom.getCtrlPoints()[0].x()
+                                              + u * fBottom.getCtrlPoints()[3].x()),
+                                       (1.0f - v) * ((1.0f - u) * fTop.getCtrlPoints()[0].y()
+                                                     + u * fTop.getCtrlPoints()[3].y())
+                                       + v * ((1.0f - u) * fBottom.getCtrlPoints()[0].y()
+                                              + u * fBottom.getCtrlPoints()[3].y()));
+            data->fPoints[dataIndex] = s0 + s1 - s2;
+            
+            if (NULL != colors) {
+                uint8_t a = uint8_t(bilerp(u, v,
+                                   SkScalar(SkColorGetA(colorsPM[kTopLeft_Corner])),
+                                   SkScalar(SkColorGetA(colorsPM[kTopRight_Corner])),
+                                   SkScalar(SkColorGetA(colorsPM[kBottomLeft_Corner])),
+                                   SkScalar(SkColorGetA(colorsPM[kBottomRight_Corner]))));
+                uint8_t r = uint8_t(bilerp(u, v,
+                                   SkScalar(SkColorGetR(colorsPM[kTopLeft_Corner])),
+                                   SkScalar(SkColorGetR(colorsPM[kTopRight_Corner])),
+                                   SkScalar(SkColorGetR(colorsPM[kBottomLeft_Corner])),
+                                   SkScalar(SkColorGetR(colorsPM[kBottomRight_Corner]))));
+                uint8_t g = uint8_t(bilerp(u, v,
+                                   SkScalar(SkColorGetG(colorsPM[kTopLeft_Corner])),
+                                   SkScalar(SkColorGetG(colorsPM[kTopRight_Corner])),
+                                   SkScalar(SkColorGetG(colorsPM[kBottomLeft_Corner])),
+                                   SkScalar(SkColorGetG(colorsPM[kBottomRight_Corner]))));
+                uint8_t b = uint8_t(bilerp(u, v,
+                                   SkScalar(SkColorGetB(colorsPM[kTopLeft_Corner])),
+                                   SkScalar(SkColorGetB(colorsPM[kTopRight_Corner])),
+                                   SkScalar(SkColorGetB(colorsPM[kBottomLeft_Corner])),
+                                   SkScalar(SkColorGetB(colorsPM[kBottomRight_Corner]))));
+                data->fColors[dataIndex] = SkPackARGB32(a,r,g,b);
+            }
+            
+            if (NULL != texCoords) {
+                data->fTexCoords[dataIndex] = SkPoint::Make(
+                                            bilerp(u, v, texCoords[kTopLeft_Corner].x(),
+                                                   texCoords[kTopRight_Corner].x(),
+                                                   texCoords[kBottomLeft_Corner].x(),
+                                                   texCoords[kBottomRight_Corner].x()),
+                                            bilerp(u, v, texCoords[kTopLeft_Corner].y(),
+                                                   texCoords[kTopRight_Corner].y(),
+                                                   texCoords[kBottomLeft_Corner].y(),
+                                                   texCoords[kBottomRight_Corner].y()));
+                
+            }
+            
+            if(x < lodX && y < lodY) {
+                int i = 6 * (x * lodY + y);
+                data->fIndices[i] = x * stride + y;
+                data->fIndices[i + 1] = x * stride + 1 + y;
+                data->fIndices[i + 2] = (x + 1) * stride + 1 + y;
+                data->fIndices[i + 3] = data->fIndices[i];
+                data->fIndices[i + 4] = data->fIndices[i + 2];
+                data->fIndices[i + 5] = (x + 1) * stride + y;
+            }
+            v = SkScalarClampMax(v + 1.f / lodY, 1);
+        }
+        u = SkScalarClampMax(u + 1.f / lodX, 1);
+    }
+    return true;
+
+}