SkPatch abstraction

src/core/SkPatch.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 "SkPatch.h"
+
+#include "SkGeometry.h"
+#include "SkColorPriv.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() { }
+    
+    /**
+     * 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);
+    }
+    
+    /**
+     * 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];
+};
+
+////////////////////////////////////////////////////////////////////////////////
+
+SkPatch::SkPatch(SkPoint points[12], SkColor colors[4]) {
+        
+    for (int i = 0; i<12; i++) {
+        fCtrlPoints[i] = points[i];
+    }
+    
+    fCornerColors[0] = SkPreMultiplyColor(colors[0]);
+    fCornerColors[1] = SkPreMultiplyColor(colors[1]);
+    fCornerColors[2] = SkPreMultiplyColor(colors[2]);
+    fCornerColors[3] = SkPreMultiplyColor(colors[3]);
+}
+
+uint8_t bilinear(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 uint8_t(a * (1.f - ty) + b * ty);
+}
+
+bool SkPatch::getVertexData(SkPatch::VertexData* data, int divisions) {
+    
+    if (divisions < 1) {
+        return false;
+    }
+    
+    int divX = divisions, divY = divisions;
+    
+    data->fVertexCount = (divX + 1) * (divY + 1);
+    data->fIndexCount = divX * divY * 6;
+
+    data->fPoints = SkNEW_ARRAY(SkPoint, data->fVertexCount);
+    data->fColors = SkNEW_ARRAY(uint32_t, data->fVertexCount);
+    data->fTexCoords = SkNEW_ARRAY(SkPoint, data->fVertexCount);
+    data->fIndices = SkNEW_ARRAY(uint16_t, data->fIndexCount);
+    
+    FwDCubicEvaluator fBottom(fCtrlPoints[kBottomP0_CubicCtrlPts],
+                              fCtrlPoints[kBottomP1_CubicCtrlPts],
+                              fCtrlPoints[kBottomP2_CubicCtrlPts],
+                              fCtrlPoints[kBottomP3_CubicCtrlPts]),
+                        fTop(fCtrlPoints[kTopP0_CubicCtrlPts],
+                             fCtrlPoints[kTopP1_CubicCtrlPts],
+                             fCtrlPoints[kTopP2_CubicCtrlPts],
+                             fCtrlPoints[kTopP2_CubicCtrlPts]),
+                        fLeft(fCtrlPoints[kLeftP0_CubicCtrlPts],
+                              fCtrlPoints[kLeftP1_CubicCtrlPts],
+                              fCtrlPoints[kLeftP2_CubicCtrlPts],
+                              fCtrlPoints[kLeftP3_CubicCtrlPts]),
+                        fRight(fCtrlPoints[kRightP0_CubicCtrlPts],
+                               fCtrlPoints[kRightP1_CubicCtrlPts],
+                               fCtrlPoints[kRightP2_CubicCtrlPts],
+                               fCtrlPoints[kRightP3_CubicCtrlPts]);
+
+    fBottom.restart(divX);
+    fTop.restart(divX);
+
+    SkScalar u = 0.0f;
+    int stride = divY + 1;
+    for (int x = 0; x <= divX; x++) {
+        SkPoint bottom = fBottom.next(), top = fTop.next();
+        fLeft.restart(divY);
+        fRight.restart(divY);
+        SkScalar v = 0.f;
+        for (int y = 0; y <= divY; y++) {
+            int dataIndex = x * (divX + 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;
+
+            uint8_t a = bilinear(u, v, 
+                            SkScalar(SkColorGetA(fCornerColors[0])), 
+                            SkScalar(SkColorGetA(fCornerColors[1])), 
+                            SkScalar(SkColorGetA(fCornerColors[2])), 
+                            SkScalar(SkColorGetA(fCornerColors[3])));
+            uint8_t r = bilinear(u, v, 
+                            SkScalar(SkColorGetR(fCornerColors[0])), 
+                            SkScalar(SkColorGetR(fCornerColors[1])), 
+                            SkScalar(SkColorGetR(fCornerColors[2])), 
+                            SkScalar(SkColorGetR(fCornerColors[3])));
+            uint8_t g = bilinear(u, v, 
+                            SkScalar(SkColorGetG(fCornerColors[0])), 
+                            SkScalar(SkColorGetG(fCornerColors[1])), 
+                            SkScalar(SkColorGetG(fCornerColors[2])), 
+                            SkScalar(SkColorGetG(fCornerColors[3])));
+            uint8_t b = bilinear(u, v, 
+                            SkScalar(SkColorGetB(fCornerColors[0])), 
+                            SkScalar(SkColorGetB(fCornerColors[1])), 
+                            SkScalar(SkColorGetB(fCornerColors[2])), 
+                            SkScalar(SkColorGetB(fCornerColors[3])));
+            data->fColors[dataIndex] = SkPackARGB32(a,r,g,b);
+            
+            data->fTexCoords[dataIndex] = SkPoint::Make(u, v);
+
+            if(x < divX && y < divY) {
+                int i = 6 * (x * divY + 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 += 1.f / divY;
+        }
+        u += 1.f / divX;
+    }
+    return true;
+}