Add initial CurveMeasure code

src/utils/SkCurveMeasure.h

+/*
+ * Copyright 2016 Google Inc.
+ *
+ * Use of this source code is governed by a BSD-style license that can be
+ * found in the LICENSE file.
+ */
+
+#ifndef SkCurveMeasure_DEFINED
+#define SkCurveMeasure_DEFINED
+
+#include "SkPoint.h"
+#include "SkNx.h"
+
+
+// These are weights and abscissae for gaussian quadrature with weight function w(x) = 1
+static SkScalar weights8[8] = {0.3626837833783620f, 0.3626837833783620f, 0.3137066458778873f, 0.3137066458778873f, 0.2223810344533745f, 0.2223810344533745f, 0.1012285362903763f, 0.1012285362903763f};
+static SkScalar absc8[8] = {-0.1834346424956498f, 0.1834346424956498f, -0.5255324099163290f, 0.5255324099163290f, -0.7966664774136267f, 0.7966664774136267f, -0.9602898564975363f, 0.9602898564975363f};
+
+static Sk8f weights = Sk8f::Load(weights8);
+static Sk8f absc = 0.5f*(Sk8f::Load(absc8) + 1.0f);
+
+
+// this is the same enum as in SkPathMeasure but it doesn't have a name there
+enum SkSegType {
+    kLine_SegType,
+    kQuad_SegType,
+    kCubic_SegType,
+    kConic_SegType,
+};
+
+class ArcLengthIntegrator {
+   public:
+    ArcLengthIntegrator() {}
+    ArcLengthIntegrator(const SkPoint* pts, SkSegType segType);
+    SkScalar computeLength(SkScalar t);
+
+   private:
+    Sk8f evaluateDerivativeLength(Sk8f ts);
+
+    SkSegType fSegType;
+
+    // TODO(hstern) make some generic things like fCoeff1x, fCoeff1y, fCoeff2x, etc.
+    // which are opaque and shared between the different curve types. Or use an array.
+    // Either way, fill in inside the constructor.
+
+    // precomputed quad coeffs for derivative
+    Sk8f A2BC_x, A2BC_y;
+    Sk8f AB_x, AB_y;
+};
+
+class SkCurveMeasure {
+   public:
+    SkCurveMeasure() {}
+    SkCurveMeasure(const SkPoint* pts, SkSegType segType);
+
+    SkScalar getTime(SkScalar targetLength);
+    void getPosTan(SkScalar distance, SkPoint* pos, SkVector* tan);
+    SkScalar getLength();
+   private:
+    SkPoint evaluateQuad(SkScalar t);
+    SkVector evaluateQuadDerivative(SkScalar t);
+    //SkPoint evaluate_cubic(SkScalar t);
+    //SkVector evaluate_cubic_derivative(SkScalar t);
+    //SkPoint evaluate_conic(SkScalar t);
+    //SkVector evaluate_conic_derivative(SkScalar t);
+
+    const SkScalar kTolerance = 0.0001f;
+    const int kNewtonIters = 5;
+    const int kBisectIters = 5;
+
+    SkSegType fSegType;
+    SkPoint fPts[4];
+    SkScalar fLength = -1.0f;
+    ArcLengthIntegrator fIntegrator;
+
+    // for debug purposes
+    int fIters;
+};
+
+#endif // SkCurveMeasure_DEFINED