Implement Conics in SkCurveMeasure

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 "SkPathMeasurePriv.h"
 #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 const SkScalar weights8[8] = {0.3626837833783620f, 0.3626837833783620f,
+                                     0.3137066458778873f, 0.3137066458778873f,
+                                     0.2223810344533745f, 0.2223810344533745f,
+                                     0.1012285362903763f, 0.1012285362903763f};
+static const 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);
+static const Sk8f weights = Sk8f::Load(weights8);
+static const Sk8f absc = 0.5f*(Sk8f::Load(absc8) + 1.0f);
 
+/* Currently this uses Gaussian quadrature with a fixed number of
+ * evaluation points (see above weights and abscissae) but in principle
+ * we could have a table of abscissae and weights and choose which to use
+ * based on an approximation of the max length of the curve.
+ *
+ * We should always use some power of 2 number of evaluation points so that
+ * the SkNx templates will compile down into SIMD-register-aligned blocks.
+ */
 
 class ArcLengthIntegrator {
 public:
     ArcLengthIntegrator() {}
     ArcLengthIntegrator(const SkPoint* pts, SkSegType segType);
     SkScalar computeLength(SkScalar t);
 
 private:
     SkSegType fSegType;
 
     // precomputed coefficients for derivatives in Horner form
-    Sk8f xCoeff[3];
-    Sk8f yCoeff[3];
+    Sk8f fXCoeff[3];
+    Sk8f fYCoeff[3];
+
+    SkScalar fConicW = 0;
 };
 
 class SkCurveMeasure {
 public:
-    SkCurveMeasure() {}
-
     // Almost exactly the same as in SkPath::Iter:
     // kLine_SegType  -> 2 points: start end
     // kQuad_SegType  -> 3 points: start control end
     // kCubic_SegType -> 4 points: start control1 control2 end
     // kConic_SegType -> 4 points: start control end (w, w)
     //
     // i.e. the only difference is that the conic's last point is a point
     // consisting of the w value twice
     SkCurveMeasure(const SkPoint* pts, SkSegType segType);
 
     SkScalar getTime(SkScalar targetLength);
     void getPosTanTime(SkScalar distance, SkPoint* pos, SkVector* tan, SkScalar* time);
     SkScalar getLength();
 
 private:
-    const SkScalar kTolerance = 0.0001f;
-    const int kNewtonIters = 5;
-    const int kBisectIters = 5;
+    static constexpr SkScalar kTolerance = 0.0001f;
+    static const int kNewtonIters = 5;
+    static const int kBisectIters = 5;
 
     SkSegType fSegType;
     SkPoint fPts[4];
     SkScalar fLength = -1.0f;
     ArcLengthIntegrator fIntegrator;
 
     // for debug purposes
     int fIters;
 };
 
 #endif  // SkCurveMeasure_DEFINED