Add an interface to the Path to support constructing Path using SVG

include/tgfx/core/Path.h

@@ -162,6 +162,28 @@ class Path {
    */
   void cubicTo(const Point& control1, const Point& control2, const Point& point);
 
+  /**
+   * Appends an arc to the Path. The arc is represented by one or more conic sections that describe
+   * part of an oval with radii (rx, ry) rotated by xAxisRotate degrees. The arc curves from the 
+   * last point in the Path to (x, y), choosing one of four possible routes: clockwise or 
+   * counterclockwise, and smaller or larger.
+   * The arc sweep is always less than 360 degrees. If either radius is zero, or if the last point 
+   * in the Path equals (x, y), a line to (x, y) is appended instead. If both radii are greater 
+   * than zero but too small to fit the arc, they are scaled to fit.
+   * This method appends up to four conic curves to represent the arc.
+   * It implements the functionality of the SVG arc, although the SVG sweep-flag value is the 
+   * opposite of the integer value of the sweep parameter; SVG uses 1 for clockwise, while 
+   * counterclockwise is represented by zero.
+   * 
+   * @param rx            x radius before x-axis rotation
+   * @param ry            y radius before x-axis rotation
+   * @param xAxisRotate   x-axis rotation in degrees; positive values are clockwise
+   * @param largeArc      chooses the larger or smaller arc
+   * @param reversed      chooses the rotation direction; false for clockwise
+   * @param endPoint      end point of the arc
+   */
+  void arcTo(float rx, float ry, float xAxisRotate, PathArcSize largeArc, bool reversed,
+             Point endPoint);
   /**
    * Closes the current contour of Path. A closed contour connects the first and last Point with
    * line, forming a continuous loop.
@@ -287,6 +309,11 @@ class Path {
    */
   int countVerbs() const;
 
+  /**
+   * Returns last point on Path in lastPoint. Returns false if point array is empty.
+   */
+  bool getLastPoint(Point* lastPoint) const;
+
  private:
   std::shared_ptr<PathRef> pathRef = nullptr;
 

include/tgfx/core/PathTypes.h

@@ -96,6 +96,20 @@ enum class PathVerb {
   Close
 };
 
+/**
+ * Specify whether the arc is greater than 180 degrees pair or less than 180 degrees pair.
+ */
+enum class PathArcSize : uint8_t {
+  /**
+   * smaller of arc pair
+   */
+  Small,
+  /**
+   * larger of arc pair
+   */
+  Large,
+};
+
 /**
  * Zero to four Point are stored in points, depending on the returned PathVerb
  */

include/tgfx/core/Point.h

@@ -60,14 +60,14 @@ struct Point {
   }
 
   /**
-   * Returns true if fX and fY are both zero.
+   * Returns true if x and y are both zero.
    */
   bool isZero() const {
     return (0 == x) && (0 == y);
   }
 
   /**
-   * Sets fX to x and fY to y.
+   * Sets x to xValue and y to yValue.
    */
   void set(float xValue, float yValue) {
     x = xValue;
@@ -104,20 +104,52 @@ struct Point {
   }
 
   /**
-   * Returns a Point from b to a; computed as (a.fX - b.fX, a.fY - b.fY).
+   * Returns a Point from b to a; computed as (a.x - b.x, a.y - b.y).
    */
   friend Point operator-(const Point& a, const Point& b) {
     return {a.x - b.x, a.y - b.y};
   }
 
+  /** 
+    * Subtracts vector Point v from Point. Sets Point to: (x - v.x, y - v.y).
+    */
+  void operator-=(const Point& v) {
+    x -= v.x;
+    y -= v.y;
+  }
+
   /**
    * Returns Point resulting from Point a offset by Point b, computed as:
-   * (a.fX + b.fX, a.fY + b.fY).
+   * (a.x + b.x, a.y + b.y).
    */
   friend Point operator+(const Point& a, const Point& b) {
     return {a.x + b.x, a.y + b.y};
   }
 
+  /** 
+    * offset vector point v from Point. Sets Point to: (x + v.x, y + v.y).
+    */
+  void operator+=(const Point& v) {
+    x += v.x;
+    y += v.y;
+  }
+
+  /** 
+    * Returns Point multiplied by scale.
+    * (x * scale, y * scale)
+    */
+  friend Point operator*(const Point& p, float scale) {
+    return {p.x * scale, p.y * scale};
+  }
+
+  /** 
+    * Multiplies Point by scale. Sets Point to: (x * scale, y * scale).
+    */
+  void operator*=(float scale) {
+    x *= scale;
+    y *= scale;
+  }
+
   /**
    * Returns the Euclidean distance from origin.
    */

src/core/Path.cpp

@@ -215,6 +215,133 @@ void Path::cubicTo(const Point& control1, const Point& control2, const Point& po
   cubicTo(control1.x, control1.y, control2.x, control2.y, point.x, point.y);
 }
 
+// This converts the SVG arc to conics based on the SVG standard.
+// Code source:
+// 1. kdelibs/kdecore/svgicons Niko's code
+// 2. webkit/chrome SVGPathNormalizer::decomposeArcToCubic()
+// See also SVG implementation notes:
+// http://www.w3.org/TR/SVG/implnote.html#ArcConversionEndpointToCenter
+// Note that arcSweep bool value is flipped from the original implementation.
+void Path::arcTo(float rx, float ry, float xAxisRotate, PathArcSize largeArc, bool reversed,
+                 Point endPoint) {
+  std::array<Point, 2> srcPoints;
+  this->getLastPoint(&srcPoints[0]);
+  // If rx = 0 or ry = 0 then this arc is treated as a straight line segment (a "lineto")
+  // joining the endpoints.
+  // http://www.w3.org/TR/SVG/implnote.html#ArcOutOfRangeParameters
+  if (FloatNearlyZero(rx) && FloatNearlyZero(ry)) {
+    return this->lineTo(endPoint);
+  }
+  // If the current point and target point for the arc are identical, it should be treated as a
+  // zero length path. This ensures continuity in animations.
+  srcPoints[1] = endPoint;
+  if (srcPoints[0] == srcPoints[1]) {
+    return this->lineTo(endPoint);
+  }
+  rx = std::abs(rx);
+  ry = std::abs(ry);
+  auto midPointDistance = (srcPoints[0] - srcPoints[1]) * 0.5f;
+
+  auto pointTransform = Matrix::MakeRotate(-xAxisRotate);
+  auto transformedMidPoint = Point::Zero();
+  pointTransform.mapPoints(&transformedMidPoint, &midPointDistance, 1);
+  auto squareRx = rx * rx;
+  auto squareRy = ry * ry;
+  auto squareX = transformedMidPoint.x * transformedMidPoint.x;
+  auto squareY = transformedMidPoint.y * transformedMidPoint.y;
+
+  // Check if the radii are big enough to draw the arc, scale radii if not.
+  // http://www.w3.org/TR/SVG/implnote.html#ArcCorrectionOutOfRangeRadii
+  auto radiiScale = squareX / squareRx + squareY / squareRy;
+  if (radiiScale > 1) {
+    radiiScale = std::sqrt(radiiScale);
+    rx *= radiiScale;
+    ry *= radiiScale;
+  }
+
+  pointTransform.setScale(1.0f / rx, 1.0f / ry);
+  pointTransform.preRotate(-xAxisRotate);
+
+  std::array<Point, 2> unitPoints;
+  pointTransform.mapPoints(unitPoints.data(), srcPoints.data(), unitPoints.size());
+  auto delta = unitPoints[1] - unitPoints[0];
+
+  auto d = delta.x * delta.x + delta.y * delta.y;
+  auto scaleFactorSquared = std::max(1 / d - 0.25f, 0.f);
+
+  auto scaleFactor = std::sqrt(scaleFactorSquared);
+  if (reversed != static_cast<bool>(largeArc)) {  // flipped from the original implementation
+    scaleFactor = -scaleFactor;
+  }
+  delta *= scaleFactor;
+  auto centerPoint = unitPoints[0] + unitPoints[1];
+  centerPoint *= 0.5f;
+  centerPoint.offset(-delta.y, delta.x);
+  unitPoints[0] -= centerPoint;
+  unitPoints[1] -= centerPoint;
+  auto theta1 = std::atan2(unitPoints[0].y, unitPoints[0].x);
+  auto theta2 = std::atan2(unitPoints[1].y, unitPoints[1].x);
+  auto thetaArc = theta2 - theta1;
+  if (thetaArc < 0 && !reversed) {  // arcSweep flipped from the original implementation
+    thetaArc += M_PI_F * 2.0f;
+  } else if (thetaArc > 0 && reversed) {  // arcSweep flipped from the original implementation
+    thetaArc -= M_PI_F * 2.0f;
+  }
+
+  // Very tiny angles cause our subsequent math to go wonky
+  // but a larger value is probably ok too.
+  if (std::abs(thetaArc) < (M_PI_F / (1000 * 1000))) {
+    return this->lineTo(endPoint);
+  }
+
+  pointTransform.setRotate(xAxisRotate);
+  pointTransform.preScale(rx, ry);
+
+  // the arc may be slightly bigger than 1/4 circle, so allow up to 1/3rd
+  auto segments = std::ceil(std::abs(thetaArc / (2 * M_PI_F / 3)));
+  auto thetaWidth = thetaArc / segments;
+  auto t = std::tan(0.5f * thetaWidth);
+  if (!FloatsAreFinite(&t, 1)) {
+    return;
+  }
+  auto startTheta = theta1;
+  auto conicW = std::sqrt(0.5f + std::cos(thetaWidth) * 0.5f);
+  auto float_is_integer = [](float scalar) -> bool { return scalar == std::floor(scalar); };
+  auto expectIntegers = FloatNearlyZero(M_PI_F * 0.5f - std::abs(thetaWidth)) &&
+                        float_is_integer(rx) && float_is_integer(ry) &&
+                        float_is_integer(endPoint.x) && float_is_integer(endPoint.y);
+
+  auto* path = &(writableRef()->path);
+  for (int i = 0; i < static_cast<int>(segments); ++i) {
+    auto endTheta = startTheta + thetaWidth;
+    auto sinEndTheta = SinSnapToZero(endTheta);
+    auto cosEndTheta = CosSnapToZero(endTheta);
+
+    unitPoints[1].set(cosEndTheta, sinEndTheta);
+    unitPoints[1] += centerPoint;
+    unitPoints[0] = unitPoints[1];
+    unitPoints[0].offset(t * sinEndTheta, -t * cosEndTheta);
+    std::array<Point, 2> mapped;
+    pointTransform.mapPoints(mapped.data(), unitPoints.data(), unitPoints.size());
+
+    // Computing the arc width introduces rounding errors that cause arcs to start outside their
+    // marks.A round rect may lose convexity as a result.If the input values are on integers,
+    // place the conic on integers as well.
+    if (expectIntegers) {
+      for (auto& point : mapped) {
+        point.x = std::round(point.x);
+        point.y = std::round(point.y);
+      }
+    }
+    path->conicTo(mapped[0].x, mapped[0].y, mapped[1].x, mapped[1].y, conicW);
+    startTheta = endTheta;
+  }
+
+  // The final point should match the input point (by definition); replace it to
+  // ensure that rounding errors in the above math don't cause any problems.
+  path->setLastPt(endPoint.x, endPoint.y);
+}
+
 void Path::close() {
   writableRef()->path.close();
 }
@@ -415,4 +542,17 @@ int Path::countPoints() const {
 int Path::countVerbs() const {
   return pathRef->path.countVerbs();
 }
+
+bool Path::getLastPoint(Point* lastPoint) const {
+  if (!lastPoint) {
+    return false;
+  }
+  auto skPoint = SkPoint::Make(0, 0);
+  if (pathRef->path.getLastPt(&skPoint)) {
+    lastPoint->set(skPoint.fX, skPoint.fY);
+    return true;
+  }
+  return false;
+};
+
 }  // namespace tgfx