LibrePCB

/*
 * LibrePCB - Professional EDA for everyone!
 * Copyright (C) 2013 LibrePCB Developers, see AUTHORS.md for contributors.
 * https://librepcb.org/
 *
 * This program is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program.  If not, see <http://www.gnu.org/licenses/>.
 */

/*******************************************************************************
 *  Includes
 ******************************************************************************/
#include "path.h"

#include "../serialization/sexpression.h"
#include "../utils/toolbox.h"

#include <QtCore>

#include <algorithm>

/*******************************************************************************
 *  Namespace
 ******************************************************************************/
namespace librepcb {

/*******************************************************************************
 *  Constructors / Destructor
 ******************************************************************************/

Path::Path(const Path& other) noexcept
  : mVertices(other.mVertices), mPainterPathPx(other.mPainterPathPx) {
}

Path::Path(const SExpression& node) {
  foreach (const SExpression* child, node.getChildren("vertex")) {
    mVertices.append(Vertex(*child));
  }
}

/*******************************************************************************
 *  Getters
 ******************************************************************************/

bool Path::isClosed() const noexcept {
  if (mVertices.count() >= 2) {
    return (mVertices.first().getPos() == mVertices.last().getPos());
  } else {
    return false;
  }
}

bool Path::isCurved() const noexcept {
  // Angle of last vertex is not relevant!
  for (int i = 0; i < (mVertices.count() - 1); ++i) {
    if (mVertices.at(i).getAngle() != Angle::deg0()) {
      return true;
    }
  }
  return false;
}

bool Path::isZeroLength() const noexcept {
  if (mVertices.count() < 2) {
    return true;
  }

  for (int i = 1; i < mVertices.count(); ++i) {
    if (mVertices.at(i).getPos() != mVertices.first().getPos()) {
      return false;
    }
  }
  return true;
}

bool Path::isOnGrid(const PositiveLength& gridInterval) const noexcept {
  for (const auto& v : mVertices) {
    if (!v.getPos().isOnGrid(gridInterval)) {
      return false;
    }
  }
  return true;
}

UnsignedLength Path::getTotalStraightLength() const noexcept {
  UnsignedLength length(0);
  if (mVertices.count() >= 2) {
    Point lastPos = mVertices.first().getPos();
    for (int i = 1; i < mVertices.count(); ++i) {
      const Point& pos = mVertices.at(i).getPos();
      length += (pos - lastPos).getLength();
      lastPos = pos;
    }
  }
  return length;
}

qreal Path::calcAreaOfStraightSegments() const noexcept {
  // https://en.wikipedia.org/wiki/Shoelace_formula
  // https://www.geeksforgeeks.org/area-of-a-polygon-with-given-n-ordered-vertices/
  qreal area = 0;
  const int n = isClosed() ? (mVertices.count() - 1) : mVertices.count();
  int j = n - 1;
  for (int i = 0; i < n; ++i) {
    const QPointF pj = mVertices.at(j).getPos().toMmQPointF();
    const QPointF pi = mVertices.at(i).getPos().toMmQPointF();
    area += (pj.x() + pi.x()) * (pj.y() - pi.y());
    j = i;
  }
  return std::abs(area / 2);
}

Point Path::calcNearestPointBetweenVertices(const Point& p) const noexcept {
  if (!mVertices.isEmpty()) {
    // Note: Does not take arcs into account yet.
    Point nearest = mVertices.first().getPos();
    for (int i = 1; i < mVertices.count(); ++i) {
      Point tmp = Toolbox::nearestPointOnLine(p, mVertices.at(i - 1).getPos(),
                                              mVertices.at(i).getPos());
      if ((tmp - p).getLength() < (nearest - p).getLength()) {
        nearest = tmp;
      }
    }
    return nearest;
  } else {
    return Point();
  }
}

Path Path::cleaned() const noexcept {
  Path p(*this);
  p.clean();
  return p;
}

Path Path::toClosedPath() const noexcept {
  Path p(*this);
  p.close();
  return p;
}

Path Path::toOpenPath() const noexcept {
  Path p(*this);
  p.open();
  return p;
}

QVector<Path> Path::toOutlineStrokes(
    const PositiveLength& width) const noexcept {
  QVector<Path> paths;
  paths.reserve(mVertices.count());
  if (mVertices.count() == 1) {
    paths.append(circle(width).translated(mVertices.first().getPos()));
  } else {
    for (int i = 1; i < mVertices.count(); ++i) {  // skip first vertex!
      const Vertex& v = mVertices.at(i);
      const Vertex& v0 = mVertices.at(i - 1);
      if (v0.getAngle() == 0) {
        paths.append(obround(v0.getPos(), v.getPos(), width));
      } else {
        paths.append(arcObround(v0.getPos(), v.getPos(), v0.getAngle(), width));
      }
    }
  }
  return paths;
}

const QPainterPath& Path::toQPainterPathPx() const noexcept {
  if (mPainterPathPx.isEmpty()) {
    for (int i = 0; i < mVertices.count(); ++i) {
      const Vertex& v = mVertices.at(i);
      if (i == 0) {
        mPainterPathPx.moveTo(v.getPos().toPxQPointF());
        continue;
      }
      const Vertex& v0 = mVertices.at(i - 1);
      if (auto center =
              Toolbox::arcCenter(v0.getPos(), v.getPos(), v0.getAngle())) {
        // Arc segment.
        const QPointF centerPx = center->toPxQPointF();
        const QPointF diffPx = v0.getPos().toPxQPointF() - centerPx;
        const qreal radiusPx =
            std::sqrt(diffPx.x() * diffPx.x() + diffPx.y() * diffPx.y());
        const qreal startAngleDeg =
            -qRadiansToDegrees(std::atan2(diffPx.y(), diffPx.x()));
        mPainterPathPx.arcTo(centerPx.x() - radiusPx, centerPx.y() - radiusPx,
                             radiusPx * 2, radiusPx * 2, startAngleDeg,
                             v0.getAngle().toDeg());
      } else {
        // Straight segment.
        mPainterPathPx.lineTo(v.getPos().toPxQPointF());
      }
    }
  }
  return mPainterPathPx;
}

QString Path::toSvgPathMm() const noexcept {
  auto formatLength = [](const Length& value) {
    QString s = value.toMmString();
    if (s.endsWith(".0")) s.chop(2);
    return s;
  };

  QString s;
  if (!mVertices.isEmpty()) {
    s.append(QString("M %1 %2 ")
                 .arg(formatLength(mVertices.first().getPos().getX()),
                      formatLength(-mVertices.first().getPos().getY())));
  }
  for (int i = 1; i < mVertices.count(); ++i) {
    const Vertex& v0 = mVertices.at(i - 1);
    const Vertex& v1 = mVertices.at(i);
    if (auto radius =
            Toolbox::arcRadius(v0.getPos(), v1.getPos(), v0.getAngle())) {
      s.append(QString("A %1 %1 %2 %3 %4 %5 %6 ")
                   .arg(formatLength(radius->abs()))
                   .arg(0)
                   .arg(v0.getAngle().abs() >= Angle::deg180() ? 1 : 0)
                   .arg(v0.getAngle() < 0 ? 1 : 0)
                   .arg(formatLength(v1.getPos().getX()))
                   .arg(formatLength(-v1.getPos().getY())));
    } else {
      s.append(QString("L %1 %2 ")
                   .arg(formatLength(v1.getPos().getX()),
                        formatLength(-v1.getPos().getY())));
    }
  }
  s.chop(1);
  return s;
}

/*******************************************************************************
 *  Transformations
 ******************************************************************************/

Path& Path::translate(const Point& offset) noexcept {
  for (Vertex& vertex : mVertices) {
    vertex.setPos(vertex.getPos() + offset);
  }
  invalidatePainterPath();
  return *this;
}

Path Path::translated(const Point& offset) const noexcept {
  return Path(*this).translate(offset);
}

Path& Path::mapToGrid(const PositiveLength& gridInterval) noexcept {
  for (Vertex& vertex : mVertices) {
    vertex.setPos(vertex.getPos().mappedToGrid(gridInterval));
  }
  invalidatePainterPath();
  return *this;
}

Path Path::mappedToGrid(const PositiveLength& gridInterval) const noexcept {
  return Path(*this).mapToGrid(gridInterval);
}

Path& Path::rotate(const Angle& angle, const Point& center) noexcept {
  for (Vertex& vertex : mVertices) {
    vertex.setPos(vertex.getPos().rotated(angle, center));
  }
  invalidatePainterPath();
  return *this;
}

Path Path::rotated(const Angle& angle, const Point& center) const noexcept {
  return Path(*this).rotate(angle, center);
}

Path& Path::mirror(Qt::Orientation orientation, const Point& center) noexcept {
  for (Vertex& vertex : mVertices) {
    vertex.setPos(vertex.getPos().mirrored(orientation, center));
    vertex.setAngle(-vertex.getAngle());
  }
  invalidatePainterPath();
  return *this;
}

Path Path::mirrored(Qt::Orientation orientation,
                    const Point& center) const noexcept {
  return Path(*this).mirror(orientation, center);
}

Path& Path::reverse() noexcept {
  QVector<Vertex> vertices;
  vertices.reserve(mVertices.count());
  for (int i = mVertices.count() - 1; i >= 0; --i) {
    vertices.append(
        Vertex(mVertices.at(i).getPos(), -mVertices.value(i - 1).getAngle()));
  }
  mVertices = vertices;
  invalidatePainterPath();
  return *this;
}

Path Path::reversed() const noexcept {
  return Path(*this).reverse();
}

Path& Path::flattenArcs(const PositiveLength& maxTolerance) noexcept {
  if (!mVertices.isEmpty()) {
    mVertices.last().setAngle(Angle::deg0());
  }
  for (int i = mVertices.count() - 2; i >= 0; --i) {
    if (mVertices.at(i).getAngle() != Angle::deg0()) {
      const Path arc =
          flatArc(mVertices.at(i).getPos(), mVertices.at(i + 1).getPos(),
                  mVertices.at(i).getAngle(), maxTolerance);
      Q_ASSERT(arc.getVertices().count() >= 2);
      mVertices.insert(i + 1, arc.getVertices().count() - 2, Vertex());
      for (int k = 0; k < arc.getVertices().count(); ++k) {
        mVertices[i + k] = arc.getVertices().at(k);
      }
    }
  }
  invalidatePainterPath();
  return *this;
}

Path Path::flattenedArcs(const PositiveLength& maxTolerance) const noexcept {
  return Path(*this).flattenArcs(maxTolerance);
}

/*******************************************************************************
 *  General Methods
 ******************************************************************************/

void Path::addVertex(const Vertex& vertex) noexcept {
  mVertices.append(vertex);
  invalidatePainterPath();
}

void Path::addVertex(const Point& pos, const Angle& angle) noexcept {
  addVertex(Vertex(pos, angle));
}

void Path::insertVertex(int index, const Vertex& vertex) noexcept {
  mVertices.insert(index, vertex);
  invalidatePainterPath();
}

void Path::insertVertex(int index, const Point& pos,
                        const Angle& angle) noexcept {
  insertVertex(index, Vertex(pos, angle));
}

bool Path::clean() noexcept {
  bool modified = false;
  for (int i = mVertices.count() - 1; i > 0; --i) {
    Vertex& v0 = mVertices[i - 1];
    Vertex& v1 = mVertices[i];
    if (v0.getPos() == v1.getPos()) {
      mVertices.removeAt(i - 1);
      modified = true;
    }
  }
  return modified;
}

bool Path::close() noexcept {
  if (!isClosed() && (mVertices.count() > 1)) {
    addVertex(mVertices.first().getPos(), Angle::deg0());
    Q_ASSERT(isClosed());
    return true;
  } else {
    return false;
  }
}

bool Path::open() noexcept {
  if ((mVertices.count() > 2) && isClosed()) {
    mVertices.removeLast();
    return true;
  } else {
    return false;
  }
}

void Path::serialize(SExpression& root) const {
  for (const Vertex& vertex : mVertices) {
    root.ensureLineBreak();
    vertex.serialize(root.appendList("vertex"));
  }
  root.ensureLineBreak();
}

/*******************************************************************************
 *  Operator Overloadings
 ******************************************************************************/

Path& Path::operator=(const Path& rhs) noexcept {
  mVertices = rhs.mVertices;
  mPainterPathPx = rhs.mPainterPathPx;
  return *this;
}

bool Path::operator<(const Path& rhs) const noexcept {
  return mVertices < rhs.mVertices;
}

/*******************************************************************************
 *  Static Methods
 ******************************************************************************/

Path Path::line(const Point& p1, const Point& p2, const Angle& angle) noexcept {
  return Path({Vertex(p1, angle), Vertex(p2)});
}

Path Path::circle(const PositiveLength& diameter) noexcept {
  return obround(diameter, diameter);
}

Path Path::donut(const PositiveLength& outerDiameter,
                 const PositiveLength& innerDiameter) noexcept {
  Path p;
  const Length ro = outerDiameter / 2;
  const Length ri = innerDiameter / 2;
  if (ro > ri) {
    p.addVertex(Point(0, ro), -Angle::deg180());
    p.addVertex(Point(0, -ro), Angle::deg0());
    p.addVertex(Point(0, -ri), Angle::deg180());
    p.addVertex(Point(0, ri), Angle::deg180());
    p.addVertex(Point(0, -ri), Angle::deg0());
    p.addVertex(Point(0, -ro), -Angle::deg180());
    p.addVertex(Point(0, ro), Angle::deg0());
  }
  return p;
}

Path Path::obround(const PositiveLength& width,
                   const PositiveLength& height) noexcept {
  Path p;
  Length rx = width / 2;
  Length ry = height / 2;
  if (width > height) {
    p.addVertex(Point(ry - rx, ry), Angle::deg0());
    p.addVertex(Point(rx - ry, ry), -Angle::deg180());
    p.addVertex(Point(rx - ry, -ry), Angle::deg0());
    p.addVertex(Point(ry - rx, -ry), -Angle::deg180());
    p.addVertex(Point(ry - rx, ry), Angle::deg0());
  } else if (width < height) {
    p.addVertex(Point(rx, ry - rx), Angle::deg0());
    p.addVertex(Point(rx, rx - ry), -Angle::deg180());
    p.addVertex(Point(-rx, rx - ry), Angle::deg0());
    p.addVertex(Point(-rx, ry - rx), -Angle::deg180());
    p.addVertex(Point(rx, ry - rx), Angle::deg0());
  } else {
    Q_ASSERT(width == height);
    p.addVertex(Point(rx, 0), -Angle::deg180());
    p.addVertex(Point(-rx, 0), -Angle::deg180());
    p.addVertex(Point(rx, 0), Angle::deg0());
  }
  return p;
}

Path Path::obround(const Point& p1, const Point& p2,
                   const PositiveLength& width) noexcept {
  Point diff = p2 - p1;
  Path p = obround(UnsignedLength(diff.getLength()) + width, width);
  p.rotate(Angle::fromRad(std::atan2(diff.getY().toMm(), diff.getX().toMm())));
  p.translate((p1 + p2) / 2);
  return p;
}

Path Path::arcObround(const Point& p1, const Point& p2, const Angle& angle,
                      const PositiveLength& width) noexcept {
  if (p1 == p2) {
    return circle(width).translated(p1);
  }
  if (auto center = Toolbox::arcCenter(p1, p2, angle)) {
    Point delta1 = p1 - (*center);
    Point delta2 = p2 - (*center);
    qreal angle1Rad = std::atan2(delta1.getY().toPx(), delta1.getX().toPx());
    qreal angle2Rad = std::atan2(delta2.getY().toPx(), delta2.getX().toPx());
    UnsignedLength radius = delta1.getLength();
    Length innerRadius = (*radius) - (*width / 2);
    Length outerRadius = (*radius) + (*width / 2);
    Point p1Inner =
        (*center) + Point(innerRadius, 0).rotated(Angle::fromRad(angle1Rad));
    Point p1Outer =
        (*center) + Point(outerRadius, 0).rotated(Angle::fromRad(angle1Rad));
    Point p2Inner =
        (*center) + Point(innerRadius, 0).rotated(Angle::fromRad(angle2Rad));
    Point p2Outer =
        (*center) + Point(outerRadius, 0).rotated(Angle::fromRad(angle2Rad));

    Path p;
    p.addVertex(p1Inner, angle);
    p.addVertex(p2Inner, angle < 0 ? Angle::deg180() : -Angle::deg180());
    p.addVertex(p2Outer, -angle);
    p.addVertex(p1Outer, angle < 0 ? Angle::deg180() : -Angle::deg180());
    p.addVertex(p1Inner, Angle::deg0());
    return p;
  } else {
    // Seems to be a straight segment.
    return Path::obround(p1, p2, width);
  }
}

Path Path::rect(const Point& p1, const Point& p2) noexcept {
  Path p;
  p.addVertex(Point(p1.getX(), p1.getY()));
  p.addVertex(Point(p2.getX(), p1.getY()));
  p.addVertex(Point(p2.getX(), p2.getY()));
  p.addVertex(Point(p1.getX(), p2.getY()));
  p.addVertex(Point(p1.getX(), p1.getY()));
  return p;
}

Path Path::centeredRect(const PositiveLength& width,
                        const PositiveLength& height,
                        const UnsignedLength& cornerRadius) noexcept {
  Path p;
  const Length rx = width / 2;
  const Length ry = height / 2;
  if (cornerRadius == 0) {
    // Regular rectangle without rounded corners.
    p.addVertex(Point(-rx, ry));
    p.addVertex(Point(rx, ry));
    p.addVertex(Point(rx, -ry));
    p.addVertex(Point(-rx, -ry));
  } else if (cornerRadius >= std::min(rx, ry)) {
    // Corner radius is too large for the given size, it's actually an obround.
    return obround(width, height);
  } else {
    // Rectangle with rounded corners.
    p.addVertex(Point(-rx + cornerRadius, ry));
    p.addVertex(Point(rx - cornerRadius, ry), -Angle::deg90());
    p.addVertex(Point(rx, ry - cornerRadius));
    p.addVertex(Point(rx, -ry + cornerRadius), -Angle::deg90());
    p.addVertex(Point(rx - cornerRadius, -ry));
    p.addVertex(Point(-rx + cornerRadius, -ry), -Angle::deg90());
    p.addVertex(Point(-rx, -ry + cornerRadius));
    p.addVertex(Point(-rx, ry - cornerRadius), -Angle::deg90());
  }
  p.close();
  return p;
}

Path Path::chamferedRect(const PositiveLength& width,
                         const PositiveLength& height,
                         const UnsignedLength& chamferSize, bool topLeft,
                         bool topRight, bool bottomLeft,
                         bool bottomRight) noexcept {
  Path p;
  const Length c = std::min(std::min(*chamferSize, (width / 2)), (height / 2));
  const Length cx = (width / 2) - c;
  const Length cy = (height / 2) - c;
  if (topLeft) {
    p.addVertex(Point(-width / 2, cy));
    p.addVertex(Point(-cx, height / 2));
  } else {
    p.addVertex(Point(-width / 2, height / 2));
  }
  if (topRight) {
    p.addVertex(Point(cx, height / 2));
    p.addVertex(Point(width / 2, cy));
  } else {
    p.addVertex(Point(width / 2, height / 2));
  }
  if (bottomRight) {
    p.addVertex(Point(width / 2, -cy));
    p.addVertex(Point(cx, -height / 2));
  } else {
    p.addVertex(Point(width / 2, -height / 2));
  }
  if (bottomLeft) {
    p.addVertex(Point(-cx, -height / 2));
    p.addVertex(Point(-width / 2, -cy));
  } else {
    p.addVertex(Point(-width / 2, -height / 2));
  }
  p.close();
  p.clean();
  return p;
}

Path Path::trapezoid(const PositiveLength& width, const PositiveLength& height,
                     const Length& dw, const Length dh) noexcept {
  Path p;
  const Length dwClipped =
      (dw >= 0) ? std::min(dw, *width) : std::max(dw, -width);
  const Length dhClipped =
      (dh >= 0) ? std::min(dh, *height) : std::max(dh, -height);
  const Length xt = (width / 2) + (dwClipped / 2);
  const Length xb = (width / 2) - (dwClipped / 2);
  const Length yl = (height / 2) - (dhClipped / 2);
  const Length yr = (height / 2) + (dhClipped / 2);
  p.addVertex(Point(-xt, yl));
  p.addVertex(Point(xt, yr));
  p.addVertex(Point(xb, -yr));
  p.addVertex(Point(-xb, -yl));
  p.close();
  p.clean();
  return p;
}

Path Path::octagon(const PositiveLength& width, const PositiveLength& height,
                   const UnsignedLength& cornerRadius) noexcept {
  Path p;
  const Length rx = width / 2;
  const Length ry = height / 2;
  const Length innerChamfer =
      Length::fromMm(std::min(rx - cornerRadius, ry - cornerRadius).toMm() *
                     (2 - std::sqrt(2))) +
      cornerRadius;
  if (cornerRadius == 0) {
    // Regular polygon without rounded corners.
    p.addVertex(Point(rx, ry - innerChamfer));
    p.addVertex(Point(rx - innerChamfer, ry));
    p.addVertex(Point(innerChamfer - rx, ry));
    p.addVertex(Point(-rx, ry - innerChamfer));
    p.addVertex(Point(-rx, innerChamfer - ry));
    p.addVertex(Point(innerChamfer - rx, -ry));
    p.addVertex(Point(rx - innerChamfer, -ry));
    p.addVertex(Point(rx, innerChamfer - ry));
  } else if (innerChamfer >= std::min(rx, ry)) {
    // Corner radius is too large for the given size, it's actually an obround.
    return obround(width, height);
  } else {
    // Octagon with rounded corners.
    const Length chamferOffset =
        Length::fromMm(cornerRadius->toMm() * (1 - (1 / std::sqrt(2))));
    const Length outerChamfer = innerChamfer - cornerRadius + chamferOffset;
    Q_ASSERT(chamferOffset >= 0);
    Q_ASSERT(chamferOffset <= outerChamfer);
    Q_ASSERT(outerChamfer <= innerChamfer);
    p.addVertex(Point(rx, ry - innerChamfer), Angle::deg45());
    p.addVertex(Point(rx - chamferOffset, ry - outerChamfer));
    p.addVertex(Point(rx - outerChamfer, ry - chamferOffset), Angle::deg45());
    p.addVertex(Point(rx - innerChamfer, ry));
    p.addVertex(Point(innerChamfer - rx, ry), Angle::deg45());
    p.addVertex(Point(outerChamfer - rx, ry - chamferOffset));
    p.addVertex(Point(chamferOffset - rx, ry - outerChamfer), Angle::deg45());
    p.addVertex(Point(-rx, ry - innerChamfer));
    p.addVertex(Point(-rx, innerChamfer - ry), Angle::deg45());
    p.addVertex(Point(chamferOffset - rx, outerChamfer - ry));
    p.addVertex(Point(outerChamfer - rx, chamferOffset - ry), Angle::deg45());
    p.addVertex(Point(innerChamfer - rx, -ry));
    p.addVertex(Point(rx - innerChamfer, -ry), Angle::deg45());
    p.addVertex(Point(rx - outerChamfer, chamferOffset - ry));
    p.addVertex(Point(rx - chamferOffset, outerChamfer - ry), Angle::deg45());
    p.addVertex(Point(rx, innerChamfer - ry));
  }
  p.close();
  return p;
}

Path Path::flatArc(const Point& p1, const Point& p2, const Angle& angle,
                   const PositiveLength& maxTolerance) noexcept {
  if (auto center = Toolbox::arcCenter(p1, p2, angle)) {
    const UnsignedLength radiusAbs = (p1 - (*center)).getLength();
    if (radiusAbs > (maxTolerance / 2)) {
      // Calculate how many lines we need to create.
      const qreal radiusAbsNm = static_cast<qreal>(radiusAbs->toNm());
      const qreal y =
          qBound(qreal(0.0), static_cast<qreal>(maxTolerance->toNm()),
                 radiusAbsNm / qreal(4));
      const qreal stepsPerRad = std::min(
          qreal(0.5) / std::acos(1 - y / radiusAbsNm), radiusAbsNm / qreal(2));
      const int steps = qCeil(stepsPerRad * angle.abs().toRad());

      // create line segments
      Path p;
      p.addVertex(p1);
      const qreal angleDelta = angle.toMicroDeg() / (qreal)steps;
      for (int i = 1; i < steps; ++i) {
        p.addVertex(p1.rotated(Angle(angleDelta * i), *center));
      }
      p.addVertex(p2);
      return p;
    }
  }

  // By default, return a straight line segment.
  return line(p1, p2);
}

QPainterPath Path::toQPainterPathPx(const QVector<Path>& paths,
                                    bool area) noexcept {
  QPainterPath p;
  p.setFillRule(Qt::WindingFill);
  foreach (const Path& path, paths) {
    if (area) {
      p |= path.toQPainterPathPx();
    } else {
      p.addPath(path.toQPainterPathPx());
    }
  }
  return p;
}

/*******************************************************************************
 *  End of File
 ******************************************************************************/

}  // namespace librepcb