如何正确绘制路径？

Question

我目前正在为Path绘图算法进行重写。 我正在使用apache-commons-math的样条插值器来获得穿过2D空间中所有给定点的平滑路径...

目前我有：

/**
 * Draws a route on a map.
 */
public class MapRouteDrawer {

  private static final SplineInterpolator splineInterpolator = new SplineInterpolator();

  /**
   * Draws the route to the screen, does nothing if null.
   */
  public static void drawRoute(final Graphics2D graphics, final RouteDescription routeDescription, final MapPanel view, final MapData mapData, final String movementLeftForCurrentUnits) {
    if (routeDescription == null) {
      return;
    }
    final Route route = routeDescription.getRoute();
    if (route == null) {
      return;
    }

    final Point[] points = getRoutePoints(routeDescription, mapData);
    final int xOffset = view.getXOffset();
    final int yOffset = view.getYOffset();
    final int jointsize = 10;
    final int numTerritories = route.getAllTerritories().size();
    //set thickness and color of the future drawings
    graphics.setStroke(new BasicStroke(3.5f, BasicStroke.CAP_ROUND, BasicStroke.JOIN_ROUND));
    graphics.setPaint(Color.red);
    graphics.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON);

    if(Arrays.asList(points).contains(null)){//If the Array is null at some point
      return;
    }

    if(numTerritories <= 1 || points.length <= 2){
      drawLineWithTranslate(graphics, new Line2D.Float(routeDescription.getStart(), routeDescription.getEnd()), xOffset, yOffset);
      graphics.fillOval((routeDescription.getEnd().x - xOffset) - jointsize / 2, (routeDescription.getEnd().y - yOffset) - jointsize / 2, jointsize, jointsize);
    }
    else{
      drawCurvedPath(graphics, points, view);
    }
  }

  }

  private static double[] getIndex(Point[] points) {
    final double[] index = new double[points.length];
    for(int i = 0; i < points.length; i++){
      index[i] = i;
    }
    return index;
  }

  private static void drawLineWithTranslate(Graphics2D graphics, Line2D line2D, double translateX, double translateY) {
      final Line2D line = (Line2D) line2D;
      final Point2D point1 = new Point2D.Double(line.getP1().getX() - translateX, line.getP1().getY() - translateY);
      final Point2D point2 = new Point2D.Double(line.getP2().getX() - translateX, line.getP2().getY() - translateY);
      graphics.draw(new Line2D.Double(point1, point2));
  }

  private static Point[] getRoutePoints(RouteDescription routeDescription, MapData mapData){
    final List<Territory> territories = routeDescription.getRoute().getAllTerritories();
    final int numTerritories = territories.size();
    final Point[] points = new Point[numTerritories];
    for (int i = 0; i < numTerritories; i++) {
      points[i] = mapData.getCenter(territories.get(i));
    }
    if (routeDescription.getStart() != null) {
      points[0] = routeDescription.getStart();
    }
    if (routeDescription.getEnd() != null && numTerritories > 1) {
      points[numTerritories - 1] = new Point(routeDescription.getEnd());
    }
    return points;
  }

  private static double[] pointsXToDoubleArray(Point[] points){
    double[] result = new double[points.length];
    for(int i = 0; i < points.length; i++){
      result[i] = points[i].getX();
    }
    return result;
  }
  private static double[] pointsYToDoubleArray(Point[] points){
    double[] result = new double[points.length];
    for(int i = 0; i < points.length; i++){
      result[i] = points[i].getY();
    }
    return result;
  }

  private static double[] getCoords(PolynomialSplineFunction curve, float stepSize){
    final double[] coords = new double[(int) (curve.getN() / stepSize)];
    for(int i = 0; i < curve.getN() / stepSize; i++){
      coords[i] = curve.value(i * stepSize);
    }
    return coords;
  }

  private static void drawCurvedPath(Graphics2D graphics, Point[] points, MapPanel view){
    final double[] index = getIndex(points);
    final float stepSize = 0.01f;//TODO calculating a step size that makes sense
    final PolynomialSplineFunction xcurve = splineInterpolator.interpolate(index, pointsXToDoubleArray(points));
    final PolynomialSplineFunction ycurve = splineInterpolator.interpolate(index, pointsYToDoubleArray(points));
    final double[] xcoords = getCoords(xcurve, stepSize);
    final double[] ycoords = getCoords(ycurve, stepSize);

    for(int i = 1; i < xcoords.length; i++){
      //TODO maybe a line is not the best way to draw this...
      drawLineWithTranslate(graphics, new Line2D.Double(xcoords[i-1], ycoords[i-1], xcoords[i], ycoords[i]), view.getXOffset(), view.getYOffset());
    }
  }
}

这背后的想法是，由于SplineInterpolator只接受函数（例如f（x）= y），并且x必须增加，因此我们将点数组拆分为2个双精度数组，并将其插值两次。
首先是X值，然后是Y值...
当X值是一个称为“索引”的“虚拟数组”时，第一个值为0，第二个为1，第三个为2，依此类推...
为了绘制此路径，我绘制了一条从点0到1、1到2、2到3的线，依此类推...

有两件事要考虑...

1. 在索引中选择1作为步长大小有意义吗？ 这可能会导致错误，因为Java double只有64位，并且我们以固定的1步长来拉伸和压缩值。 如果是这样，我可以改变些什么来优化此...
2. 其次，如何绘制这两个双精度数组？ 我画多条线的尝试看起来不太好-这是因为我以太大的步长读取插值吗？

任何帮助都非常感谢

编辑：

Answer 1

为“索引”数组选择1作为步长是所谓的统一参数化，除非您的数据点也相对均匀地分布，否则通常不会产生良好的结果。 我建议使用弦长参数化或向心参数化，如下所示：

t0 = 0.0
t1 = d1/L
t2 = t1 + d2/L  
t3 = t2 + d3/L
............
t(n-1)= 1.0.

哪里

d1=|P1-P0|^e, d2=|P2-P1|^e, d3=|P3-P2|^e and L = d1+d2+d3+.....d(n-1). 

对于和弦长度参数化，在上式中使用e = 1.0。 对于向心参数化，请使用e = 0.5。 注意，使用e = 0.0只会导致统一的参数化。 如果您的数据点具有非常不均匀的分布（即，点之间的一些距离很大而有些距离很小），则向心参数化通常会比弦长参数化产生更好的结果。