Step by Step solution about How to resolve the algorithm Ramer-Douglas-Peucker line simplification step by step in the Java programming language

The provided Java code demonstrates the Ramer-Douglas-Peucker (RDP) algorithm for simplifying a polyline by reducing the number of points while preserving its overall shape. The algorithm works as follows:

1. Point Class: It defines a Point class that extends Pair<Double, Double> to represent points in two-dimensional space.

2. Perpendicular Distance: The perpendicularDistance method calculates the perpendicular distance between a point and a line segment defined by two other points.

3. Ramer-Douglas-Peucker Simplification: The ramerDouglasPeucker method recursively simplifies a list of points by finding the point with the maximum perpendicular distance from the line segment connecting the start and end points. If this distance exceeds a specified epsilon, the line is further divided, and the algorithm is applied recursively to each segment.

4. Main Function: The main function creates a sample list of points and calls the ramerDouglasPeucker method to simplify it with an epsilon of 1.0. The simplified list is then printed to the console.

Here's a detailed explanation of each part of the code:

• Point Class: The Point class is a simple extension of Pair<Double, Double> that represents a point in two-dimensional space. It overrides the toString method to provide a convenient representation of the point as a string, e.g., "(0.0, 0.0)".

• Perpendicular Distance: The perpendicularDistance method calculates the perpendicular distance between a point pt and a line segment defined by two other points, lineStart and lineEnd. It uses vector math to find the projection of pt onto the normalized direction vector of the line segment and then calculates the distance between the projected point and pt.

• Ramer-Douglas-Peucker Simplification: The ramerDouglasPeucker method implements the RDP algorithm for simplifying polylines. It takes a list of points, pointList, an epsilon tolerance for the maximum perpendicular distance, and an output list, out. It follows these steps:

  • If the number of points in pointList is less than 2, it raises an IllegalArgumentException because there are not enough points to simplify.

  • It iterates through the points in pointList, excluding the first and last points, and calculates the perpendicular distance of each point from the line segment connecting the first and last points. The point with the maximum distance is stored in index with its distance in dmax.

  • If dmax is greater than epsilon, indicating that the line is not sufficiently straight, it splits pointList into two segments: firstLine from the first to the index point and lastLine from the index point to the last. It then recursively calls ramerDouglasPeucker on each segment, storing the results in recResults1 and recResults2, respectively.

  • It assembles the simplified result by combining the simplified first and last lines, removing the duplicate point at index. If the resulting output has less than two points, it throws a RuntimeException.

  • If dmax is less than or equal to epsilon, it means the line segment is sufficiently straight, and it simply adds the first and last points to the output.

• Main Function: The main function creates a sample list of points pointList and calls the ramerDouglasPeucker method to simplify it with an epsilon of 1.0. The simplified list is stored in pointListOut and printed to the console.

By running the program, you can see the original list of points and the simplified version that preserves the overall shape while reducing the number of points.

import javafx.util.Pair;

import java.util.ArrayList;
import java.util.List;

public class LineSimplification {
    private static class Point extends Pair<Double, Double> {
        Point(Double key, Double value) {
            super(key, value);
        }

        @Override
        public String toString() {
            return String.format("(%f, %f)", getKey(), getValue());
        }
    }

    private static double perpendicularDistance(Point pt, Point lineStart, Point lineEnd) {
        double dx = lineEnd.getKey() - lineStart.getKey();
        double dy = lineEnd.getValue() - lineStart.getValue();

        // Normalize
        double mag = Math.hypot(dx, dy);
        if (mag > 0.0) {
            dx /= mag;
            dy /= mag;
        }
        double pvx = pt.getKey() - lineStart.getKey();
        double pvy = pt.getValue() - lineStart.getValue();

        // Get dot product (project pv onto normalized direction)
        double pvdot = dx * pvx + dy * pvy;

        // Scale line direction vector and subtract it from pv
        double ax = pvx - pvdot * dx;
        double ay = pvy - pvdot * dy;

        return Math.hypot(ax, ay);
    }

    private static void ramerDouglasPeucker(List<Point> pointList, double epsilon, List<Point> out) {
        if (pointList.size() < 2) throw new IllegalArgumentException("Not enough points to simplify");

        // Find the point with the maximum distance from line between the start and end
        double dmax = 0.0;
        int index = 0;
        int end = pointList.size() - 1;
        for (int i = 1; i < end; ++i) {
            double d = perpendicularDistance(pointList.get(i), pointList.get(0), pointList.get(end));
            if (d > dmax) {
                index = i;
                dmax = d;
            }
        }

        // If max distance is greater than epsilon, recursively simplify
        if (dmax > epsilon) {
            List<Point> recResults1 = new ArrayList<>();
            List<Point> recResults2 = new ArrayList<>();
            List<Point> firstLine = pointList.subList(0, index + 1);
            List<Point> lastLine = pointList.subList(index, pointList.size());
            ramerDouglasPeucker(firstLine, epsilon, recResults1);
            ramerDouglasPeucker(lastLine, epsilon, recResults2);

            // build the result list
            out.addAll(recResults1.subList(0, recResults1.size() - 1));
            out.addAll(recResults2);
            if (out.size() < 2) throw new RuntimeException("Problem assembling output");
        } else {
            // Just return start and end points
            out.clear();
            out.add(pointList.get(0));
            out.add(pointList.get(pointList.size() - 1));
        }
    }

    public static void main(String[] args) {
        List<Point> pointList = List.of(
                new Point(0.0, 0.0),
                new Point(1.0, 0.1),
                new Point(2.0, -0.1),
                new Point(3.0, 5.0),
                new Point(4.0, 6.0),
                new Point(5.0, 7.0),
                new Point(6.0, 8.1),
                new Point(7.0, 9.0),
                new Point(8.0, 9.0),
                new Point(9.0, 9.0)
        );
        List<Point> pointListOut = new ArrayList<>();
        ramerDouglasPeucker(pointList, 1.0, pointListOut);
        System.out.println("Points remaining after simplification:");
        pointListOut.forEach(System.out::println);
    }
}