What I want to do:
I want to get the minimal amount of points from a polygon that will create the same polygon:
For example, if I had this polygon:
(0, 0), (1, 0), (2, 0), (3, 0), (4, 0), (0,4), (4,4)
It will create a polygon that its location is 0, 0, its width 4 and its height 4.
If I were to enter this polygon to the hypothetical algorithm it will return:
(0, 0), (4, 0), (0, 4), (4, 4)
Why I want to do it:
I'm creating a game, and the game has animations, each animation has its own images and polygons (the bounds of the images), I already have the images for the animations, but I don't have the polygons for them, of course, I could just create the polygons myself but it would be exhausting to create polygons manually for 100+ images, not to talk about adding/modifying animations.
What I've tried:
My idea was this:
Scan the image, pixel by pixel, check if the pixel is blank, and if it isn't, add it to a list, once this is done use some sort of algorithm to get the minimal amount of points to create the same polygon.
I did some research and I thought the LLTS (Long Live The Square) algorithm was what I needed, so I've written this code using cansik's implementation of it in C#:
private readonly Bitmap _image;
private Point[] _result;
private void Calculate()
{
List<Vector2D> points = new List<Vector2D>();
for (int x = 0; x < _image.Width; x++)
{
for (int y = 0; y < _image.Height; y++)
{
// Check if the pixel is blank
if (_image.GetPixel(x, y).ToArgb() != 16777215)
{
// If the pixel isn't blank, add it to the list
points.Add(new Vector2D(x, y));
}
}
}
Vector2D[] resultInVectors = GeoAlgos.MonotoneChainConvexHull(points.ToArray());
_result = new Point[resultInVectors.Length];
for (int i = 0; i < resultInVectors.Length; i++)
{
_result[i] = new Point((int)resultInVectors[i].X, (int)resultInVectors[i].Y);
}
}
I added the paint code:
private void Form_Paint(object sender, PaintEventArgs e)
{
e.Graphics.DrawPolygon(Pens.Black, _result);
e.Graphics.DrawImage(_image, new Point(100, 0));
}
In the end, I run the program and this is what I got:
This is not exactly what I've had in mind, to say the least, I expected it to be something like this:
Any ideas?
EDIT - FINALLY SOLVED IT
I used Wowa's answer to Trevor Elliott's question, then, I minimized the number of points in the result by using this function that I created:
private static List<Point> MinimizePoints(List<Point> points)
{
if (points.Count < 3)
{
return points;
}
List<Point> minimumPoints = new List<Point>(points);
for (int i = minimumPoints.Count - 1; i > 2; i -= 3)
{
List<Point> currentPoints = minimumPoints.GetRange(i - 3, 3);
try
{
if ((currentPoints[2].X - currentPoints[0].X) / (currentPoints[1].X - currentPoints[0].X) ==
(currentPoints[2].Y - currentPoints[0].Y) / (currentPoints[1].Y - currentPoints[0].Y))
{
minimumPoints.Remove(minimumPoints[i + 1]);
}
}
catch (DivideByZeroException)
{
// Ignore
}
}
return minimumPoints;
}
I used Oliver Charlesworth's answer to Prashant C's question.
SECOND EDIT - A MORE OPTIMIZED SOLUTION
Instead of using my own meh algorithm for reducing points I used the Ramer–Douglas–Peucker algorithm and set ε (the tolerance) to 0. Here's the implementation that I used:
private static class DouglasPeuckerReduction
{
public static Point[] ReducePoints(Point[] existingPolygon)
{
if (existingPolygon == null || existingPolygon.Length < 3)
return existingPolygon;
int firstPoint = 0;
int lastPoint = existingPolygon.Length - 1;
List<int> pointIndexsToKeep = new List<int>();
//Add the first and last index to the keepers
pointIndexsToKeep.Add(firstPoint);
pointIndexsToKeep.Add(lastPoint);
//The first and the last point cannot be the same
while (existingPolygon[firstPoint].Equals(existingPolygon[lastPoint]))
{
lastPoint--;
}
ReducePoints(existingPolygon, firstPoint, lastPoint,
0, ref pointIndexsToKeep);
pointIndexsToKeep.Sort();
return pointIndexsToKeep.Select(index => existingPolygon[index]).ToArray();
}
/// <summary>
/// Douglases the peucker reduction.
/// </summary>
/// <param name="points">The points.</param>
/// <param name="firstPoint">The first point.</param>
/// <param name="lastPoint">The last point.</param>
/// <param name="tolerance">The tolerance.</param>
/// <param name="pointIndexesToKeep">The point index to keep.</param>
private static void ReducePoints(IReadOnlyList<Point> points, int firstPoint, int lastPoint, double tolerance,
ref List<int> pointIndexesToKeep)
{
double maxDistance = 0;
int indexFarthest = 0;
for (int index = firstPoint; index < lastPoint; index++)
{
double distance = PerpendicularDistance
(points[firstPoint], points[lastPoint], points[index]);
if (distance > maxDistance)
{
maxDistance = distance;
indexFarthest = index;
}
}
if (maxDistance > tolerance && indexFarthest != 0)
{
//Add the largest point that exceeds the tolerance
pointIndexesToKeep.Add(indexFarthest);
ReducePoints(points, firstPoint,
indexFarthest, tolerance, ref pointIndexesToKeep);
ReducePoints(points, indexFarthest,
lastPoint, tolerance, ref pointIndexesToKeep);
}
}
/// <summary>
/// The distance of a point from a line made from point1 and point2.
/// </summary>
/// <param name="pt1">The PT1.</param>
/// <param name="pt2">The PT2.</param>
/// <param name="p">The p.</param>
/// <returns></returns>
private static double PerpendicularDistance
(Point Point1, Point Point2, Point Point)
{
//Area = |(1/2)(x1y2 + x2y3 + x3y1 - x2y1 - x3y2 - x1y3)| *Area of triangle
//Base = v((x1-x2)²+(x1-x2)²) *Base of Triangle*
//Area = .5*Base*H *Solve for height
//Height = Area/.5/Base
double area = Math.Abs(.5 * (Point1.X * Point2.Y + Point2.X *
Point.Y + Point.X * Point1.Y - Point2.X * Point1.Y - Point.X *
Point2.Y - Point1.X * Point.Y));
double bottom = Math.Sqrt(Math.Pow(Point1.X - Point2.X, 2) +
Math.Pow(Point1.Y - Point2.Y, 2));
double height = area / bottom * 2;
return height;
}
}
