/// <summary>
/// Modifies a polygon and creates a random shape.
///
/// Algorithm:
///
/// * create a new polygon, subdivided this way:
/// + get center of polygon
/// + create a list of angles for iteration
/// + iterate through the angles, create a line using the angle and find the intersection with a line of the polygon
/// * iterate through the subdivided polygon
/// + move the vertex towards the center
/// + consider previous vertex in order to not move in too large steps
/// </summary>
public static List <Vector> CreateRandomShape(List <Vector> polygon, double ellipseRelaxationFactor, int angleStepCount, bool randomAngleMovement, bool keepOriginalShape, bool randomStartAngle)
{
Vector meanVector = PolygonUtils.GetMeanVector(polygon);
double length = meanVector.Length * 2;
// get the list of angles to step through
List <double> angleRadList = CreateAngleList(angleStepCount, randomAngleMovement, randomStartAngle);
// resample the original polygon by angle line intersection
List <Vector> resampledPolygon = ResamplePolygon(polygon, meanVector, angleRadList, keepOriginalShape);
#region create new polygon using the intersections
List <Vector> newPolygon = new List <Vector>();
for (int i = 0; i < resampledPolygon.Count; i++)
{
Vector curr = resampledPolygon[i];
// position on the ellipse
Vector position = curr;
// from center to position
double distance = (position - meanVector).Length;
Vector direction = (position - meanVector);
direction.Normalize();
// move from center towards new position. but not too much, let it depend on the previous distance
{
// move initially from 0 to max distance. otherwise use the previous value
double min = distance * ellipseRelaxationFactor;
double max = distance;
// the radius must be smaller during the next iteration, we are navigating around an ellipse => clamp the values
if (min > max)
{
min = max;
}
double moveDistance = Utils.GetRandomRange(min, max);
distance = moveDistance;
}
position = meanVector + distance * direction;
newPolygon.Add(position);
}
#endregion create new polygon using the intersections
/*
* TODO: Douglas-Peucker reduction
*/
// sort again
PolygonUtils.SortClockWise(newPolygon);
return(newPolygon);
}
// resample the polygon by creating vertices which are created by casting lines from mean vector to the polygon lines and using the intersection points
// this assumes that the mean vector is enclosed in a polygon
public static List <Vector> ResamplePolygon(List <Vector> polygon, Vector meanVector, List <double> angleRadList, bool keepOriginalShape)
{
double length = meanVector.Length * 2;
List <Vector> resampledPolygon = new List <Vector>();
// add existing points in order to keep the general voronoi shape
if (keepOriginalShape)
{
resampledPolygon.AddRange(polygon);
}
for (int i = 0; i < angleRadList.Count; i++)
{
// convert angle from deg to rad
double angle = angleRadList[i];
double x = meanVector.X + length * Math.Cos(angle);
double z = meanVector.X + length * Math.Sin(angle);
// position on the ellipse
Vector line1PositionA = meanVector;
Vector line1PositionB = new Vector(x, z);
for (var j = 0; j < polygon.Count; j++)
{
int currIndex = j;
int nextIndex = j + 1;
if (nextIndex == polygon.Count)
{
nextIndex = 0;
}
Vector line2PositionA = new Vector(polygon[currIndex].X, polygon[currIndex].Y);
Vector line2PositionB = new Vector(polygon[nextIndex].X, polygon[nextIndex].Y);
Vector intersection = new Vector(0, 0);
// try and find an intersection. if one is found, add the point to the list
if (PolygonUtils.LineSegmentsIntersection(line1PositionA, line1PositionB, line2PositionA, line2PositionB, out intersection))
{
resampledPolygon.Add(intersection);
break;
}
}
}
// sort again
PolygonUtils.SortClockWise(resampledPolygon);
return(resampledPolygon);
}
/// <summary>
/// Create a random ellipse and paint all voronoi cells in the same color which have the the centroid inside the ellipse
/// </summary>
/// <param name="sender"></param>
/// <param name="e"></param>
private void Testing_ColorizeVoronoiWithinRandomEllipseBounds(object sender, RoutedEventArgs e)
{
// parameters
double ellipseWidthMin = 50;
double ellipseHeightMin = 50;
double ellipseWidthMax = 200;
double ellipseHeightMax = 200;
double width = CanvasBorder.ActualWidth;
double height = CanvasBorder.ActualHeight;
double positionMargin = 0;
double x = Utils.GetRandomRange(positionMargin, width - positionMargin);
double y = Utils.GetRandomRange(positionMargin, height - positionMargin);
Vector position = new Vector(x, y);
double ellipseWidth = Utils.GetRandomRange(ellipseWidthMin, ellipseWidthMax);
double ellipseHeight = Utils.GetRandomRange(ellipseHeightMin, ellipseHeightMax);
// ellipse x/y (and check if point is in ellipse) spans the entire canvas
var ellipseX = position.X;
var ellipseY = position.Y;
// check if point is inside ellipse
Vector[] clipPolygon = GetClipPolygon();
for (int i = 0; i < graph.GetAllVectors().Count; i++)
{
Cell cell = graph.GetVoronoiCell(i, clipPolygon);
Vector compareVector = cell.Centroid;
double checkEllipse = PolygonUtils.IsInEllipse(ellipseX, ellipseY, ellipseWidth / 2, ellipseHeight / 2, compareVector.X, compareVector.Y);
if (checkEllipse < 1)
{
colorMap[i] = Colors.Black;
}
}
CreateGraph();
// draw ellipse
SolidColorBrush brush = new SolidColorBrush(Colors.Black);
// create ellipse
var ellipse = new Ellipse
{
Stroke = brush,
StrokeThickness = 2,
HorizontalAlignment = HorizontalAlignment.Left,
VerticalAlignment = VerticalAlignment.Top,
Width = ellipseWidth,
Height = ellipseHeight
};
var ellipseDrawX = ellipseX - 0.5 * ellipseWidth;
var ellipseDrawY = ellipseY - 0.5 * ellipseHeight;
ellipse.Margin = new Thickness(ellipseDrawX, ellipseDrawY, 0, 0);
Graph.Children.Add(ellipse);
}
