using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Windows;
using System.Windows.Controls;
using System.Windows.Data;
using System.Windows.Documents;
using System.Windows.Input;
using System.Windows.Media;
using System.Windows.Media.Imaging;
using System.Windows.Shapes;
namespace TextOnAPath
{
public static class GeometryHelper
{
public static List<Point> GetIntersectionPoints(PathGeometry FlattenedPath, double[] SegmentLengths)
{
List<Point> intersectionPoints = new List<Point>();
List<Point> pointsOnFlattenedPath = GetPointsOnFlattenedPath(FlattenedPath);
if (pointsOnFlattenedPath == null || pointsOnFlattenedPath.Count < 2)
return intersectionPoints;
Point currPoint = pointsOnFlattenedPath[0];
intersectionPoints.Add(currPoint);
// find point on flattened path that is segment length away from current point
int flattedPathIndex = 0;
int segmentIndex = 1;
while (flattedPathIndex < pointsOnFlattenedPath.Count - 1 &&
segmentIndex < SegmentLengths.Length + 1)
{
Point? intersectionPoint = GetIntersectionOfSegmentAndCircle(
pointsOnFlattenedPath[flattedPathIndex],
pointsOnFlattenedPath[flattedPathIndex + 1], currPoint, SegmentLengths[segmentIndex - 1]);
if (intersectionPoint == null)
flattedPathIndex++;
else
{
intersectionPoints.Add((Point)intersectionPoint);
currPoint = (Point)intersectionPoint;
pointsOnFlattenedPath[flattedPathIndex] = currPoint;
segmentIndex++;
}
}
return intersectionPoints;
}
static List<Point> GetPointsOnFlattenedPath(PathGeometry FlattenedPath)
{
List<Point> flattenedPathPoints = new List<Point>();
// for flattened geometry there should be just one PathFigure in the Figures
if (FlattenedPath.Figures.Count != 1)
return null;
PathFigure pathFigure = FlattenedPath.Figures[0];
flattenedPathPoints.Add(pathFigure.StartPoint);
// SegmentsCollection should contain PolyLineSegment and LineSegment
foreach (PathSegment pathSegment in pathFigure.Segments)
{
if (pathSegment is PolyLineSegment)
{
PolyLineSegment seg = pathSegment as PolyLineSegment;
foreach (Point point in seg.Points)
flattenedPathPoints.Add(point);
}
else if (pathSegment is LineSegment)
{
LineSegment seg = pathSegment as LineSegment;
flattenedPathPoints.Add(seg.Point);
}
else
throw new Exception("GetIntersectionPoint - unexpected path segment type: " + pathSegment.ToString());
}
return (flattenedPathPoints);
}
static Point? GetIntersectionOfSegmentAndCircle(Point SegmentPoint1, Point SegmentPoint2,
Point CircleCenter, double CircleRadius)
{
// linear equation for segment: y = mx + b
double slope = (SegmentPoint2.Y - SegmentPoint1.Y) / (SegmentPoint2.X - SegmentPoint1.X);
double intercept = SegmentPoint1.Y - (slope * SegmentPoint1.X);
// special case when segment is vertically oriented
if (double.IsInfinity(slope))
{
double root = Math.Pow(CircleRadius, 2.0) - Math.Pow(SegmentPoint1.X - CircleCenter.X, 2.0);
if (root < 0)
return null;
// soln 1
double SolnX1 = SegmentPoint1.X;
double SolnY1 = CircleCenter.Y - Math.Sqrt(root);
Point Soln1 = new Point(SolnX1, SolnY1);
// have valid result if point is between two segment points
if (IsBetween(SolnX1, SegmentPoint1.X, SegmentPoint2.X) &&
IsBetween(SolnY1, SegmentPoint1.Y, SegmentPoint2.Y))
//if (ValidSoln(Soln1, SegmentPoint1, SegmentPoint2, CircleCenter))
{
// found solution
return (Soln1);
}
// soln 2
double SolnX2 = SegmentPoint1.X;
double SolnY2 = CircleCenter.Y + Math.Sqrt(root);
Point Soln2 = new Point(SolnX2, SolnY2);
// have valid result if point is between two segment points
if (IsBetween(SolnX2, SegmentPoint1.X, SegmentPoint2.X) &&
IsBetween(SolnY2, SegmentPoint1.Y, SegmentPoint2.Y))
//if (ValidSoln(Soln2, SegmentPoint1, SegmentPoint2, CircleCenter))
{
// found solution
return (Soln2);
}
}
else
{
// use soln to quadradratic equation to solve intersection of segment and circle:
// x = (-b +/ sqrt(b^2-4ac))/(2a)
double a = 1 + Math.Pow(slope, 2.0);
double b = (-2 * CircleCenter.X) + (2 * (intercept - CircleCenter.Y) * slope);
double c = Math.Pow(CircleCenter.X, 2.0) + Math.Pow(intercept - CircleCenter.Y, 2.0) - Math.Pow(CircleRadius, 2.0);
// check for no solutions, is sqrt negative?
double root = Math.Pow(b, 2.0) - (4 * a * c);
if (root < 0)
return null;
// we might have two solns...
// soln 1
double SolnX1 = (-b + Math.Sqrt(root)) / (2 * a);
double SolnY1 = slope * SolnX1 + intercept;
Point Soln1 = new Point(SolnX1, SolnY1);
// have valid result if point is between two segment points
if (IsBetween(SolnX1, SegmentPoint1.X, SegmentPoint2.X) &&
IsBetween(SolnY1, SegmentPoint1.Y, SegmentPoint2.Y))
//if (ValidSoln(Soln1, SegmentPoint1, SegmentPoint2, CircleCenter))
{
// found solution
return (Soln1);
}
// soln 2
double SolnX2 = (-b - Math.Sqrt(root)) / (2 * a);
double SolnY2 = slope * SolnX2 + intercept;
Point Soln2 = new Point(SolnX2, SolnY2);
// have valid result if point is between two segment points
if (IsBetween(SolnX2, SegmentPoint1.X, SegmentPoint2.X) &&
IsBetween(SolnY2, SegmentPoint1.Y, SegmentPoint2.Y))
//if (ValidSoln(Soln2, SegmentPoint1, SegmentPoint2, CircleCenter))
{
// found solution
return (Soln2);
}
}
// shouldn't get here...but in case
return null;
}
static bool IsBetween(double X, double X1, double X2)
{
if (X1 >= X2 && X <= X1 && X >= X2)
return true;
if (X1 <= X2 && X >= X1 && X <= X2)
return true;
return false;
}
}
}