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C# | 120 lines | 87 code | 15 blank | 18 comment | 12 complexity | c7bf63e199cd9415f49b0a541ab44208 MD5 | raw file
```  1using System;
2using System.Collections.Generic;
3using System.Linq;
4using System.Text;
5using System.Windows;
6
8{
9	// todo check a license
10	public static class BezierBuilder
11	{
12		public static IEnumerable<Point> GetBezierPoints(Point[] points)
13		{
14			if (points == null)
15				throw new ArgumentNullException("points");
16
17			Point[] firstControlPoints;
18			Point[] secondControlPoints;
19
20			int n = points.Length - 1;
21			if (n < 1)
22				throw new ArgumentException("At least two knot points required", "points");
23			if (n == 1)
24			{ // Special case: Bezier curve should be a straight line.
25				firstControlPoints = new Point[1];
26				// 3P1 = 2P0 + P3
27				firstControlPoints[0].X = (2 * points[0].X + points[1].X) / 3;
28				firstControlPoints[0].Y = (2 * points[0].Y + points[1].Y) / 3;
29
30				secondControlPoints = new Point[1];
31				// P2 = 2P1 – P0
32				secondControlPoints[0].X = 2 *
33					firstControlPoints[0].X - points[0].X;
34				secondControlPoints[0].Y = 2 *
35					firstControlPoints[0].Y - points[0].Y;
36
37				return Join(points, firstControlPoints, secondControlPoints);
38			}
39
40			// Calculate first Bezier control points
41			// Right hand side vector
42			double[] rhs = new double[n];
43
44			// Set right hand side X values
45			for (int i = 1; i < n - 1; ++i)
46				rhs[i] = 4 * points[i].X + 2 * points[i + 1].X;
47			rhs[0] = points[0].X + 2 * points[1].X;
48			rhs[n - 1] = (8 * points[n - 1].X + points[n].X) / 2.0;
49			// Get first control points X-values
50			double[] x = GetFirstControlPoints(rhs);
51
52			// Set right hand side Y values
53			for (int i = 1; i < n - 1; ++i)
54				rhs[i] = 4 * points[i].Y + 2 * points[i + 1].Y;
55			rhs[0] = points[0].Y + 2 * points[1].Y;
56			rhs[n - 1] = (8 * points[n - 1].Y + points[n].Y) / 2.0;
57			// Get first control points Y-values
58			double[] y = GetFirstControlPoints(rhs);
59
60			// Fill output arrays.
61			firstControlPoints = new Point[n];
62			secondControlPoints = new Point[n];
63			for (int i = 0; i < n; ++i)
64			{
65				// First control point
66				firstControlPoints[i] = new Point(x[i], y[i]);
67				// Second control point
68				if (i < n - 1)
69					secondControlPoints[i] = new Point(2 * points
70						[i + 1].X - x[i + 1], 2 *
71						points[i + 1].Y - y[i + 1]);
72				else
73					secondControlPoints[i] = new Point((points
74						[n].X + x[n - 1]) / 2,
75						(points[n].Y + y[n - 1]) / 2);
76			}
77
78			return Join(points, firstControlPoints, secondControlPoints);
79		}
80
81		private static IEnumerable<Point> Join(Point[] points, Point[] firstControlPoints, Point[] secondControlPoints)
82		{
83			var length = firstControlPoints.Length;
84			for (int i = 0; i < length; i++)
85			{
86				yield return points[i];
87				yield return firstControlPoints[i];
88				yield return secondControlPoints[i];
89			}
90
91			yield return points[length];
92		}
93
94		/// <summary>
95		/// Solves a tridiagonal system for one of coordinates (x or y)
96		/// of first Bezier control points.
97		/// </summary>
98		/// <param name="rhs">Right hand side vector.</param>
99		/// <returns>Solution vector.</returns>
100		private static double[] GetFirstControlPoints(double[] rhs)
101		{
102			int n = rhs.Length;
103			double[] x = new double[n]; // Solution vector.
104			double[] tmp = new double[n]; // Temp workspace.
105
106			double b = 2.0;
107			x[0] = rhs[0] / b;
108			for (int i = 1; i < n; i++) // Decomposition and forward substitution.
109			{
110				tmp[i] = 1 / b;
111				b = (i < n - 1 ? 4.0 : 3.5) - tmp[i];
112				x[i] = (rhs[i] - x[i - 1]) / b;
113			}
114			for (int i = 1; i < n; i++)
115				x[n - i - 1] -= tmp[n - i] * x[n - i]; // Backsubstitution.
116
117			return x;
118		}
119	}
120}
```