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262 lines
9.2 KiB
C#
262 lines
9.2 KiB
C#
#region --- License ---
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/* Licensed under the MIT/X11 license.
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* Copyright (c) 2006-2008 the OpenTK Team.
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* This notice may not be removed from any source distribution.
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* See license.txt for licensing detailed licensing details.
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*
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* Contributions by Georg W<>chter.
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*/
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#endregion
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using System;
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using System.Collections.Generic;
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using System.Text;
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namespace OpenTK
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{
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/// <summary>
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/// Represents a bezier curve with as many points as you want.
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/// </summary>
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[Serializable]
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public struct BezierCurve
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{
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#region Fields
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private List<Vector2> points;
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/// <summary>
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/// The parallel value.
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/// </summary>
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/// <remarks>This value defines whether the curve should be calculated as a
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/// parallel curve to the original bezier curve. A value of 0.0f represents
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/// the original curve, 5.0f i.e. stands for a curve that has always a distance
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/// of 5.0f to the orignal curve at any point.</remarks>
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public float Parallel;
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#endregion
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#region Properties
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/// <summary>
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/// Gets the points of this curve.
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/// </summary>
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/// <remarks>The first point and the last points represent the anchor points.</remarks>
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public IList<Vector2> Points
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{
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get
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{
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return points;
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}
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}
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#endregion
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#region Constructors
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/// <summary>
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/// Constructs a new <see cref="BezierCurve"/>.
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/// </summary>
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/// <param name="points">The points.</param>
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public BezierCurve(IEnumerable<Vector2> points)
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{
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if (points == null)
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throw new ArgumentNullException("points", "Must point to a valid list of Vector2 structures.");
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this.points = new List<Vector2>(points);
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this.Parallel = 0.0f;
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}
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/// <summary>
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/// Constructs a new <see cref="BezierCurve"/>.
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/// </summary>
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/// <param name="points">The points.</param>
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public BezierCurve(params Vector2[] points)
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{
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if (points == null)
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throw new ArgumentNullException("points", "Must point to a valid list of Vector2 structures.");
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this.points = new List<Vector2>(points);
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this.Parallel = 0.0f;
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}
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/// <summary>
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/// Constructs a new <see cref="BezierCurve"/>.
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/// </summary>
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/// <param name="parallel">The parallel value.</param>
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/// <param name="points">The points.</param>
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public BezierCurve(float parallel, params Vector2[] points)
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{
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if (points == null)
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throw new ArgumentNullException("points", "Must point to a valid list of Vector2 structures.");
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this.Parallel = parallel;
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this.points = new List<Vector2>(points);
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}
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/// <summary>
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/// Constructs a new <see cref="BezierCurve"/>.
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/// </summary>
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/// <param name="parallel">The parallel value.</param>
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/// <param name="points">The points.</param>
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public BezierCurve(float parallel, IEnumerable<Vector2> points)
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{
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if (points == null)
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throw new ArgumentNullException("points", "Must point to a valid list of Vector2 structures.");
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this.Parallel = parallel;
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this.points = new List<Vector2>(points);
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}
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#endregion
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#region Functions
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/// <summary>
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/// Calculates the point with the specified t.
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/// </summary>
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/// <param name="t">The t value, between 0.0f and 1.0f.</param>
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/// <returns>Resulting point.</returns>
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public Vector2 CalculatePoint(float t)
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{
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return BezierCurve.CalculatePoint(points, t, Parallel);
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}
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/// <summary>
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/// Calculates the length of this bezier curve.
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/// </summary>
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/// <param name="precision">The precision.</param>
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/// <returns>Length of curve.</returns>
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/// <remarks>The precision gets better as the <paramref name="precision"/>
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/// value gets smaller.</remarks>
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public float CalculateLength(float precision)
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{
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return BezierCurve.CalculateLength(points, precision, Parallel);
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}
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#region Static methods
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/// <summary>
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/// Calculates the length of the specified bezier curve.
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/// </summary>
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/// <param name="points">The points.</param>
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/// <param name="precision">The precision value.</param>
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/// <returns>The precision gets better as the <paramref name="precision"/>
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/// value gets smaller.</returns>
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public static float CalculateLength(IList<Vector2> points, float precision)
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{
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return BezierCurve.CalculateLength(points, precision, 0.0f);
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}
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/// <summary>
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/// Calculates the length of the specified bezier curve.
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/// </summary>
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/// <param name="points">The points.</param>
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/// <param name="precision">The precision value.</param>
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/// <param name="parallel">The parallel value.</param>
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/// <returns>Length of curve.</returns>
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/// <remarks><para>The precision gets better as the <paramref name="precision"/>
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/// value gets smaller.</para>
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/// <para>The <paramref name="parallel"/> parameter defines whether the curve should be calculated as a
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/// parallel curve to the original bezier curve. A value of 0.0f represents
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/// the original curve, 5.0f represents a curve that has always a distance
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/// of 5.0f to the orignal curve.</para></remarks>
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public static float CalculateLength(IList<Vector2> points, float precision, float parallel)
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{
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float length = 0.0f;
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Vector2 old = BezierCurve.CalculatePoint(points, 0.0f, parallel);
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for (float i = precision; i < (1.0f + precision); i += precision)
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{
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Vector2 n = CalculatePoint(points, i, parallel);
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length += (n - old).Length;
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old = n;
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}
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return length;
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}
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/// <summary>
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/// Calculates the point on the given bezier curve with the specified t parameter.
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/// </summary>
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/// <param name="points">The points.</param>
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/// <param name="t">The t parameter, a value between 0.0f and 1.0f.</param>
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/// <returns>Resulting point.</returns>
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public static Vector2 CalculatePoint(IList<Vector2> points, float t)
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{
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return BezierCurve.CalculatePoint(points, t, 0.0f);
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}
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/// <summary>
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/// Calculates the point on the given bezier curve with the specified t parameter.
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/// </summary>
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/// <param name="points">The points.</param>
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/// <param name="t">The t parameter, a value between 0.0f and 1.0f.</param>
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/// <param name="parallel">The parallel value.</param>
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/// <returns>Resulting point.</returns>
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/// <remarks>The <paramref name="parallel"/> parameter defines whether the curve should be calculated as a
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/// parallel curve to the original bezier curve. A value of 0.0f represents
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/// the original curve, 5.0f represents a curve that has always a distance
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/// of 5.0f to the orignal curve.</remarks>
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public static Vector2 CalculatePoint(IList<Vector2> points, float t, float parallel)
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{
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Vector2 r = new Vector2();
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double c = 1.0d - (double)t;
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float temp;
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int i = 0;
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foreach (Vector2 pt in points)
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{
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temp = (float)MathHelper.BinomialCoefficient(points.Count - 1, i) * (float)(System.Math.Pow(t, i) *
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System.Math.Pow(c, (points.Count - 1) - i));
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r.X += temp * pt.X;
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r.Y += temp * pt.Y;
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i++;
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}
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if (parallel == 0.0f)
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return r;
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Vector2 perpendicular = new Vector2();
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if (t != 0.0f)
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perpendicular = r - BezierCurve.CalculatePointOfDerivative(points, t);
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else
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perpendicular = points[1] - points[0];
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return r + Vector2.Normalize(perpendicular).PerpendicularRight * parallel;
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}
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/// <summary>
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/// Calculates the point with the specified t of the derivative of the given bezier function.
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/// </summary>
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/// <param name="points">The points.</param>
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/// <param name="t">The t parameter, value between 0.0f and 1.0f.</param>
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/// <returns>Resulting point.</returns>
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private static Vector2 CalculatePointOfDerivative(IList<Vector2> points, float t)
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{
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Vector2 r = new Vector2();
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double c = 1.0d - (double)t;
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float temp;
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int i = 0;
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foreach (Vector2 pt in points)
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{
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temp = (float)MathHelper.BinomialCoefficient(points.Count - 2, i) * (float)(System.Math.Pow(t, i) *
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System.Math.Pow(c, (points.Count - 2) - i));
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r.X += temp * pt.X;
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r.Y += temp * pt.Y;
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i++;
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}
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return r;
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}
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#endregion
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#endregion
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}
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}
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