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