mirror of
https://github.com/Ryujinx/Opentk.git
synced 2024-12-30 21:35:33 +00:00
263 lines
9.3 KiB
C#
263 lines
9.3 KiB
C#
#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
|
||
}
|
||
}
|