Opentk/Source/OpenTK/Math/BezierCurveCubic.cs

#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<EFBFBD>chter.
 */
#endregion

using System;
using System.Collections.Generic;
using System.Text;

namespace OpenTK
{
	/// <summary>
	/// Represents a cubic bezier curve with two anchor and two control points.
	/// </summary>
	[Serializable]
	public struct BezierCurveCubic
	{
		#region Fields

		/// <summary>
		/// Start anchor point.
		/// </summary>
		public Vector2 StartAnchor;

		/// <summary>
		/// End anchor point.
		/// </summary>
		public Vector2 EndAnchor;

		/// <summary>
		/// First control point, controls the direction of the curve start.
		/// </summary>
		public Vector2 FirstControlPoint;

		/// <summary>
		/// Second control point, controls the direction of the curve end.
		/// </summary>
		public Vector2 SecondControlPoint;

		/// <summary>
		/// Gets or sets 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.f to the orignal curve at any point.</remarks>
		public float Parallel;

		#endregion

		#region Constructors

		/// <summary>
		/// Constructs a new <see cref="BezierCurveCubic"/>.
		/// </summary>
		/// <param name="startAnchor">The start anchor point.</param>
		/// <param name="endAnchor">The end anchor point.</param>
		/// <param name="firstControlPoint">The first control point.</param>
		/// <param name="secondControlPoint">The second control point.</param>
		public BezierCurveCubic(Vector2 startAnchor, Vector2 endAnchor, Vector2 firstControlPoint, Vector2 secondControlPoint)
		{
			this.StartAnchor = startAnchor;
			this.EndAnchor = endAnchor;
			this.FirstControlPoint = firstControlPoint;
			this.SecondControlPoint = secondControlPoint;
			this.Parallel = 0.0f;
		}

		/// <summary>
		/// Constructs a new <see cref="BezierCurveCubic"/>.
		/// </summary>
		/// <param name="parallel">The parallel value.</param>
		/// <param name="startAnchor">The start anchor point.</param>
		/// <param name="endAnchor">The end anchor point.</param>
		/// <param name="firstControlPoint">The first control point.</param>
		/// <param name="secondControlPoint">The second control point.</param>
		public BezierCurveCubic(float parallel, Vector2 startAnchor, Vector2 endAnchor, Vector2 firstControlPoint, Vector2 secondControlPoint)
		{
			this.Parallel = parallel;
			this.StartAnchor = startAnchor;
			this.EndAnchor = endAnchor;
			this.FirstControlPoint = firstControlPoint;
			this.SecondControlPoint = secondControlPoint;
		}

		#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)
		{
			Vector2 r = new Vector2();
			float c = 1.0f - t;

			r.X = (StartAnchor.X * c * c * c) + (FirstControlPoint.X * 3 * t * c * c) + (SecondControlPoint.X * 3 * t * t * c)
				+ EndAnchor.X * t * t * t;
			r.Y = (StartAnchor.Y * c * c * c) + (FirstControlPoint.Y * 3 * t * c * c) + (SecondControlPoint.Y * 3 * t * t * c)
				+ EndAnchor.Y * t * t * t;

			if (Parallel == 0.0f)
				return r;

			Vector2 perpendicular = new Vector2();

			if (t == 0.0f)
				perpendicular = FirstControlPoint - StartAnchor;
			else
				perpendicular = r - CalculatePointOfDerivative(t);

			return r + Vector2.Normalize(perpendicular).PerpendicularRight * Parallel;
		}

		/// <summary>
		/// Calculates the point with the specified t of the derivative of this function.
		/// </summary>
		/// <param name="t">The t, value between 0.0f and 1.0f.</param>
		/// <returns>Resulting point.</returns>
		private Vector2 CalculatePointOfDerivative(float t)
		{
			Vector2 r = new Vector2();
			float c = 1.0f - t;

			r.X = (c * c * StartAnchor.X) + (2 * t * c * FirstControlPoint.X) + (t * t * SecondControlPoint.X);
			r.Y = (c * c * StartAnchor.Y) + (2 * t * c * FirstControlPoint.Y) + (t * t * SecondControlPoint.Y);

			return r;
		}

		/// <summary>
		/// Calculates the length of this bezier curve.
		/// </summary>
		/// <param name="precision">The precision.</param>
		/// <returns>Length of the curve.</returns>
		/// <remarks>The precision gets better when the <paramref name="precision"/>
		/// value gets smaller.</remarks>
		public float CalculateLength(float precision)
		{
			float length = 0.0f;
			Vector2 old = CalculatePoint(0.0f);

			for (float i = precision; i < (1.0f + precision); i += precision)
			{
				Vector2 n = CalculatePoint(i);
				length += (n - old).Length;
				old = n;
			}

			return length;
		}

		#endregion
	}
}