Opentk/Source/OpenTK/Math/BezierCurve.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 bezier curve with as many points as you want.
    /// </summary>
    [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)MathHelper.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)MathHelper.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
    }
}