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
    }
}