MoonTools.Curve/Curve/QuadraticBezierCurve3D.cs

using System.Numerics;

namespace MoonTools.Core.Curve
{
    /// <summary>
    /// A 3-dimensional Bezier curve defined by 3 points.
    /// </summary>
    public struct QuadraticBezierCurve3D
    {
        /// <summary>
        /// The start point.
        /// </summary>
        public Vector3 p0;

        /// <summary>
        /// The control point.
        /// </summary>
        public Vector3 p1;

        /// <summary>
        /// The end point.
        /// </summary>
        public Vector3 p2;

        /// <param name="p0">The start point.</param>
        /// <param name="p1">The control point.</param>
        /// <param name="p2">The end point.</param>
        public QuadraticBezierCurve3D(Vector3 p0, Vector3 p1, Vector3 p2)
        {
            this.p0 = p0;
            this.p1 = p1;
            this.p2 = p2;
        }

        /// <summary>
        /// Returns the curve coordinate given by t.
        /// </summary>
        /// <param name="t">A value between 0 and 1.</param>
        public Vector3 Point(float t) => Point(p0, p1, p2, t);

        /// <summary>
        /// Returns the curve coordinate given by a normalized time value.
        /// </summary>
        /// <param name="t">A time value between startTime and endTime.</param>
        /// <param name="startTime"></param>
        /// <param name="endTime"></param>
        public Vector3 Point(float t, float startTime, float endTime) => Point(p0, p1, p2, t, startTime, endTime);

        /// <summary>
        /// Returns the instantaneous velocity on the curve given by t.
        /// </summary>
        /// <param name="t">A value between 0 and 1.</param>
        public Vector3 Velocity(float t) => Velocity(p0, p1, p2, t);

        /// <summary>
        /// Returns the instantaneous velocity on the curve given by a normalized time value.
        /// </summary>
        /// <param name="t">An arbitrary value between startTime and endTime.</param>
        /// <param name="startTime"></param>
        /// <param name="endTime"></param>
        public Vector3 Velocity(float t, float startTime, float endTime) => Velocity(p0, p1, p2, t, startTime, endTime);

        /// <summary>
        /// Performs degree elevation on the curve to turn it into a Cubic Bezier curve.
        /// </summary>
        /// <returns>The same curve expressed as a cubic curve.</returns>
        public CubicBezierCurve3D AsCubic()
        {
            var (p0, p1, p2, p3) = AsCubic(this.p0, this.p1, this.p2);
            return new CubicBezierCurve3D(p0, p1, p2, p3);
        }

        /// <summary>
        /// Given quadratic control points, returns cubic control points.
        /// </summary>
        public static (Vector3, Vector3, Vector3, Vector3) AsCubic(Vector3 p0, Vector3 p1, Vector3 p2)
        {
            var cubicP0 = p0;
            var cubicP1 = (2f / 3f * p1) + ((1f / 3f) * p0);
            var cubicP2 = (2f / 3f * p1) + ((1f / 3f) * p2);
            var cubicP3 = p2;

            return (cubicP0, cubicP1, cubicP2, cubicP3);
        }

        /// <summary>
        /// Returns the curve coordinate given by 3 points and a time value.
        /// </summary>
        /// <param name="p0">The start point.</param>
        /// <param name="p1">The control point.</param>
        /// <param name="p2">The end point.</param>
        /// <param name="t">A value between 0 and 1.</param>
        public static Vector3 Point(Vector3 p0, Vector3 p1, Vector3 p2, float t)
        {
            var (cubicP0, cubicP1, cubicP2, cubicP3) = AsCubic(p0, p1, p2);
            return CubicBezierCurve3D.Point(cubicP0, cubicP1, cubicP2, cubicP3, t);
        }

        /// <summary>
        /// Returns the curve coordinate given by 3 points and a normalized time value.
        /// </summary>
        /// <param name="p0">The start point.</param>
        /// <param name="p1">The control point.</param>
        /// <param name="p2">The end point.</param>
        /// <param name="t">A value between startTime and endTime.</param>
        /// <param name="startTime"></param>
        /// <param name="endTime"></param>
        public static Vector3 Point(Vector3 p0, Vector3 p1, Vector3 p2, float t, float startTime, float endTime)
        {
            var (cubicP0, cubicP1, cubicP2, cubicP3) = AsCubic(p0, p1, p2);
            return CubicBezierCurve3D.Point(cubicP0, cubicP1, cubicP2, cubicP3, t, startTime, endTime);
        }

        /// <summary>
        /// Returns the instantaneous velocity given by 3 points and a normalized time value.
        /// </summary>
        /// <param name="p0">The start point.</param>
        /// <param name="p1">The control point.</param>
        /// <param name="p2">The end point.</param>
        /// <param name="t">A value between 0 and 1.</param>
        public static Vector3 Velocity(Vector3 p0, Vector3 p1, Vector3 p2, float t)
        {
            var (cubicP0, cubicP1, cubicP2, cubicP3) = AsCubic(p0, p1, p2);
            return CubicBezierCurve3D.Velocity(cubicP0, cubicP1, cubicP2, cubicP3, t);
        }

        /// <summary>
        /// Returns the instantaneous velocity given by 3 points and a normalized time value.
        /// </summary>
        /// <param name="p0">The start point.</param>
        /// <param name="p1">The control point.</param>
        /// <param name="p2">The end point.</param>
        /// <param name="t">A value between startTime and endTime.</param>
        /// <param name="startTime"></param>
        /// <param name="endTime"></param>
        public static Vector3 Velocity(Vector3 p0, Vector3 p1, Vector3 p2, float t, float startTime, float endTime)
        {
            var (cubicP0, cubicP1, cubicP2, cubicP3) = AsCubic(p0, p1, p2);
            return CubicBezierCurve3D.Velocity(cubicP0, cubicP1, cubicP2, cubicP3, t, startTime, endTime);
        }
    }
}