142 lines
5.7 KiB
C#
142 lines
5.7 KiB
C#
using Microsoft.Xna.Framework;
|
|
|
|
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);
|
|
}
|
|
}
|
|
} |