MoonTools.Curve/Curve/CubicBezierCurve3D.cs

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using System;
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using System.Numerics;
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namespace MoonTools.Core.Curve
{
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/// <summary>
/// A 3-dimensional Bezier curve defined by 4 points.
/// </summary>
public struct CubicBezierCurve3D : IEquatable<CubicBezierCurve3D>
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{
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/// <summary>
/// The start point.
/// </summary>
public Vector3 P0 { get; }
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/// <summary>
/// The first control point.
/// </summary>
public Vector3 P1 { get; }
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/// <summary>
/// The second control point.
/// </summary>
public Vector3 P2 { get; }
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/// <summary>
/// The end point.
/// </summary>
public Vector3 P3 { get; }
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/// <summary>
/// A representation of a 3D cubic Bezier curve.
/// </summary>
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/// <param name="p0">The start point.</param>
/// <param name="p1">The first control point.</param>
/// <param name="p2">The second control point.</param>
/// <param name="p3">The end point.</param>
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public CubicBezierCurve3D(Vector3 p0, Vector3 p1, Vector3 p2, Vector3 p3)
{
P0 = p0;
P1 = p1;
P2 = p2;
P3 = p3;
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}
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/// <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, P3, t);
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/// <summary>
/// Returns the curve coordinate given by a normalized time value.
/// </summary>
/// <param name="t"></param>
/// <param name="startTime"></param>
/// <param name="endTime"></param>
public Vector3 Point(float t, float startTime, float endTime) => Point(P0, P1, P2, P3, t, startTime, endTime);
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/// <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, P3, t);
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/// <summary>
/// Returns the instantaneous velocity on the curve given by a normalized time value.
/// </summary>
/// <param name="t">A value between 0 and 1.</param>
/// <param name="startTime"></param>
/// <param name="endTime"></param>
public Vector3 Velocity(float t, float startTime, float endTime) => Velocity(P0, P1, P2, P3, t, startTime, endTime);
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/// <summary>
/// Returns the curve coordinate given by 4 points and a time value.
/// </summary>
/// <param name="p0">The start point.</param>
/// <param name="p1">The first control point.</param>
/// <param name="p2">The second control point.</param>
/// <param name="p3">The end point.</param>
/// <param name="t">A value between 0 and 1.</param>
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public static Vector3 Point(Vector3 p0, Vector3 p1, Vector3 p2, Vector3 p3, float t)
{
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ArgumentChecker.CheckT(t);
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return ((1f - t) * (1f - t) * (1f - t) * p0) +
(3f * (1f - t) * (1f - t) * t * p1) +
(3f * (1f - t) * t * t * p2) +
(t * t * t * p3);
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}
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/// <summary>
/// Returns the curve coordinate given by 4 points and a normalized time value.
/// </summary>
/// <param name="p0">The start point.</param>
/// <param name="p1">The first control point.</param>
/// <param name="p2">The second control point.</param>
/// <param name="p3">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, Vector3 p3, float t, float startTime, float endTime)
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{
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ArgumentChecker.CheckT(t, startTime, endTime);
return Point(p0, p1, p2, p3, TimeHelper.Normalized(t, startTime, endTime));
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}
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/// <summary>
/// Returns the instantaneous velocity given by 4 points and a time value.
/// </summary>
/// <param name="p0">The start point.</param>
/// <param name="p1">The first control point.</param>
/// <param name="p2">The second control point.</param>
/// <param name="p3">The end point.</param>
/// <param name="t">A value between 0 and 1.</param>
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public static Vector3 Velocity(Vector3 p0, Vector3 p1, Vector3 p2, Vector3 p3, float t)
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{
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ArgumentChecker.CheckT(t);
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return (3f * (1f - t) * (1f - t) * (p1 - p0)) +
(6f * (1f - t) * t * (p2 - p1)) +
(3f * t * t * (p3 - p2));
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}
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/// <summary>
/// Returns the instantaneous velocity given by 4 points and a normalized time value.
/// </summary>
/// <param name="p0">The start point.</param>
/// <param name="p1">The first control point.</param>
/// <param name="p2">The second control point.</param>
/// <param name="p3">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, Vector3 p3, float t, float startTime, float endTime)
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{
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ArgumentChecker.CheckT(t, startTime, endTime);
return Velocity(p0, p1, p2, p3, TimeHelper.Normalized(t, startTime, endTime));
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}
public override bool Equals(object obj)
{
return obj is CubicBezierCurve3D d && Equals(d);
}
public bool Equals(CubicBezierCurve3D other)
{
return P0.Equals(other.P0) &&
P1.Equals(other.P1) &&
P2.Equals(other.P2) &&
P3.Equals(other.P3);
}
public override int GetHashCode()
{
return HashCode.Combine(P0, P1, P2, P3);
}
public static bool operator ==(CubicBezierCurve3D left, CubicBezierCurve3D right)
{
return left.Equals(right);
}
public static bool operator !=(CubicBezierCurve3D left, CubicBezierCurve3D right)
{
return !(left == right);
}
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}
}