Class LengthPath2

Namespace

Thunder.UnitsNET.Vectors.Geometry

Assembly

Thunder.UnitsNET.Vectors.Geometry.dll

An arc-length parameterised polyline defined by a sequence of LengthPoint2 waypoints.

Use Evaluate(Length) to convert a scalar arc-length distance into a world-space position, and TangentAt(Length) to get the forward direction at that point.

public sealed class LengthPath2

Inheritance

object

LengthPath2

Inherited Members

object.Equals(object)

object.Equals(object, object)

object.GetHashCode()

object.GetType()

object.ReferenceEquals(object, object)

object.ToString()

Constructors

LengthPath2(IReadOnlyList<LengthPoint2>)

Creates a LengthPath2 from a sequence of world-space waypoints. The arc-length table is computed once at construction.

public LengthPath2(IReadOnlyList<LengthPoint2> points)

Parameters

points IReadOnlyList<LengthPoint2>

The ordered waypoints that define the path. Must contain at least 2 points.

Exceptions

ArgumentException

Thrown when points contains fewer than 2 elements.

Properties

Points

Gets the ordered waypoints that define this path.

public IReadOnlyList<LengthPoint2> Points { get; }

Property Value

IReadOnlyList<LengthPoint2>

TotalLength

Gets the total arc length of the path from the first to the last waypoint.

public Length TotalLength { get; }

Property Value

Length

Methods

Evaluate(Length)

Returns the world-space position at the given arc-length distance. Distances outside [0, TotalLength] are clamped.

public LengthPoint2 Evaluate(Length distance)

Parameters

distance Length

The arc-length distance from the path start.

Returns

LengthPoint2

The interpolated world-space position.

FromArc(Arc2, int)

Creates a LengthPath2 that approximates an Arc2 as a polyline with resolution + 1 evenly-spaced sample points.

public static LengthPath2 FromArc(Arc2 arc, int resolution = 32)

Parameters

arc Arc2

The arc to approximate.

resolution int

Number of segments. Must be ≥ 1. Defaults to 32.

Returns

LengthPath2

A LengthPath2 approximating the arc.

Remarks

Accuracy improves with higher resolution. At 32 segments a unit-radius semicircle is within ~0.05 m of its true arc length. Mirror of FromBezier(LengthPoint2, LengthPoint2, LengthPoint2, LengthPoint2, int) and FromCatmullRom(IReadOnlyList<LengthPoint2>, int) in sampling strategy.

var arc = new Arc2(new Circle2(LengthPoint2.FromMeters(0, 0), Length.FromMeters(5)), Direction2.East, Angle.FromDegrees(180));
var path = LengthPath2.FromArc(arc, 32);
var midpoint = path.Evaluate(path.TotalLength / 2);

FromBezier(LengthPoint2, LengthPoint2, LengthPoint2, LengthPoint2, int)

Creates a LengthPath2 that approximates a cubic Bézier curve as a polyline with resolution + 1 uniformly-spaced waypoints. The path is guaranteed to pass through p0 (t=0) and p3 (t=1).

public static LengthPath2 FromBezier(LengthPoint2 p0, LengthPoint2 p1, LengthPoint2 p2, LengthPoint2 p3, int resolution = 64)

Parameters

p0 LengthPoint2

Start point.

p1 LengthPoint2

First control point.

p2 LengthPoint2

Second control point.

p3 LengthPoint2

End point.

resolution int

Number of segments. Must be ≥ 1. Defaults to 64.

Returns

LengthPath2

A LengthPath2 approximating the cubic Bézier curve.

FromCatmullRom(IReadOnlyList<LengthPoint2>, int)

Creates a LengthPath2 that approximates a Catmull-Rom spline as a polyline. The spline passes through all supplied waypoints.

public static LengthPath2 FromCatmullRom(IReadOnlyList<LengthPoint2> waypoints, int resolution = 16)

Parameters

waypoints IReadOnlyList<LengthPoint2>

The ordered waypoints. Must contain at least 2 points.

resolution int

Segments per spline segment. Must be ≥ 1. Defaults to 16.

Returns

LengthPath2

A LengthPath2 approximating the Catmull-Rom spline.

Project(LengthPoint2)

Returns the arc-length distance along the path of the point nearest to worldPoint. O(n) in the number of segments.

public Length Project(LengthPoint2 worldPoint)

Parameters

worldPoint LengthPoint2

The world-space query point.

Returns

Length

Arc-length distance of the nearest point on the path.

Reverse()

Returns a new LengthPath2 with the waypoints in reverse order.

public LengthPath2 Reverse()

Returns

LengthPath2

A new path traversed in reverse.

SegmentAt(Length)

Returns the LengthSegment2 that contains the given arc-length distance. Distances outside [0, TotalLength] are clamped to the first or last segment respectively.

public LengthSegment2 SegmentAt(Length distance)

Parameters

distance Length

The arc-length distance from the path start.

Returns

LengthSegment2

The segment that spans that distance on the path.

TangentAt(Length)

Returns the forward direction (tangent) of the path at the given arc-length distance. Distances outside [0, TotalLength] are clamped; the direction of the nearest endpoint segment is returned.

public Direction2 TangentAt(Length distance)

Parameters

distance Length

The arc-length distance from the path start.

Returns

Direction2

The unit forward direction at that point on the path.