Struct CubicBezier

Namespace

Xui.Core.Curves2D

Assembly

Core.dll

Represents a cubic Bézier curve defined by four control points.

public readonly struct CubicBezier : ICurve

Implements

ICurve

Inherited Members

ValueType.Equals(object)

ValueType.GetHashCode()

ValueType.ToString()

object.Equals(object, object)

object.GetType()

object.ReferenceEquals(object, object)

Remarks

A cubic Bézier curve provides smooth interpolation between P0 and P3, influenced by the control points P1 and P2. This is commonly used in vector graphics, animation timing, and layout paths.

Constructors

CubicBezier(Point, Point, Point, Point)

Initializes a new cubic Bézier curve with the specified control points.

public CubicBezier(Point p0, Point p1, Point p2, Point p3)

Parameters

p0 Point

p1 Point

p2 Point

p3 Point

Fields

P0

The starting point of the curve.

public readonly Point P0

Field Value

Point

P1

The first control point, influencing the curve near P0.

public readonly Point P1

Field Value

Point

P2

The second control point, influencing the curve near P3.

public readonly Point P2

Field Value

Point

P3

The ending point of the curve.

public readonly Point P3

Field Value

Point

Properties

this[NFloat]

Gets the interpolated point on the curve at the specified parameter.

public Point this[NFloat t] { get; }

Parameters

t NFloat

A normalized parameter in the range [0, 1].

Property Value

Point

QuadraticApproximation

public QuadraticBezier QuadraticApproximation { get; }

Property Value

QuadraticBezier

Methods

ClosestT(Point)

Returns the parameter t ∈ [0, 1] at which the curve is closest to the specified target point. This version uses uniform sampling with 16 segments and is fast enough for interactive use.

public NFloat ClosestT(Point target)

Parameters

target Point

The point to compare against the curve.

Returns

NFloat

The approximate t value where the curve is closest to target.

ClosestT(Point, NFloat)

Returns the parameter t ∈ [0, 1] at which the curve is closest to the specified target point, using recursive ternary subdivision until the difference in t range is less than precision.

public NFloat ClosestT(Point target, NFloat precision)

Parameters

target Point

The point to compare against the curve.

precision NFloat

The minimum resolution for t convergence. Smaller values yield more accurate results.

Returns

NFloat

The t value where the curve is closest to target within the specified precision.

Drag(NFloat, Vector)

Returns a new CubicBezier curve where the control points P1 and P2 are adjusted based on a drag gesture at a given parametric position t.

public CubicBezier Drag(NFloat t, Vector delta)

Parameters

t NFloat

A normalized value (between 0 and 1) representing the position on the curve where the drag occurs.

delta Vector

The drag vector representing how far the user dragged the point at t.

Returns

CubicBezier

A new CubicBezier with P0 and P3 unchanged, and P1 and P2 adjusted proportionally to the drag direction and distance.

Remarks

The influence of the drag on P1 and P2 is weighted quadratically based on their distance from t along the curve: P1 is influenced by (1 - t)² and P2 by t². This preserves the endpoints while allowing intuitive manipulation of the curve shape.

DragAt(Point, Vector)

Returns a new cubic Bézier curve with adjusted control points so the point on the curve nearest to origin is moved by delta.

public CubicBezier DragAt(Point origin, Vector delta)

Parameters

origin Point

delta Vector

Returns

CubicBezier

DragAt(Point, Vector, NFloat)

Returns a new cubic Bézier curve with adjusted control points so the point on the curve nearest to origin is moved by delta. Uses recursive refinement based on the specified precision.

public CubicBezier DragAt(Point origin, Vector delta, NFloat precision)

Parameters

origin Point

delta Vector

precision NFloat

Returns

CubicBezier

Length()

Approximates the arc length of the curve using uniform sampling with 16 segments.

public NFloat Length()

Returns

NFloat

Length(NFloat)

Approximates the arc length of the curve using recursive adaptive subdivision.

public NFloat Length(NFloat precision)

Parameters

precision NFloat

The tolerance value used to determine when a segment is flat enough to stop subdividing. Smaller values result in more accurate results but require more computation.

Returns

NFloat

Lerp(NFloat)

Computes the interpolated point on the curve at parameter t using De Casteljau’s algorithm.

public Point Lerp(NFloat t)

Parameters

t NFloat

A normalized parameter in the range [0, 1].

Returns

Point

SplitIntoYMonotonicCurves()

public MonotonicCubicBezier SplitIntoYMonotonicCurves()

Returns

MonotonicCubicBezier

Subdivide(NFloat)

Subdivides this cubic Bézier curve at parameter t, returning two curves.

public (CubicBezier, CubicBezier) Subdivide(NFloat t)

Parameters

t NFloat

Returns

(CubicBezier, CubicBezier)

Tangent(NFloat)

Computes the tangent vector of the curve at parameter t.

public Vector Tangent(NFloat t)

Parameters

t NFloat

A normalized parameter in the range [0, 1].

Returns

Vector

ToQuadratics(Span<QuadraticBezier>, NFloat, out int)

Converts this cubic Bézier curve into a sequence of Y-monotonic quadratic Bézier segments, each approximating a portion of the original curve within the specified flatness precision.

public void ToQuadratics(Span<QuadraticBezier> buffer, NFloat precision, out int count)

Parameters

buffer Span<QuadraticBezier>

A span to receive the quadratic segments. Must be large enough to hold the result. A typical size is between 4 and 32. Must be at least 3 to accommodate the initial monotonic split.

precision NFloat

The maximum allowed distance between the original cubic curve and its quadratic approximation. Lower values yield more accurate approximations but may require more output segments.

count int

The number of segments written to buffer.

Remarks

This method uses an adaptive, flatness-aware subdivision strategy. It begins by splitting the cubic curve into up to 3 Y-monotonic segments. Each is then approximated with a quadratic Bézier, and the segments with the highest deviation are recursively subdivided until the total number of segments fits within buffer and all segments meet the precision requirement.

The output segments are returned in order, forming a continuous piecewise-curve that follows the original cubic. Suitable for SDF tessellation or scanline-based rasterization.

Exceptions

ArgumentException

Thrown if buffer has fewer than 3 elements.

Operators

implicit operator CubicBezier((Point p0, Point p1, Point p2, Point p3))

Implicitly converts a tuple of four points into a CubicBezier.

public static implicit operator CubicBezier((Point p0, Point p1, Point p2, Point p3) value)

Parameters

value (Point p0, Point p1, Point p2, Point p3)

A tuple representing the start point, two control points, and end point.

Returns

CubicBezier

implicit operator CubicBezier(CubicSpline)

Implicitly converts this cubic Catmull–Rom spline to a CubicBezier.

public static implicit operator CubicBezier(CubicSpline spline)

Parameters

spline CubicSpline

Returns

CubicBezier

Remarks

Uses the canonical Catmull–Rom to Bézier mapping, interpolating between P1 and P2.

implicit operator CubicBezier(QuadraticBezier)

Implicitly converts a QuadraticBezier to a CubicBezier using interpolation for smooth parameterization.

public static implicit operator CubicBezier(QuadraticBezier quadratic)

Parameters

quadratic QuadraticBezier

Returns

CubicBezier

Remarks

This conversion evaluates the quadratic Bézier at fixed steps (1⁄3 and 2⁄3) to generate the internal control points of the cubic, resulting in a visually smooth upgrade path.