Class Bezier

A Bezier curve. Parameterization of the curve is 0 -> 1.

Examples
var a = Vector3.Origin;
var b = new Vector3(5, 0, 1);
var c = new Vector3(5, 5, 2);
var d = new Vector3(0, 5, 3);
var e = new Vector3(0, 0, 4);
var f = new Vector3(5, 0, 5);
var ctrlPts = new List<Vector3> { a, b, c, d, e, f };

var bezier = new Bezier(ctrlPts);
Inheritance
System.Object
Curve
BoundedCurve
Bezier
Inherited Members
System.Object.Equals(System.Object)
System.Object.Equals(System.Object, System.Object)
System.Object.GetHashCode()
System.Object.GetType()
System.Object.MemberwiseClone()
System.Object.ReferenceEquals(System.Object, System.Object)
System.Object.ToString()
Namespace: Elements.Geometry
Assembly: Hypar.Elements.dll
Syntax
public class Bezier : BoundedCurve, ICurve, ITransformable<Curve>, IBoundedCurve

Constructors

Bezier(List<Vector3>, FrameType)

Construct a bezier.

Declaration
public Bezier(List<Vector3> controlPoints, FrameType frameType = FrameType.Frenet)
Parameters
Type Name Description
System.Collections.Generic.List<Vector3> controlPoints

The control points of the curve.
FrameType frameType

The frame type to use when calculating frames.

Properties

ControlPoints

A collection of points describing the bezier's frame. https://en.wikipedia.org/wiki/B%C3%A9zier_curve

Declaration
public List<Vector3> ControlPoints { get; set; }
Property Value
Type Description
System.Collections.Generic.List<Vector3>

Domain

The domain of the curve.

Declaration
[JsonIgnore]
public override Domain1d Domain { get; }
Property Value
Type Description
Domain1d
Overrides

FrameType

The frame type to use when calculating transforms along the curve.

Declaration
public FrameType FrameType { get; set; }
Property Value
Type Description
FrameType

Methods

AccelerationAt(Double)

Get the acceleration of the curve at parameter u.

Declaration
public Vector3 AccelerationAt(double u)
Parameters
Type Name Description
System.Double u

A parameter between 0.0 and 1.0.
Returns
Type Description
Vector3

ArcLength(Double, Double)

Calculate the length of the bezier between start and end parameters.

Declaration
public override double ArcLength(double start, double end)
Parameters
Type Name Description
System.Double start
System.Double end
Returns
Type Description
System.Double

The length of the bezier between start and end.
Overrides

BinormalAt(Double)

Get the binormal to the curve at parameter u.

Declaration
public Vector3 BinormalAt(double u)
Parameters
Type Name Description
System.Double u

A parameter between 0.0 and 1.0.
Returns
Type Description
Vector3

Bounds()

Get the bounding box of the curve's control points.

Declaration
public override BBox3 Bounds()
Returns
Type Description
BBox3
Overrides

GetSubdivisionParameters(Double, Double)

Get parameters to be used to find points along the curve for visualization.

Declaration
public override double[] GetSubdivisionParameters(double startSetbackDistance = 0, double endSetbackDistance = 0)
Parameters
Type Name Description
System.Double startSetbackDistance

An optional setback from the start of the curve.
System.Double endSetbackDistance

An optional setback from the end of the curve.
Returns
Type Description
System.Double[]

A collection of parameter values.
Overrides

Length()

Get a piecewise linear approximation of the length of the curve. https://en.wikipedia.org/wiki/Arc_length

Declaration
public override double Length()
Returns
Type Description
System.Double
Overrides

NormalAt(Double)

Get the normal of the curve at parameter u.

Declaration
public Vector3 NormalAt(double u)
Parameters
Type Name Description
System.Double u

A parameter between 0.0 and 1.0.
Returns
Type Description
Vector3

ParameterAtDistanceFromParameter(Double, Double)

Get the parameter at a distance from the start parameter along the curve.

Declaration
public override double ParameterAtDistanceFromParameter(double distance, double start)
Parameters
Type Name Description
System.Double distance

The distance from the start parameter.
System.Double start

The parameter from which to measure the distance.
Returns
Type Description
System.Double
Overrides

PointAt(Double)

Get the point on the curve at parameter u.

Declaration
public override Vector3 PointAt(double u)
Parameters
Type Name Description
System.Double u

The parameter between 0.0 and 1.0.
Returns
Type Description
Vector3
Overrides

TangentAt(Double)

Get the tangent to the curve at parameter u.

Declaration
public Vector3 TangentAt(double u)
Parameters
Type Name Description
System.Double u

A parameter between 0.0 and 1.0.
Returns
Type Description
Vector3

TransformAt(Double)

Get the transform on the curve at parameter u.

Declaration
public override Transform TransformAt(double u)
Parameters
Type Name Description
System.Double u

The parameter along the curve between 0.0 and 1.0.
Returns
Type Description
Transform
Overrides

Transformed(Transform)

Construct a transformed copy of this Curve.

Declaration
public override Curve Transformed(Transform transform)
Parameters
Type Name Description
Transform transform

The transform to apply.
Returns
Type Description
Curve
Overrides

TransformedBezier(Transform)

Construct a transformed copy of this Bezier.

Declaration
public Bezier TransformedBezier(Transform transform)
Parameters
Type Name Description
Transform transform

The transform to apply.
Returns
Type Description
Bezier

VelocityAt(Double)

Get the velocity to the curve at parameter u.

Declaration
public Vector3 VelocityAt(double u)
Parameters
Type Name Description
System.Double u

A parameter between 0.0 and 1.0.
Returns
Type Description
Vector3

Implements