BH.oM.Geometry.NurbsCurve¶

A non-uniform rational basis spline (or B-spline). Enables definition of smooth and continuous curves as piece-wise polynomial basis functions evaluated from discrete geometrical ControlPoints. A NurbsCurve, through its use of ControlPoint Weightings, has the ability to precisely represent the conic sections, such as the circle and parabolas etc.

Class structure¶

Implemented interfaces and base types¶

The NurbsCurve is inheriting from the following base type(s) and implements the following interfaces:

BH.oM.Geometry.ICurve
BH.oM.Geometry.IGeometry
BH.oM.Base.IObject
BH.oM.Dimensional.IElement1D
BH.oM.Dimensional.IElement

Properties¶

Defining properties¶

The following properties are defined on the class

Name	Type	Description	Quantity
ControlPoints	List<Point>	An ordered set of three-dimensional points defining the curve shape. The control point locations are approximating, as opposed to interpolating, meaning in the general case the resulting curve will not pass through the control point locations themselves. The special case of where both Knot and ControlPoint count are equal defines a NurbsCurve of Degree 1. This shape will pass through all ControlPoints, linearly interpolating beween them and being equivalent to a Polyline.	-
Weights	List<double>	A list of scalar factors, one for each ControlPoint. The weights in effect add an additional degree of freedom, allowing control over the relative influence of each control point on the curve shape	-
Knots	List<double>	The knot vector is a non-decreasing list of numbers, the relative spacing of which define the spans and transition points of the basis functions along the curve's domain. Knot vector length must be equal to or greater than the number of ControlPoints, such that together, the difference in counts defines the order (and degree) of the NurbsCurve. The NurbsCurve degree is equal to order plus one.	-

Derived properties¶

The following properties are defined as extension methods in one of the BHoM_Engines

Name	Type	Description	Quantity	Engine
Bounds	BoundingBox	Returns the global world axis oriented BoundingBox for all control points of the NurbsCurve. Note that this is not the minimum eclosing box of the NurbsCurve.	-	Geometry_Engine
Bounds	BoundingBox	Queries the IElement1Ds BoundingBox. Acts on the ICurve definition of the IElement1D through the Geometry_Engine.	-	Spatial_Engine
Centroid	Point	Queries the centre of weight for a IElement1Ds ICurve representation.	-	Spatial_Engine
ControlPoints	List<Point>	Gets the ControlPoints of the NurbsCurve. Note that these points might not be on the curve.	-	Geometry_Engine
ControlPoints	List<Point>	Queries the control points of the one dimensional representation of the IElement1D.	-	Spatial_Engine
Degree	int	-	-	Geometry_Engine
DominantVector	Vector	Gets the the dominant vector (orientation) of an Element1D based on its lines lengths.	-	Spatial_Engine
ElementCurves	List<ICurve>	Queries the defining curves of an IElement1D.	-	Spatial_Engine
ElementVertices	List<Point>	Returns the discontinuity points from the defining ICurve of the IElement1D.	-	Spatial_Engine
EndPoint	Point	-	-	Geometry_Engine
Geometry	ICurve	-	-	Geometry_Engine
GeometryHash	string	Returns a signature of the input geometry, useful for diffing. The hash is computed as a serialised array representing the coordinate of significant points taken on the geometry. The number of points is reduced to the minimum essential to determine uniquely any geometry. Additionally, the resulting points are transformed based on the source geometry type, to remove or minimize collisions. (Any transformation so performed is translational only, in order to support geometrical tolerance, i.e. numerical distance, when comparing GeometryHashes downstream).	-	Geometry_Engine
Height	double	Returns the height of a BHoM Geometry ICurve based on the bounding box of the curve	-	Environment_Engine
IArea	double	Queries the area of the geometrical representation of an IElement.	Area [m²]	Spatial_Engine
IArea	double	Calculates the area of the provided geometry.	Area [m²]	Geometry_Engine
IBounds	BoundingBox	Returns the global world axis oriented enclosing BoundingBox for all points of the geometry, i.e. the box with the smallest volume within which all the points on the geometry lie.	-	Geometry_Engine
IBounds	BoundingBox	Queries the IElements BoundingBox. Acts on the elements geometrical definition of the IElement through the Geometry_Engine.	-	Spatial_Engine
ICentroid	Point	Queries the centre of weight for the homogeneous geometrical representation of an IElement.	-	Spatial_Engine
ICentroid	Point	Interface method that queries the centre of area for any ICurve.	-	Geometry_Engine
IControlPoints	List<Point>	Gets the ControlPoints of the ICurve. Result will depend on the curve provided. Note that for NurbsCurves might not returns curves that are on the curve.	-	Geometry_Engine
IControlPoints	List<Point>	Queries the control points of the geometrical representation of an IElement.	-	Spatial_Engine
IDiscontinuityPoints	List<Point>	Gets the points at kinks of the curve, i.e. points where the tangent between two segments coming in to the same point is outside of the provided tolerance.	-	Geometry_Engine
IElementCurves	List<ICurve>	Queries the geometricly defining curves of the IElements geometry.	-	Spatial_Engine
IElements0D	List<IElement0D>	Queries the IElement0Ds from a IElement1D. Returns null if no IElement0Ds are defined for the type of IElement1D.	-	Spatial_Engine
IElementVertices	List<Point>	Returns the discontinuity points from the defining ICurves of the IElement.	-	Spatial_Engine
IEndDir	Vector	Gets the tangent vector at the end of the curve.	-	Geometry_Engine
IEndPoint	Point	-	-	Geometry_Engine
IGeometry	ICurve	Queries the defining geometrical object which all spatial operations will act on.	-	Spatial_Engine
IGeometry	ICurve	-	-	Geometry_Engine
IHashArray	double[]	Returns a signature of the input geometry, useful for distance-based comparisons and diffing. The hash is computed as an array representing the coordinate of significant points taken on the geometry. The number of points is reduced to the minimum essential to determine uniquely any geometry. Additionally, the resulting points are transformed based on the source geometry type, to remove or minimize collisions. (Any transformation so performed is translational only, in order to support geometrical tolerance, i.e. numerical distance, when comparing GeometryHashes downstream).	-	Geometry_Engine
IIsClosed	bool	Checks if the ICurve is closed, i.e. forms a closed loop.	-	Geometry_Engine
IIsLinear	bool	Returns if the curve is Linear or not.	-	Geometry_Engine
IIsPlanar	bool	Checks whether all control points of an element lie in a single plane.	-	Spatial_Engine
IIsPlanar	bool	Checks if the IGeometry is planar, i.e. all of its parts fit in a single plane.	-	Geometry_Engine
IIsPolylinear	bool	Returns if the curve is polylinear or not.	-	Geometry_Engine
IIsSelfIntersecting	bool	Checks if any of the curves defining an IElement is closer to itself than the tolerance at any two points (is self intersecting). In case of IElement2D, does not check for intersections between external and internal curves, or between different internal curves.	-	Spatial_Engine
IIsSelfIntersecting	bool	Checks if any part of the the ICurve is intersecting with any other part of the curve.	-	Geometry_Engine
IIsValid	bool	-	-	Geometry_Engine
ILength	double	Calculates the length of a Curve.	Length [m]	Geometry_Engine
INormal	Vector	Interface method that returns a vector normal to the plane of any ICurve and oriented according to the right hand rule. Works only for closed and planar curves with an exception for single Arcs.	-	Geometry_Engine
INormals	List<Vector>	Interface method that returns the list of vectors normal to any IGeometry.	-	Geometry_Engine
IPrimaryPropertyName	string	Returns the name of an elements primary defining property	-	Facade_Engine
IsClosed	bool	Checks if the NurbsCurve is closed, i.e. forms a closed loop, by checking if the end points are within tolerance of each other or if it is a periodic curve.	-	Geometry_Engine
IsNull	bool	Checks if a Geometry is null and outputs relevant error message.	-	Geometry_Engine
IsNurbsCurve	bool	Queries if any part of the curve is a nurbs curve.	-	Geometry_Engine
IsPeriodic	bool	-	-	Geometry_Engine
IsPlanar	bool	Checks if the NurbsCurve is planar, i.e. all of its parts fit in a single plane. Check is done by evaluating if all the controlpoints are co-planar within the provided tolerance.	-	Geometry_Engine
IsPlanar	bool	Checks whether all control points of an element lie in a single plane.	-	Spatial_Engine
IsSelfIntersecting	bool	Checks if the one dimensional representation of the IElement1D is closer to itself than the tolerance at any two points.	-	Spatial_Engine
IStartDir	Vector	Gets the tangent vector at the start of the curve.	-	Geometry_Engine
IStartPoint	Point	-	-	Geometry_Engine
ISubParts	IEnumerable<ICurve>	-	-	Geometry_Engine
ISubParts	IEnumerable<IGeometry>	-	-	Geometry_Engine
IsValid	bool	-	-	Geometry_Engine
Length	double	Returns the length of the IElement1Ds curve.	Length [m]	Spatial_Engine
PointInRegion	Point	-	-	Geometry_Engine
StartPoint	Point	-	-	Geometry_Engine
ToEdges	List<Edge>	Returns a collection of Environment Edges from a BHoM Geomtry Polyline	-	Environment_Engine
Width	double	Returns the width of a BHoM Geometry ICurve based on the bounding box of the curve	-	Environment_Engine

Code and Schema¶

C# implementation¶

C#

public class NurbsCurve : BH.oM.Geometry.ICurve, BH.oM.Geometry.IGeometry, BH.oM.Base.IObject, BH.oM.Dimensional.IElement1D, BH.oM.Dimensional.IElement

Assembly: Geometry_oM.dll

The C# class definition is available on github:

NurbsCurve.cs

All history and changes of the class can be found by inspection the history.

JSON Schema implementation¶

The object is defined as a JSON schema. You can validate a JSON instance against this schema by reference. To do this, use the schema reference below in a validator like this one.

JSON Schema

{
 "$ref" : "https://raw.githubusercontent.com/BHoM/BHoM_JSONSchema/develop/Geometry_oM/NurbsCurve.json"
}

The JSON Schema is available on github here:

NurbsCurve.json

Example JSON instance¶

Example JSON instance of type NurbsCurve.

Example JSON

{
  "_t": "BH.oM.Geometry.NurbsCurve",
  "ControlPoints": [
    {
      "_t": "BH.oM.Geometry.Point",
      "X": -5.0,
      "Y": -5.0,
      "Z": 0.0
    },
    {
      "_t": "BH.oM.Geometry.Point",
      "X": 5.0,
      "Y": 0.0,
      "Z": 0.0
    },
    {
      "_t": "BH.oM.Geometry.Point",
      "X": -5.0,
      "Y": 5.0,
      "Z": 0.0
    },
    {
      "_t": "BH.oM.Geometry.Point",
      "X": 0.0,
      "Y": 10.0,
      "Z": 0.0
    }
  ],
  "Weights": [
    1.0,
    1.0,
    1.0,
    1.0
  ],
  "Knots": [
    0.0,
    0.0,
    0.0,
    29.431747586863374,
    29.431747586863374,
    29.431747586863374
  ],
  "_bhomVersion": "8.2"
}