Class NurbsSurface
This class represents a NURBS surface.
Inheritance
System.Object
NurbsSurface
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)
Syntax
public class NurbsSurface : IGeometry<NurbsSurface>, IEquatable<NurbsSurface>, ITransformable<NurbsSurface>Examples
Point3 p1 = new Point3(0.0, 0.0, 0.0);
Point3 p2 = new Point3(10.0, 0.0, 0.0);
Point3 p3 = new Point3(10.0, 10.0, 2.0);
Point3 p4 = new Point3(0.0, 10.0, 4.0);
NurbsSurface surface = NurbsSurface.FromCorners(p1, p2, p3, p4);
Properties
| Improve this Doc View SourceControlPointLocations
A 2D collection of points, V direction increases from left to right, the U direction from bottom to top.
Declaration
public List<List<Point3>> ControlPointLocations { get; }Property Value
| Type | Description |
|---|---|
| System.Collections.Generic.List<System.Collections.Generic.List<Point3>> |
ControlPoints
A 2d collection of control points, V direction increases from left to right, the U direction from bottom to top.
Declaration
public List<List<Point4>> ControlPoints { get; }Property Value
| Type | Description |
|---|---|
| System.Collections.Generic.List<System.Collections.Generic.List<Point4>> |
DegreeU
The degree in U direction.
Declaration
public int DegreeU { get; }Property Value
| Type | Description |
|---|---|
| System.Int32 |
DegreeV
The degree in V direction.
Declaration
public int DegreeV { get; }Property Value
| Type | Description |
|---|---|
| System.Int32 |
KnotsU
The knotVector in U direction.
Declaration
public KnotVector KnotsU { get; }Property Value
| Type | Description |
|---|---|
| KnotVector |
KnotsV
The knotVector in V direction.
Declaration
public KnotVector KnotsV { get; }Property Value
| Type | Description |
|---|---|
| KnotVector |
Weights
A 2d collection of weight values.
Declaration
public List<List<double>> Weights { get; }Property Value
| Type | Description |
|---|---|
| System.Collections.Generic.List<System.Collections.Generic.List<System.Double>> |
Methods
| Improve this Doc View SourceBoundaryEdges()
Extracts the boundary curves of the surface.
Declaration
public NurbsBase[] BoundaryEdges()Returns
| Type | Description |
|---|---|
| NurbsBase[] | The boundary edges. |
ClosestParameter(Point3)
Computes the U and V parameters of the surface that is closest to the test point.
Declaration
public (double U, double V) ClosestParameter(Point3 point)Parameters
| Type | Name | Description |
|---|---|---|
| Point3 | point | The point to test against. |
Returns
| Type | Description |
|---|---|
| System.ValueTuple<System.Double, System.Double> | The U and V parameters of the surface that are closest to the test point. |
ClosestPoint(Point3)
Computes the point on the surface that is closest to the test point.
Declaration
public Point3 ClosestPoint(Point3 point)Parameters
| Type | Name | Description |
|---|---|---|
| Point3 | point | The point to test against. |
Returns
| Type | Description |
|---|---|
| Point3 | The closest point on the surface. |
Equals(NurbsSurface)
Compares if two NURBS surfaces are the same.
Two NURBS curves are equal when the have same degrees, same control points order and dimension, and same knots.
Declaration
public bool Equals(NurbsSurface other)Parameters
| Type | Name | Description |
|---|---|---|
| NurbsSurface | other | The NURBS surface. |
Returns
| Type | Description |
|---|---|
| System.Boolean | Return true if the NURBS surface are equal. |
EvaluateAt(Double, Double, EvaluateSurfaceDirection)
Evaluate the surface at the given U and V parameters.
Declaration
public Vector3 EvaluateAt(double u, double v, EvaluateSurfaceDirection direction)Parameters
| Type | Name | Description |
|---|---|---|
| System.Double | u | U parameter. |
| System.Double | v | V parameter. |
| EvaluateSurfaceDirection | direction | The evaluate direction required as result. |
Returns
| Type | Description |
|---|---|
| Vector3 | The unitized tangent vector in the direction selected. |
FromCorners(Point3, Point3, Point3, Point3)
Constructs a NURBS surface from four corners.
If the corners are ordered ccw the normal of the surface will point up otherwise, if corners ordered cw the normal will point down.
The surface is defined of degree 1.
Declaration
public static NurbsSurface FromCorners(Point3 p1, Point3 p2, Point3 p3, Point3 p4)Parameters
| Type | Name | Description |
|---|---|---|
| Point3 | p1 | The first point. |
| Point3 | p2 | The second point. |
| Point3 | p3 | The third point. |
| Point3 | p4 | The fourth point. |
Returns
| Type | Description |
|---|---|
| NurbsSurface |
FromExtrusion(Vector3, NurbsBase)
Constructs a surface extruding a curve profile long a direction.
Declaration
public static NurbsSurface FromExtrusion(Vector3 direction, NurbsBase profile)Parameters
| Type | Name | Description |
|---|---|---|
| Vector3 | direction | The extrusion direction. |
| NurbsBase | profile | The profile curve to extrude. |
Returns
| Type | Description |
|---|---|
| NurbsSurface | The extruded surface. |
FromLoft(IList<NurbsBase>, LoftType)
Constructs a NURBS surface from a set of NURBS curves.
Declaration
public static NurbsSurface FromLoft(IList<NurbsBase> curves, LoftType loftType = LoftType.Normal)Parameters
| Type | Name | Description |
|---|---|---|
| System.Collections.Generic.IList<NurbsBase> | curves | Set of a minimum of two curves to create the surface. |
| LoftType | loftType | Enum to choose the type of loft generation. |
Returns
| Type | Description |
|---|---|
| NurbsSurface | A NURBS surface. |
FromPoints(Int32, Int32, List<List<Point3>>, List<List<Double>>)
Constructs a NURBS surface from a 2D grid of points.
The grid of points should be organized as, the V direction from left to right and the U direction increases from bottom to top.
Declaration
public static NurbsSurface FromPoints(int degreeU, int degreeV, List<List<Point3>> points, List<List<double>> weight = null)Parameters
| Type | Name | Description |
|---|---|---|
| System.Int32 | degreeU | Degree of surface in U direction. |
| System.Int32 | degreeV | Degree of surface in V direction. |
| System.Collections.Generic.List<System.Collections.Generic.List<Point3>> | points | Points locations. |
| System.Collections.Generic.List<System.Collections.Generic.List<System.Double>> | weight | A 2D collection of weights. |
Returns
| Type | Description |
|---|---|
| NurbsSurface | A NURBS surface. |
FromSweep(NurbsBase, NurbsBase, Nullable<Vector3>, Nullable<Vector3>)
Constructs a sweep surface with one rail curve. Follows the algorithm A10.2 at page 477 of The NURBS Book by Piegl and Tiller.
Declaration
public static NurbsSurface FromSweep(NurbsBase rail, NurbsBase profile, Vector3? startTangent = null, Vector3? endTangent = null)Parameters
| Type | Name | Description |
|---|---|---|
| NurbsBase | rail | The rail curve. |
| NurbsBase | profile | The section curve. |
| System.Nullable<Vector3> | startTangent | If not null override start tangent vector. |
| System.Nullable<Vector3> | endTangent | If not null override end tangent vector. |
Returns
| Type | Description |
|---|---|
| NurbsSurface | The sweep surface. |
IsClosed(SurfaceDirection)
Checks if the surface is closed.
A surface is closed if the first points and the lasts in a direction are coincident.
Declaration
public bool IsClosed(SurfaceDirection direction)Parameters
| Type | Name | Description |
|---|---|---|
| SurfaceDirection | direction |
Returns
| Type | Description |
|---|---|
| System.Boolean | True if the curve is closed. |
IsoCurve(Double, SurfaceDirection)
Extracts the isoparametric curves (isocurves) at the given parameter and surface direction.
Declaration
public NurbsCurve IsoCurve(double parameter, SurfaceDirection direction)Parameters
| Type | Name | Description |
|---|---|---|
| System.Double | parameter | The parameter between 0.0 to 1.0 whether the isocurve will be extracted. |
| SurfaceDirection | direction | The U or V direction whether the isocurve will be extracted. |
Returns
| Type | Description |
|---|---|
| NurbsCurve | The isocurve extracted. |
IsPlanar(Double)
Checks is surface is planar within specified tolerance.
Declaration
public bool IsPlanar(double tolerance = 1E-10)Parameters
| Type | Name | Description |
|---|---|---|
| System.Double | tolerance |
Returns
| Type | Description |
|---|---|
| System.Boolean |
PointAt(Double, Double)
Evaluates a point at a given U and V parameters.
Declaration
public Point3 PointAt(double u, double v)Parameters
| Type | Name | Description |
|---|---|---|
| System.Double | u | Evaluation U parameter. |
| System.Double | v | Evaluation V parameter. |
Returns
| Type | Description |
|---|---|
| Point3 | A evaluated point. |
Reverse(SurfaceDirection)
Reverses the parameterization of a surface in the specified direction. The domain is unaffected.
Declaration
public NurbsSurface Reverse(SurfaceDirection surfaceDirection)Parameters
| Type | Name | Description |
|---|---|---|
| SurfaceDirection | surfaceDirection | The U or V direction whether the surface will be reversed. |
Returns
| Type | Description |
|---|---|
| NurbsSurface | A surface reversed in the specified direction. |
Revolved(NurbsBase, Ray, Double)
Creates a surface of revolution through an arbitrary angle, and axis. Corresponds the algorithm A8.1 of The NURBS Book by Piegl and Tiller.
Declaration
public static NurbsSurface Revolved(NurbsBase curveProfile, Ray axis, double rotationAngle)Parameters
| Type | Name | Description |
|---|---|---|
| NurbsBase | curveProfile | Profile curve. |
| Ray | axis | Revolution axis. |
| System.Double | rotationAngle | Angle in radiance. |
Returns
| Type | Description |
|---|---|
| NurbsSurface | The revolution surface. |
Ruled(NurbsBase, NurbsBase)
Constructs a ruled surface between two curves. Follows the algorithm at page 337 of The NURBS Book by Piegl and Tiller.
Declaration
public static NurbsSurface Ruled(NurbsBase curveA, NurbsBase curveB)Parameters
| Type | Name | Description |
|---|---|---|
| NurbsBase | curveA | The first curve. |
| NurbsBase | curveB | The second curve. |
Returns
| Type | Description |
|---|---|
| NurbsSurface | A ruled surface. |
SplitAt(Double, SplitDirection)
Splits (divides) the surface into two parts at the specified parameter
Declaration
public NurbsSurface[] SplitAt(double parameter, SplitDirection direction)Parameters
| Type | Name | Description |
|---|---|---|
| System.Double | parameter | The parameter at which to split the surface, parameter should be between 0 and 1. |
| SplitDirection | direction | Where to split in the U or V direction of the surface. |
Returns
| Type | Description |
|---|---|
| NurbsSurface[] | If the surface is split vertically (U direction) the left side is returned as the first surface and the right side is returned as the second surface. |
ToString()
Implements the override method to string.
Declaration
public override string ToString()Returns
| Type | Description |
|---|---|
| System.String | The representation of a NURBS surface in string. |
Overrides
System.Object.ToString()
|
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Transform(TransformMatrix)
Transforms a NURBS surface with the given transformation matrix.
Declaration
public NurbsSurface Transform(TransformMatrix transformation)Parameters
| Type | Name | Description |
|---|---|---|
| TransformMatrix | transformation | The transformation matrix. |
Returns
| Type | Description |
|---|---|
| NurbsSurface | A new NURBS surface transformed. |
Implements
System.IEquatable<T>