NurbsCurve Class

Initializes a NURBS curve by copying its values from another NURBS curve.

Constructs a new NURBS curve with a specific degree and control point count.

Protected constructor for internal use.

Constructs a new NURBS curve with knot and CV memory allocated.

Gets the maximum algebraic degree of any span or a good estimate if curve spans are not algebraic.

Gets the dimension of the object.

The dimension is typically three. For parameter space trimming curves the dimension is two. In rare cases the dimension can be one or greater than three.

Indicates if this object has been disposed or the document it originally belonged to has been disposed.

Gets or sets the domain of the curve.

Returns true if the NURBS curve has Bezier spans (all distinct knots have multiplicity = degree)

Returns true if the Brep.TryConvertBrep function will be successful for this object

Gets true if this class has any custom information attached to it through UserData.

Gets a value indicating whether or not this curve is a closed curve.

true if object can be accurately modified with "squishy" transformations like projections, shears, and non-uniform scaling.

If true this object may not be modified. Any properties or functions that attempt to modify this object when it is set to "IsReadOnly" will throw a NotSupportedException.

Gets a value indicating whether or not this curve is considered to be Periodic.

Gets a value indicating whether or not the curve is rational. Rational curves have control-points with custom weights.

Returns true if the curve is a cubic, non-rational, uniform NURBS curve that is either periodic or has natural end conditions. Otherwise, false is returned.

Tests an object to see if it is valid.

Gets access to the knots (or "knot vector") of this NURBS curve.

Useful for switch statements that need to differentiate between basic object types like points, curves, surfaces, and so on.

Gets the order of the curve. Order = Degree + 1.

Evaluates point at the end of the curve.

Evaluates point at the start of the curve.

Gets access to the control points of this NURBS curve.

Gets the number of non-empty smooth (c-infinity) spans in the curve.

Evaluate unit tangent vector at the end of the curve.

Evaluates the unit tangent vector at the start of the curve.

List of custom information that is attached to this class.

Dictionary of custom information attached to this class. The dictionary is actually user data provided as an easy to use shareable set of information.

Gets the amount of user strings.

Appends a NURBS curve to this curve.

If this curve is closed, then modify it so that the start/end point is at curve parameter t.

Changes the dimension of a curve.

Determines the orientation (counterclockwise or clockwise) of a closed, planar curve in the world XY plane. Only works with simple (no self intersections) closed, planar curves.

Determines the orientation (counterclockwise or clockwise) of a closed, planar curve in a given plane. Only works with simple (no self intersections) closed, planar curves.

Determines the orientation (counterclockwise or clockwise) of a closed, planar curve. Only works with simple (no self intersections) closed, planar curves.

Determines the orientation (counterclockwise or clockwise) of a closed, planar curve in a given plane. Only works with simple (no self intersections) closed, planar curves.

Finds parameter of the point on a curve that is closest to testPoint. If the maximumDistance parameter is > 0, then only points whose distance to the given point is <= maximumDistance will be returned. Using a positive value of maximumDistance can substantially speed up the search.

Finds the parameter of the point on a curve that is closest to testPoint. If the maximumDistance parameter is > 0, then only points whose distance to the given point is <= maximumDistance will be returned. Using a positive value of maximumDistance can substantially speed up the search.

Gets closest points between this and another curves.

Finds the object (and the closest point in that object) that is closest to this curve.

Breps, surfaces, curves and point clouds are examples of objects that can be passed to this function.

Finds the object (and the closest point in that object) that is closest to this curve.

Breps, surfaces, curves and point clouds are examples of objects that can be passed to this function.

Looks for segments that are shorter than tolerance that can be combined. For NURBS of degree greater than 1, spans are combined by removing knots. Similarly for NURBS segments of polycurves. Otherwise, RemoveShortSegments() is called. Does not change the domain, but it will change the relative parameterization.

If this piece of geometry is a component in something larger, like a BrepEdge in a Brep, then this function returns the component index.

Assigns a parent object and a sub-object index to this.

Computes the relationship between a point and a closed curve region. This curve must be closed or the return value will be Unset. Both curve and point are projected to the World XY plane.

Computes the relationship between a point and a closed curve region. This curve must be closed or the return value will be Unset.

Computes the relationship between a point and a closed curve region. This curve must be closed or the return value will be Unset.

Gets the curve's control polygon.

Converts a span of the NURBS curve into a Bezier.

Constructs a 3D NURBS curve from a list of control points.

Gets a rational degree 2 NURBS curve representation of the arc. Note that the parameterization of NURBS curve does not match arc's transcendental parameterization.

Create a uniform non-rational cubic NURBS approximation of an arc.

Gets a rational degree 2 NURBS curve representation of the circle. Note that the parameterization of NURBS curve does not match circle's transcendental parameterization. Use GetRadianFromNurbFormParameter() and GetParameterFromRadian() to convert between the NURBS curve parameter and the transcendental parameter.

Create a uniform non-rational cubic NURBS approximation of a circle.

Gets a rational degree 2 NURBS curve representation of the ellipse.

Note that the parameterization of the NURBS curve does not match with the transcendental parameterization of the ellipsis.

Fits a NURBS curve to a dense, ordered set of points.

Fits a NURBS curve to a dense, ordered set of points.

Gets a non-rational, degree 1 NURBS curve representation of the line.

Construct an H-spline from a sequence of interpolation points

Construct an H-spline from a sequence of interpolation points and optional start and end derivative information

Creates a non-rational approximation of a rational arc as a single bezier segment

Creates a parabola from focus and end points.

Creates a parabola from three points.

Creates a parabola from vertex and end points.

Computes planar rail sweep frames at specified parameters.

Computes relatively parallel rail sweep frames at specified parameters.

Creates a C1 cubic NURBS approximation of a helix or spiral. For a helix, you may have radius0 == radius1. For a spiral radius0 == radius1 produces a circle. Zero and negative radii are permissible.

Create a C2 non-rational uniform cubic NURBS approximation of a swept helix or spiral.

Create a NURBS curve, that is suitable for calculations like lofting SubD objects, from an existing curve.

Create a NURBS curve, that is suitable for calculations like lofting SubD objects, from an existing curve.

Create a NURBS curve, that is suitable for calculations like lofting SubD objects, through a sequence of curves.

Evaluate the curvature vector at a curve parameter.

Returns a CRC calculated from the information that defines the object. This CRC can be used as a quick way to see if two objects are not identical.

Evaluate the derivatives at the specified curve parameter.

Evaluate the derivatives at the specified curve parameter.

Actively reclaims unmanaged resources that this instance uses.

For derived class implementers.

This method is called with argument true when class user calls Dispose(), while with argument false when the Garbage Collector invokes the finalizer, or Finalize() method.

You must reclaim all used unmanaged resources in both cases, and can use this chance to call Dispose on disposable fields if the argument is true.

Also, you must call the base virtual method within your overriding method.

Divides this curve at fixed steps along a defined contour line.

Divide the curve into a number of equal-length segments.

Divide the curve into a number of equal-length segments.

Divide the curve into specific length segments.

Divide the curve into specific length segments.

Divide the curve into specific length segments.

Divide the curve into specific length segments.

Calculates 3d points on a curve where the linear distance between the points is equal.

Constructs an exact duplicate of this Curve.

Constructs an exact duplicate of this curve.

Duplicates curve segments. Explodes polylines, polycurves and G1 discontinuous NURBS curves. Single segment curves, such as lines, arcs, unkinked NURBS curves, are duplicated.

Constructs a light copy of this object. By "light", it is meant that the same underlying data is used until something is done to attempt to change it. For example, you could have a shallow copy of a very heavy mesh object and the same underlying data will be used when doing things like inspecting the number of faces on the mesh. If you modify the location of one of the mesh vertices, the shallow copy will create a full duplicate of the underlying mesh data and the shallow copy will become a deep copy.

If you want to keep a copy of this class around by holding onto it in a variable after a command completes, call EnsurePrivateCopy to make sure that this class is not tied to the document. You can call this function as many times as you want.

Check that all values in other are within epsilon of the values in this

Determines whether the specified object is equal to the current object.

Where possible, analytically extends curve to include the given domain. This will not work on closed curves. The original curve will be identical to the restriction of the resulting curve to the original curve domain.

Where possible, analytically extends curve to include the given domain. This will not work on closed curves. The original curve will be identical to the restriction of the resulting curve to the original curve domain.

Extends a curve to a point.

Extends a curve until it intersects a collection of objects.

Extends a curve by a specific length.

Extends a curve by an Arc until it intersects a collection of objects.

Extends a curve by a line until it intersects a collection of objects.

Extends a curve on a surface.

Extends a curve on a surface.

Returns the parameter values of all local extrema. Parameter values are in increasing order so consecutive extrema define an interval on which each component of the curve is monotone. Note, non-periodic curves always return the end points.

Fairs a curve object. Fair works best on degree 3 (cubic) curves. Attempts to remove large curvature variations while limiting the geometry changes to be no more than the specified tolerance.

Creates a constant-radius fillet surface between a surface and the curve.

Creates a surface between two surfaces, with a fixed rail curve on the first surface.

Passively reclaims unmanaged resources when the class user did not explicitly call Dispose().

Local minimization for point on a curve with tangent perpendicular to N.

Fits a new curve through an existing curve.

Returns a 3d frame at a parameter.

Bounding box solver. Gets the world axis aligned bounding box for the geometry.

Aligned Bounding box solver. Gets the plane aligned bounding box.

Aligned Bounding box solver. Gets the world axis aligned bounding box for the transformed geometry.

Aligned Bounding box solver. Gets the plane aligned bounding box.

Returns the type of conic section based on the curve's shape.

Returns the type of conic section based on the curve's shape.

Convert a NURBS curve parameter to a curve parameter.

Serves as the default hash function.

Gets the length of the curve with a fractional tolerance of 1.0e-8.

Get the length of the curve.

Get the length of a sub-section of the curve with a fractional tolerance of 1e-8.

Get the length of a sub-section of the curve.

Search for a location on the curve, near seedParmameter, that is perpendicular to a test point.

Search for a location on the curve, near seedParmameter, that is perpendicular to a test point.

Search for a location on the curve, near seedParmameter, that is tangent to a test point.

Search for a location on the curve, near seedParmameter, that is tangent to a test point.

Searches for a derivative, tangent, or curvature discontinuity.

Searches for a derivative, tangent, or curvature discontinuity.

Convert a curve parameter to a NURBS curve parameter.

Populates a System.Runtime.Serialization.SerializationInfo with the data needed to serialize the target object.

Gets a collection of perpendicular frames along the curve. Perpendicular frames are also known as 'Zero-twisting frames' and they minimize rotation from one frame to the next.

Gets subcurves from a curve. The results will be similar to what is produced by Rhino's Explode command.

Gets the Type of the current instance.

Gets user string from this geometry.

Gets a copy of all (user key string, user value string) pairs attached to this geometry.

Gets the greville (edit point) parameter that belongs to the control point at the specified index.

Gets all Greville parameters for this curve.

Gets the Greville parameter that belongs to the control point at the specified index.

Gets all Greville points for this curve.

Gets Greville points for this curve.

Does a NURBS curve representation of this curve exist?

Increase the degree of this curve.

Returns a curve's inflection points. An inflection point is a location on a curve at which the sign of the curvature (i.e., the concavity) changes. The curvature at these locations is always 0.

Returns a curve's inflection points. An inflection point is a location on a curve at which the sign of the curvature (i.e., the concavity) changes. The curvature at these locations is always 0.

Test a curve to see if it can be represented by an arc or circle within RhinoMath.ZeroTolerance.

Test a curve to see if it can be represented by an arc or circle within the given tolerance.

Test a curve to see if it can be represented by a circle within RhinoMath.ZeroTolerance.

Test a curve to see if it can be represented by a circle within the given tolerance.

Decide if it makes sense to close off this curve by moving the endpoint to the start based on start-end gap size and length of curve as approximated by chord defined by 6 points.

Decide if it makes sense to close off this curve by moving the endpoint to the start based on start-end gap size and length of curve as approximated by chord defined by 6 points.

Test continuity at a curve parameter value.

Determines if two curves are similar.

Test a curve to see if it can be represented by an ellipse within RhinoMath.ZeroTolerance.

Test a curve to see if it can be represented by an ellipse within a given tolerance.

Test a curve to see if it lies in a specific plane.

Test a curve to see if it lies in a specific plane.

Test a curve to see if it is linear to within RhinoMath.ZeroTolerance units (1e-12).

Test a curve to see if it is linear to within the custom tolerance.

Test a curve for planarity.

Test a curve for planarity.

Several types of Curve can have the form of a polyline including a degree 1 NurbsCurve, a PolylineCurve, and a PolyCurve all of whose segments are some form of polyline. IsPolyline tests a curve to see if it can be represented as a polyline.

Used to quickly find short curves.

Used to quickly find short curves.

Determines if an object is valid. Also provides a report on errors if this object happens not to be valid.

Gets the parameter along the curve which coincides with a given length along the curve. A fractional tolerance of 1e-8 is used in this version of the function.

Gets the parameter along the curve which coincides with a given length along the curve. A fractional tolerance of 1e-8 is used in this version of the function.

Gets the parameter along the curve which coincides with a given length along the curve.

Gets the parameter along the curve which coincides with a given length along the curve.

Find parameter of the point on a curve that is locally closest to the testPoint. The search for a local close point starts at a seed parameter.

If IsClosed, just return true. Otherwise, decide if curve can be closed as follows: Linear curves polylinear curves with 2 segments, NURBS with 3 or less control points cannot be made closed. Also, if tolerance > 0 and the gap between start and end is larger than tolerance, curve cannot be made closed. Adjust the curve's endpoint to match its start point.

For expert use only. From the input curves, make an array of compatible NURBS curves.

If possible, converts the object into a form that can be accurately modified with "squishy" transformations like projections, shears, an non-uniform scaling.

Clamps ends and adds knots so the NURBS curve has Bezier spans (all distinct knots have multiplicity = degree).

Constructs a NURBS curve with the start and end matching the start and end of targetCurve, and Greville points on targetCurve.

Returns a curve's maximum curvature points. The maximum curvature points identify where the curvature starts to decrease in both directions from the points.

Returns a curve's maximum curvature points. The maximum curvature points identify where the curvature starts to decrease in both directions from the points.

Creates a shallow copy of the current Object.

Computes an estimate of the number of bytes that this object is using in memory.

For derived classes implementers.

Defines the necessary implementation to free the instance from being constant.

Input the parameter of the point on the curve that is a prescribed arc length from the start of the curve. A fractional tolerance of 1e-8 is used in this version of the function.

Input the parameter of the point on the curve that is a prescribed arc length from the start of the curve. A fractional tolerance of 1e-8 is used in this version of the function.

Input the parameter of the point on the curve that is a prescribed arc length from the start of the curve.

Input the parameter of the point on the curve that is a prescribed arc length from the start of the curve.

Input the parameter of the point on the curve that is a prescribed arc length from the start of the curve. A fractional tolerance of 1e-8 is used in this version of the function.

Input the parameter of the point on the curve that is a prescribed arc length from the start of the curve. A fractional tolerance of 1e-8 is used in this version of the function.

Input the parameter of the point on the curve that is a prescribed arc length from the start of the curve.

Input the parameter of the point on the curve that is a prescribed arc length from the start of the curve.

Offsets this curve. If you have a nice offset, then there will be one entry in the array. If the original curve had kinks or the offset curve had self intersections, you will get multiple segments in the output array.

Offsets this curve. If you have a nice offset, then there will be one entry in the array. If the original curve had kinks or the offset curve had self intersections, you will get multiple segments in the output array.

Offsets this curve. If you have a nice offset, then there will be one entry in the array. If the original curve had kinks or the offset curve had self intersections, you will get multiple segments in the output array.

Finds a curve by offsetting an existing curve normal to a surface. The caller is responsible for ensuring that the curve lies on the input surface.

Offset a curve on a brep face surface. This curve must lie on the surface.

This overload allows to specify a surface point at which the offset will pass.

Offset this curve on a brep face surface. This curve must lie on the surface.

Offset a curve on a surface. This curve must lie on the surface.

This overload allows to specify a surface point at which the offset will pass.

Offset a curve on a surface. This curve must lie on the surface.

Offset a curve on a brep face surface. This curve must lie on the surface.

This overload allows to specify different offsets for different curve parameters.

Offset this curve on a surface. This curve must lie on the surface.

This overload allows to specify different offsets for different curve parameters.

Finds a curve by offsetting an existing curve tangent to a surface. The caller is responsible for ensuring that the curve lies on the input surface.

Is called when a non-constant operation occurs.

Return a 3d frame at a parameter. This is slightly different than FrameAt in that the frame is computed in a way so there is minimal rotation from one frame to the next.

Evaluates point at a curve parameter.

Gets a point at a certain length along the curve. The length must be non-negative and less than or equal to the length of the curve. Lengths will not be wrapped when the curve is closed or periodic.

Gets a point at a certain normalized length along the curve. The length must be between or including 0.0 and 1.0, where 0.0 equals the start of the curve and 1.0 equals the end of the curve.

Pulls this curve to a brep face and returns the result of that operation.

Makes a polyline approximation of the curve and gets the closest point on the mesh for each point on the curve. Then it "connects the points" so that you have a polyline on the mesh.

Rebuild a curve with a specific point count.

Looks for segments that are shorter than tolerance that can be removed. Does not change the domain, but it will change the relative parameterization.

Repairs a curve.

Use a linear fractional transformation to re-parameterize the NURBS curve. This does not change the curve's domain.

Reverses the direction of the curve.

Ribbon offset method to mimic RibbonOffset command

Offsets a closed curve in the following way: pProject the curve to a plane with given normal. Then, loose Offset the projection by distance + blend_radius and trim off self-intersection. THen, Offset the remaining curve back in the opposite direction by blend_radius, filling gaps with blends. Finally, use the elevations of the input curve to get the correct elevations of the result.

Offsets a closed curve in the following way: pProject the curve to a plane with given normal. Then, loose Offset the projection by distance + blend_radius and trim off self-intersection. THen, Offset the remaining curve back in the opposite direction by blend_radius, filling gaps with blends. Finally, use the elevations of the input curve to get the correct elevations of the result.

Offsets a closed curve in the following way: pProject the curve to a plane with given normal. Then, loose Offset the projection by distance + blend_radius and trim off self-intersection. THen, Offset the remaining curve back in the opposite direction by blend_radius, filling gaps with blends. Finally, use the elevations of the input curve to get the correct elevations of the result.

Rotates the object about the specified axis. A positive rotation angle results in a counter-clockwise rotation about the axis (right hand rule).

Scales the object by the specified factor. The scale is centered at the origin.

Set end condition of a NURBS curve to point, tangent and curvature.

Set end condition of a NURBS curve to point, tangent and curvature.

Forces the curve to end at a specified point. Not all curve types support this operation.

Sets all Greville edit points for this curve.

Forces the curve to start at a specified point. Not all curve types support this operation.

Attach a user string (key,value combination) to this geometry.

Returns a geometrically equivalent PolyCurve.

The PolyCurve has the following properties

1. All the PolyCurve segments are LineCurve, PolylineCurve, ArcCurve, or NurbsCurve.

2. The NURBS Curves segments do not have fully multiple interior knots.

3. Rational NURBS curves do not have constant weights.

4. Any segment for which IsLinear() or IsArc() is true is a Line, Polyline segment, or an Arc.

5. Adjacent co-linear or co-circular segments are combined.

6. Segments that meet with G1-continuity have there ends tuned up so that they meet with G1-continuity to within machine precision.

Same as SimplifyCurve, but simplifies only the last two segments at "side" end.

Smooths a curve by averaging the positions of control points in a specified region.

Smooths a curve by averaging the positions of control points in a specified region.

Get the domain of the curve span with the given index. Use the SpanCount property to test how many spans there are.

Splits (divides) the curve at the specified parameter. The parameter must be in the interior of the curve's domain.

Splits (divides) the curve at a series of specified parameters. The parameter must be in the interior of the curve domain.

Splits a curve into pieces using a polysurface.

Splits a curve into pieces using a surface.

Splits a curve into pieces using a polysurface.

Splits a curve into pieces using a surface.

Evaluates the unit tangent vector at a curve parameter.

Converts a curve into polycurve consisting of arc segments. Sections of the input curves that are nearly straight are converted to straight-line segments.

Create a JSON string representation of this object

Constructs a NURBS curve representation of this curve.

Constructs a NURBS curve representation of this curve.

Gets a polyline approximation of a curve.

Gets a polyline approximation of a curve.

Gets a polyline approximation of a curve.

Evaluate the torsion of a curve at a parameter. Sometimes also called the "second curvature", torsion is the rate of change of a curve's osculating plane.

Returns a string that represents the current object.

Transforms the geometry. If the input Transform has a SimilarityType of OrientationReversing, you may want to consider flipping the transformed geometry after calling this function when it makes sense. For example, you may want to call Flip() on a Brep after transforming it.

Translates the object along the specified vector.

Translates the object along the specified vector.

Removes portions of the curve outside the specified interval.

Shortens a curve by a given length

Removes portions of the curve outside the specified interval.

Try to convert this curve into an Arc using RhinoMath.ZeroTolerance.

Try to convert this curve into an Arc using a custom tolerance.

Try to convert this curve into an Arc using RhinoMath.ZeroTolerance.

Try to convert this curve into an Arc using a custom tolerance.

Try to convert this curve into a circle using RhinoMath.ZeroTolerance.

Try to convert this curve into a Circle using a custom tolerance.

Try to convert this curve into an Ellipse within RhinoMath.ZeroTolerance.

Try to convert this curve into an Ellipse using a custom tolerance.

Try to convert this curve into an Ellipse within RhinoMath.ZeroTolerance.

Try to convert this curve into an Ellipse using a custom tolerance.

Test a curve for planarity and return the plane.

Test a curve for planarity and return the plane.

Several types of Curve can have the form of a polyline including a degree 1 NurbsCurve, a PolylineCurve, and a PolyCurve all of whose segments are some form of polyline. IsPolyline tests a curve to see if it can be represented as a polyline.

Several types of Curve can have the form of a polyline including a degree 1 NurbsCurve, a PolylineCurve, and a PolyCurve all of whose segments are some form of polyline. IsPolyline tests a curve to see if it can be represented as a polyline.

Calculates the u, V, and N directions of a NURBS curve at a parameter similar to the method used by Rhino's MoveUVN command.