Extensible 3D (X3D)

Part 1: Architecture and base components

27 NURBS component

The name of this component is "NURBS". This name shall be used when referring to this component in the COMPONENT statement (see 7.2.5.4 Component statement).

This subclause describes the Non-uniform Rational B-Spline (NURBS) component of this document. Table 27.1 provides links to the major topics in this subclause.

Non-uniform Rational B-Splines (NURBS) provide a convenient and efficient manner to generate curved lines and surfaces which can be smooth at any viewing distance. Since these surfaces are generated parametrically, only a small amount of data need be provided for describing complex surfaces.

The characteristics of a NURBS surfaces and curves are defined according to the mathematical definitions for Non-Uniform Rational B-Spline geometry.

There are many construction techniques including:

- special cases of NURBS surfaces such as sphere, cylinder or Bezier surfaces;
- Extrusion/swept surfaces, constructed given a spine curve and a cross-section curve either or both of which can be NURBS curves;
- surfaces of revolution, constructed given a circle/arc and a NURBS cross-section curve;
- skinned surfaces constructed from a set of curves;
- Gordon surfaces interpolating two sets of curves;
- Coons patches, a bi-cubic blended surface constructed from four border curves;
- Surfaces interpolating a set of points.

For this standard, it is assumed that creation of such surfaces is only a construction
step at authoring time and that the surface will be represented as one of the
*X3DParametricGeometryNode* nodes for X3D run-time delivery.

Background information on NURBS and some implementation strategies are described in [NURBS].

NURBS require input to be specified using control points, weights, knots and the order. Each of these inputs are defined using separate fields of the appropriate data type.

The control points and the corresponding *weight* values are held in separate
fields. This separation also allows independent animation of the *controlPoint*
fields using a CoordinateInterpolator node.

All nodes that use NURBs principles use the same field names (or u/v variations on them for the surface case). Those field names shall be interpreted as follows:

The *order* field defines the order of curve. From a mathematical point of view,
the curve is defined by a polynomial of the degree `order-1`.
The value of *order* shall be greater than or equal to 2. An implementation
may limit order to a certain number. If it does so, then a warning shall be
generated and the surface not displayed. An implementation shall at least
support orders 2,3 and 4. The number of control points shall be at least equal
to the order of the curve. The order defines the number of adjacent control
points that influence a given control point.

The *controlPoint* field defines the
*X3DCoordinateNode* instance that provides the
source of coordinates used to control the curve or surface. Depending on the
weight value and the order, this piecewise linear curve is approximated by the
resulting parametric curve. The number of control points shall be equal to or
greater than the order. A closed B-Spline curve can be specified by repeating
the limiting control points, specifying a periodic knot vector, and setting the
*closed* field to TRUE. If the last control point
is not identical to the first or there exists a non-unitary value of weight
within (order-1) control
points of the seam, the *closed* field is ignored.

A *weight* value that shall be greater than zero is assigned to each
*controlPoint*. The ordering of the values is equivalent to the ordering of
the control point values. The number of values shall be identical to the number
of control points. If the length of the weight vector is 0, the default weight
1.0 is assumed for each control point, thus defining a non-Rational curve. If
the number of weight values is less than the number of control points, all
weight values shall be ignored and a value of 1.0 shall be used.

The *knots* field defines the knot vector. The number of knots shall be equal to
the number of control points plus the order of the curve. The order shall be
non-decreasing. Within the knot vector there may not be more than `order-1`
consecutive knots of equal value. If the length of a knot vector is 0 or not the
exact number required ( *numcontrolPoint + order*), a default uniform knot vector is computed.

Because low-level real-time rendering systems currently can handle only planar
triangles, a NURBS surface needs to be broken down ( *i.e.*, tessellated) into
a set of triangles approximating the true surface.

Tessellation can be done in different coordinate spaces:

- Tessellation in object space and the internal computation of the equivalent to an X3D IndexedFaceSet.
- Transforming the control vertices to screen space, and tessellation in screen space

There are different methods to determine tessellation points on the surface:

- fixed tessellation based on a absolute number of subdivisions;
- adaptive tessellation based on chord length;
- adaptive tessellation based on the angle between two triangles;
- view dependent tessellation, fine tessellation near silhouette edges.

This standard does not specify which method is used to tessellate the surface. However, the implementation shall render the NURBS such that the approximation produces a rendered image in which the edges of the tessellation can not be perceived.

NOTE Tessellation in screen space requires the ability to pass already transformed vertices for rendering. This requires the application to already light the vertices (see 17 Lighting component) and pass the resulting color and specular RGB values for each vertex of a triangle.

To avoid cracks at the junction of two surfaces, tessellation values of a whole set of surfaces can be specified in a NurbsSet.

The trimming curve specifies a NURBS-curve that limits the NURBS surface in order to create NURBS surfaces that contain holes or have smooth boundaries. Trimming curves are curves in the parametric space of the surface.

A trimming region is defined by a set of closed trimming loops in the parameter space of a surface. When a loop is oriented counter-clockwise, the area within the loop is retained, and the part outside is discarded. When the loop is oriented clockwise, the area within the loop is discarded, and the rest is retained. Loops may be nested, but a nested loop shall be oriented oppositely from the loop that contains it. The outermost loop shall be oriented counter-clockwise. Clockwiseness is determined by viewing the parametric surface from the side defined by the cross-product between the u and v axes of the parametric space.

A trimming loop consists of a connected sequence of NURBS curves and piecewise linear curves. The last point of every curve in the sequence shall be the same as the first point of the next curve, and the last point of the last curve shall be the same as the first point of the first curve. Self intersecting curves are not allowed.

X3DNurbsControlCurveNode : X3DNode { MFVec2d [in,out] controlPoint [] (-∞,∞) SFNode [in,out] metadata NULL [X3DMetadataObject] }

The *X3DNurbsControlCurveNode* abstract node type is the base type for all node types that provide
control curve information in 2D space.

The control points are defined in 2D coordinate space and interpreted according to the descendent node type as well as the user of this node instance.

X3DNurbsSurfaceGeometryNode : X3DParametricGeometryNode { SFNode [in,out] controlPoint NULL [X3DCoordinateNode] SFNode [in,out] metadata NULL [X3DMetadataObject] SFNode [in,out] texCoord NULL [X3DTextureCoordinateNode|NurbsTextureCoordinate] SFInt32 [in,out] uTessellation 0 (-∞,∞) SFInt32 [in,out] vTessellation 0 (-∞,∞) MFDouble [in,out] weight [] (0,∞) SFBool [] solid TRUE SFBool [] uClosed FALSE SFInt32 [] uDimension 0 [0,∞) MFDouble [] uKnot [] (-∞,∞) SFInt32 [] uOrder 3 [2,∞) SFBool [] vClosed FALSE SFInt32 [] vDimension 0 [0,∞) MFDouble [] vKnot [] (-∞,∞) SFInt32 [] vOrder 3 [2,∞) }

The X3DNurbsSurfaceGeometryNode represents the abstract geometry type for all types of NURBS surfaces.

*uDimension* and *vDimension* define the number of control points
in the u and v dimensions.

*uOrder* and *vOrder* define the order of the surface in the u and
v dimensions.

*uKnot* and *vKnot* define the knot values of the surface in the u
and v dimensions.

*uClosed* and *vClosed* define whether or not the specific
dimension is to be evaluated as a closed surface along the u and v directions,
respectively.

*controlPoint* defines a set of control points of dimension
*uDimension* × *vDimension*. This set of points defines a mesh where the
points do not have a uniform spacing. *uDimension* points define a polyline
in u-direction followed by further u-polylines with the v-parameter in ascending
order. The number of control points shall be equal or greater than the order. A
closed surface shall be specified by repeating the limiting control points and
setting the *closed* field to TRUE. If the
*closed* field is set to FALSE, the implementation
shall not be required to smoothly blend the edges of the surface in that
dimension into a continuous surface. A closed surface in either the u-dimension
or the v-dimension shall be specified by repeating the limiting control points
for that dimension and setting the respective *uClosed* or *vClosed* field to
TRUE. If the last control point is not identical with
the first control point, the field is ignored. If either the *uClosed* or
the *vClosed* field is set to FALSE, the
implementation shall not be required to smoothly blend the edges of the surface
in that dimension into a continuous surface.

The control vertex corresponding to the control point P[i,j] on the control grid is:

P[i,j].x = controlPoint[i + (j × uDimension)].x P[i,j].y = controlPoint[i + (j × uDimension)].y P[i,j].z = controlPoint[i + (j × uDimension)].z P[i,j].w = weight[ i + (j × uDimension)] where 0 ≤ i < uDimension and 0 ≤ j < vDimension.

For an implementation subdividing the surface in a equal number of subdivision steps, tessellation values might be interpreted in the following way:

- if a tessellation value is greater than 0, the number of tessellation
points is:

*tessellation+1*;

- if a tessellation value is smaller than 0, the number of tessellation
points is:

*−tessellation × (u/v)dimension)+1*;

- if a tessellation value is 0, the number of tessellation points is:

*(2 × (u/v)dimension)+1*.

For implementations doing tessellations based on chord length, tessellation values less than zero are interpreted as the maximum chord length deviation in pixels. Implementations doing fully automatic tessellation may ignore the tessellation hint parameters.

*texCoord* provides additional information on how to generate texture
coordinates. By default, texture coordinates in the unit square (or cube for 3D
coordinates) are generated automatically from the parametric subdivision. A
NurbsTextureCoordinate node or simply a
TextureCoordinate node can then be used
to compute a texture coordinate given a u/v parameter of the
*X3DParametricGeometryNode*.
The NurbsTextureCoordinate also supports non-animated surfaces to specify a
"chord length"-based texture coordinate parametrization.

The *solid* field determines whether the surface is visible when viewed
from the inside. 11.2.3 Common
geometry fields provides a complete description of the *solid* field.
When *solid*=TRUE is used, the surface shall be
visible only from the side that appears ccw (counter-clockwise) on the screen,
assuming a surface's quads would be rendered in this order:

point(u , v ); point(u-1, v ); point(u-1, v-1); point(u , v-1);

where u is the parameter generating successive points along the u dimension, and v is the parameter generating successive points along the v dimension.

X3DParametricGeometryNode : X3DGeometryNode { SFNode [in,out] metadata NULL [X3DMetadataObject] }

The *X3DParametricGeometryNode* abstract node type is the base type for all geometry node types that are
created parametrically and use control points to describe the final shape of the
surface. How the control points are described and interpreted shall be a
property of the individual node type.

Contour2D : X3DNode { MFNode [in] addChildren [NurbsCurve2D|ContourPolyline2D] MFNode [in] removeChildren [NurbsCurve2D|ContourPolyline2D] MFNode [in,out] children [] [NurbsCurve2D|ContourPolyline2D] SFNode [in,out] metadata NULL [X3DMetadataObject] }

The Contour2D node groups a set of curve segments to a composite contour. The
children shall form a closed loop with the first point of the first child
repeated as the last point of the last child, and the last point of a segment
repeated as the first point of the consecutive one. The segments shall be
defined by concrete nodes that implement the *X3DNurbsControlCurveNode*
abstract type nodes, and shall be enumerated in the child field in consecutive order
according to the topology of the contour.

The 2D coordinates used by the node shall be interpreted to lie in the (u, v) coordinate space defined by the NURBS surface.

ContourPolyline2D : X3DNurbsControlCurveNode { SFNode [in,out] metadata NULL [X3DMetadataObject] MFVec2d [in,out] controlPoint [] (-∞, ∞) }

The ContourPolyline2D node defines a piecewise linear curve segment as a part of a trimming contour in the u,v domain of a surface.

The *controlPoint* field specifies the end points of each segment of the
piecewise linear curve.

ContourPolyline2D nodes are used as children of the Contour2D group.

NurbsCurve : X3DParametricGeometryNode { SFNode [in,out] controlPoint NULL [X3DCoordinateNode] SFNode [in,out] metadata NULL [X3DMetadataObject] SFInt32 [in,out] tessellation 0 (-∞,∞) MFDouble [in,out] weight [] (0,∞) SFBool [] closed FALSE MFDouble [] knot [] (-∞,∞) SFInt32 [] order 3 [2,∞) }

The NurbsCurve node is a geometry node defining a parametric curve in 3D space (see Figure 27.1)

The *tessellation* field gives a hint to the curve tessellator by
setting an absolute number of subdivision steps. These values shall be greater
than or equal to the *Order* field. A value of 0 indicates that the X3D browser
choose a suitable tessellation. Interpretation of values below 0 is
implementation dependent.

For an implementation subdividing the curve into an equal number of subdivision steps, tessellation values are interpreted as follows:

- if a tessellation value is greater than 0, the number of tessellation
points is:

*tessellation+1*;

- if a tessellation value is smaller than 0, the number of tessellation
points is:

*−tessellation × (number of control points)+1*;

- if a tessellation value is 0, the number of tessellation points is:

*(2 × (number of control points)+1*.

For implementations doing tessellations based on chord length, tessellation values less than zero are interpreted as the maximum chord length deviation in pixels. Implementations doing fully automatic tessellation may ignore the tessellation hint parameters.

NurbsCurve2D : X3DNurbsControlCurveNode { MFVec2d [in,out] controlPoint [] (-∞,∞) SFNode [in,out] metadata NULL [X3DMetadataObject] SFInt32 [in,out] tessellation 0 (-∞,∞) MFDouble [in,out] weight [] (0,∞) SFBool [] closed FALSE MFDouble [] knot [] (-∞,∞) SFInt32 [] order 3 [2,∞) }

The NurbsCurve2D node defines a trimming segment that is part of a trimming contour in the u,v domain of the surface.

NurbsCurve2D nodes are used as children of the Contour2D group.

NurbsOrientationInterpolator : X3DChildNode { SFFloat [in] set_fraction (-∞,∞) SFNode [in,out] controlPoint NULL [X3DCoordinateNode] MFDouble [in,out] knot [] (-∞,∞) SFNode [in,out] metadata NULL [X3DMetadataObject] SFInt32 [in,out] order 3 (2,∞) MFDouble [in,out] weight [] (0,∞) SFRotation [out] value_changed }

NurbsOrientationInterpolator interpolates the orientation along a 3D NURBS curve using the same fields as described for the NurbsCurve node.

The field *set_fraction* has the same meaning as in the
NurbsPositionInterpolator.

Sending a *set_fraction* input computes a 3D position on the curve, from
which a tangent to the curve at that position is calculated. The tangent
direction shall be oriented to point along the curve from the first knot value
towards the last value. This orientation value
shall be then sent by *value_changed*. Given the same definition for
control points, knots, order and weights, and the same value for *set_fraction*
the orientation interpolator shall generate the orientation of the tangent of
the curve at the same position as the NurbsPositionInterpolator.

NurbsPatchSurface : X3DNurbsSurfaceGeometryNode { SFNode [in,out] controlPoint NULL [X3DCoordinateNode] SFNode [in,out] metadata NULL [X3DMetadataObject] SFNode [in,out] texCoord NULL [X3DTextureCoordinateNode|NurbsTextureCoordinate] SFInt32 [in,out] uTessellation 0 (-∞,∞) SFInt32 [in,out] vTessellation 0 (-∞,∞) MFDouble [in,out] weight [] (0,∞) SFBool [] solid TRUE SFBool [] uClosed FALSE SFInt32 [] uDimension 0 [0,∞) MFDouble [] uKnot [] (-∞,∞) SFInt32 [] uOrder 3 [2,∞) SFBool [] vClosed FALSE SFInt32 [] vDimension 0 [0,∞) MFDouble [] vKnot [] (-∞,∞) SFInt32 [] vOrder 3 [2,∞) }

The NurbsPatchSurface node is a contiguous NURBS surface patch. Figure 27.2 shows an example of a NurbsPatchSurface node:

NurbsPositionInterpolator : X3DChildNode { SFFloat [in] set_fraction (-∞,∞) SFNode [in,out] controlPoint NULL [X3DCoordinateNode] MFDouble [in,out] knot [] (-∞,∞) SFNode [in,out] metadata NULL [X3DMetadataObject] SFInt32 [in,out] order 3 (2,∞) MFDouble [in,out] weight [] (0,∞) SFVec3f [out] value_changed }

NurbsPositionInterpolator interpolates the position along a 3D NURBS curve as specified in 27.4.3 NurbsCurve.

The fields *set_fraction*
and *value_changed* have the same meaning as specified in
19.4.6 PositionInterpolator.

Sending a *set_fraction*
input computes a 3D position on the curve, which is sent by *value_changed*.
The *set_fraction* value is used as the input value for
the tessellation function. Thereby, the *knot* corresponds
to the *key* field of a conventional interpolator node;
*i.e.*, if the *set_fraction* value is within [0,1] and the
knot vector within [0,2], only half of the curve is computed.

NurbsSet : X3DChildNode, X3DBoundedObject { MFNode [in] addGeometry [X3DParametricGeometryNode] MFNode [in] removeGeometry [X3DParametricGeometryNode] SFBool [in,out] bboxDisplay TRUE MFNode [in,out] geometry [] [X3DParametricGeometryNode] SFNode [in,out] metadata NULL [X3DMetadataObject] SFFloat [in,out] tessellationScale 1.0 (0,∞) SFBool [in,out] visible TRUE SFVec3f [] bboxCenter 0 0 0 (-∞,∞) SFVec3f [] bboxSize -1 -1 -1 [0,∞) or −1 −1 −1 }

The NurbsSet node groups a set of Nurbs surface nodes to a common group for
rendering purposes only. This informs the X3D browser that the set of Nurbs surfaces shall be treated as a unit during tessellation to enforce
tessellation continuity along borders. The *tessellationScale* parameter is
scaling the tessellation values in
contained
Nurbs surface nodes. A set of
Nurbs surfaces that use a matching set of *controlPoint* along the borders shall
result in a common tessellation stepping.

The geometry represented in the children of this node shall not be directly rendered. It is an informational node only. Surfaces not represented elsewhere in the transformation hierarchy shall not be rendered.

The bounds information is provided for optimization purposes only. A X3D browser may choose to use this information about when to apply trimming or smooth tessellation between patches based on the bounds information (EXAMPLE only smooth when the viewer is within the bounds).

NurbsSurfaceInterpolator : X3DChildNode { SFVec2f [in] set_fraction (-∞,∞) SFNode [in,out] controlPoint NULL [X3DCoordinateNode] SFNode [in,out] metadata NULL [X3DMetadataObject] MFDouble [in,out] weight [] (0,∞) SFVec3f [out] position_changed SFVec3f [out] normal_changed SFInt32 [] uDimension 0 [0,∞) MFDouble [] uKnot [] (-∞,∞) SFInt32 [] uOrder 3 [2,∞) SFInt32 [] vDimension 0 [0,∞) MFDouble [] vKnot [] (-∞,∞) SFInt32 [] vOrder 3 [2,∞) }

NurbsSurfaceInterpolator interpolates over a 3D NURBS surface as specified in 27.4.6 NurbsPatchSurface.

Sending a *set_fraction* input computes a 3D position and normal on
the surface for the given u and v coordinates. The computed position on the
surface shall be sent by *position_changed*, and the computed normal
shall be sent by *normal_changed*.

Normals generated by *normal_changed* events shall point from the ccw
(counter-clockwise) side of the surface, assuming the order of surface quads is
as specified for *X3DNurbsSurfaceGeometryNode*.

NurbsSweptSurface : X3DParametricGeometryNode { SFNode [in,out] crossSectionCurve NULL [X3DNurbsControlCurveNode] SFNode [in,out] metadata NULL [X3DMetadataObject] SFNode [in,out] trajectoryCurve NULL [NurbsCurve] SFBool [] ccw TRUE SFBool [] solid TRUE }

NurbsSweptSurface describes a generalized surface that defines a path in 3D space and constant cross section that may be 2D or 3D of the path as illustrated in Figure 27.3. Conceptually it is the NURBS equivalent of the Extrusion node (see 13.3.5 Extrusion) but permits the use of non-closed cross sections.

The *crossSectionCurve*
is a 2D curve in the yz-plane that describes the
cross-sectional shape of the object.

The *trajectoryCurve*
is a 3D curve that describes the path
over which to trace the cross-section.

The *solid* and *ccw* fields are defined as specified in
11.2.3 Common
geometry fields. To have the polygons' normals facing away from the axis, the
trajectory curve should be oriented so that it is moving counterclockwise when
looking down the −Y axis, thus defining a concept of "inside" and "outside".

With *solid* TRUE and *ccw*
TRUE, the cylinder is visible from the outside.
Changing *ccw* to FALSE makes it visible from the inside.

NurbsSwungSurface : X3DParametricGeometryNode { SFNode [in,out] metadata NULL [X3DMetadataObject] SFNode [in,out] profileCurve NULL [X3DNurbsControlCurveNode] SFNode [in,out] trajectoryCurve NULL [X3DNurbsControlCurveNode] SFBool [] ccw TRUE SFBool [] solid TRUE }

NurbsSwungSurface describes a generalized surface that defines a path and constant cross section of the path as illustrated in Figure 27.4.

The *profileCurve* is a 2D curve in the yz-plane that describes the
cross-sectional shape of the object.

The *trajectoryCurve* is a 2D curve in the xz-plane that describes the path
over which to trace the cross-section.

The *solid* and *ccw* fields are defined in
11.2.3 Common
geometry fields. To have the normals of the polygons facing away from the axis,
the trajectory curve should be oriented so that it is moving counterclockwise
when looking down the −Y axis, thus defining a concept of "inside" and "outside".

With *solid* TRUE and *ccw*
TRUE, the cylinder is visible from the outside.
Changing *ccw* to FALSE specifies that the
cylinder is visible from the inside.

NurbsTextureCoordinate : X3DNode { MFVec2f [in,out] controlPoint [] (-∞,∞) SFNode [in,out] metadata NULL [X3DMetadataObject] MFDouble [in,out] weight [] (0,∞) SFInt32 [] uDimension 0 [0,∞) MFDouble [] uKnot [] (-∞,∞) SFInt32 [] uOrder 3 [2,∞) SFInt32 [] vDimension 0 [0,∞) MFDouble [] vKnot [] (-∞,∞) SFInt32 [] vOrder 3 [2,∞) }

The NurbsTextureCoordinate node is a NURBS surface existing in the parametric domain of its surface host specifying the mapping of the texture onto the surface.

The parameters are as specified in X3DNurbsSurfaceGeometryNode with the exception that the control points are specified in (u, v) coordinates.

The tessellation process generates 2D texture coordinates. If a NurbsTextureCoordinate is undefined, texture coordinates are computed by the client on the basis of parametric step size. Conventional vertex parameters do not apply on NURBS surfaces because triangles are only available after polygonalization. However, the conventional texture transform may be used.

NurbsTextureCoordinate nodes are accessed through the *texCoord* field
of a node derived from
*X3DNurbsSurfaceGeometryNode*. A NurbsTextureCoordinate node separately
encountered is ignored.

NurbsTrimmedSurface : X3DNurbsSurfaceGeometryNode { MFNode [in] addTrimmingContour [Contour2D] MFNode [in] removeTrimmingContour [Contour2D] SFNode [in,out] controlPoint NULL [X3DCoordinateNode] SFNode [in,out] metadata NULL [X3DMetadataObject] SFNode [in,out] texCoord NULL [X3DTextureCoordinateNode|NurbsTextureCoordinate] MFNode [in,out] trimmingContour [] [Contour2D] SFInt32 [in,out] uTessellation 0 (-∞,∞) SFInt32 [in,out] vTessellation 0 (-∞,∞) MFDouble [in,out] weight [] (0,∞) SFBool [] solid TRUE SFBool [] uClosed FALSE SFInt32 [] uDimension 0 [0,∞) MFDouble [] uKnot [] (-∞,∞) SFInt32 [] uOrder 3 [2,∞) SFBool [] vClosed FALSE SFInt32 [] vDimension 0 [0,∞) MFDouble [] vKnot [] (-∞,∞) SFInt32 [] vOrder 3 [2,∞) }

The NurbsTrimmedSurface node defines a NURBS surface (see 27.4.6 NurbsPatchSurface) that is trimmed by a set of trimming loops. The outermost trimming loop shall be defined in a counterclockwise direction. An example of a NurbsTrimmedSurface node is shown in Figure 27.5.

The *trimmingContour* field, if specified, shall contain a set of
Contour2D (see 27.4.1 Contour2D) nodes. Trimming loops shall be processed as described for
the Contour2D node. If no trimming contours are defined, the NurbsTrimmedSurface
node shall have the same semantics as the NurbsPatchSurface node.

The Non-uniform Rational B-spline (NURBS) component provides four levels of support as specified in Table 27.2. Level 1 provides basic NURBS support. Level 2 adds the ability to ensure controlled tessellation along the boundaries between two NURBS surfaces. Level 3 adds specialized NURBS nodes. Level 4 adds trimmed NURBS surfaces.

**Table 27.2 — NURBS component support levels**

Level | Prerequisites | Nodes/Features | Support |
---|---|---|---|

1 |
Core 1 Grouping 1 Shape 1 Interpolator 1 Texturing 1 Rendering 1 |
||

X3DNurbsControlCurveNode
(abstract) |
n/a | ||

X3DNurbsSurfaceGeometryNode
(abstract) |
n/a | ||

X3DParametricGeometryNode
(abstract) |
n/a | ||

NurbsCurve | All fields fully supported. | ||

NurbsOrientationInterpolator | All fields fully supported. | ||

NurbsPatchSurface | All fields fully supported. | ||

NurbsPositionInterpolator | All fields fully supported. | ||

NurbsSurfaceInterpolator | All fields fully supported. | ||

NurbsTextureCoordinate | All fields fully supported. | ||

2 |
Core 1 Grouping 1 Shape 1 Interpolator 1 Texturing 1 |
||

All Level 1 NURBS nodes | As supported in Level 1. | ||

NurbsSet | All fields fully supported. | ||

3 |
Core 1 Grouping 1 Shape 1 Interpolator 1 Texturing 1 |
||

All Level 2 NURBS nodes | As supported in Level 2. | ||

NurbsCurve2D | All fields fully supported. | ||

ContourPolyline2D | All fields fully supported. | ||

NurbsSweptSurface | All fields fully supported. | ||

NurbsSwungSurface | All fields fully supported. | ||

4 |
Core 1 Grouping 1 Shape 1 Interpolator 1 Texturing 1 |
||

All Level 3 NURBS nodes | As supported in Level 3. | ||

Contour2D | All fields fully supported. | ||

NurbsTrimmedSurface | All fields fully supported. |