NURBS in VRML

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necessary to resolve the set of the surface control points as a 2dimensional area.NurbsGroupNurbsGroup {eventIn MFNode addChildreneventIn MFNode removeChildrenexposedField MFNode children []field SFVec3f bboxCenter 0 0 0 # (-∞,∞)field SFVec3f bboxSize -1 -1 -1 # (0,∞)or -1,-1,-1exposedField SFFloat tessellationScale 1.0}The NurbsGroup node groups a set of NurbsSurface nodes to acommon group. This provides a hint to the browser to treat the setof NurbsSurface as a unit during tessellation to enforcetessellation continuity along borders. The tessellationScaleparameter scales the tessellation values in lower-levelNurbsSurface nodes. If a set of NurbsSurfaces uses a matching setof controlPoints along the borders, this results in a commontessellation stepping.NurbsPositionInterpolatorNurbsPositionInterpolator {}eventIn SFFloat set_fractionexposedField SFBool fractionAbsolute TRUEexposedField SFInt32 dimension 0exposedField MFFloat knot []exposedField SFInt32 order 4exposedField MFVec3f keyValue []exposedField MFFloat keyWeight []eventOut SFVec3f value_changedNurbsPositionInterpolator describes a 3D NURBS Curve usingdimension keyValue, keyWeight, knot and order. Sending aset_fraction input computes a 3D position on the curve, which issent by value_changed. The set_fraction value is used as the inputvalue for the tessellation function. Thereby the knot coresponds tothe key field of a conventional interpolator node, i.e. if theset_fraction value is within [0;1] and the knot vector within [0;2]only the half of the curve is computed. To traverse an arbitraryknot span with the normal input span of [0;1] of a TimeSensornode a mapping function can be activated by setting thefractionAbsolute to FALSE.It is under consideration to expand the functionality to alsocompute tangents:exposedField SFBool computeTangent FALSEeventOut SFVec3f tangent_changedThe tangent is computed if the computeTangent field is TRUE.This eventOut can be used to compute a frame of reference at thecurrent position along the curve.Using a VRML PositionInterpolator, it is not possible to specify asmooth movement like a path along a circle until the curve issampled to a very fine resolution. In a lot of existing VRMLcontent, the data for Interpolators make up a substantial portion ofthe total size of the VRML file. Using Spline- (NURBS-) basedinterpolation, we hope that this amount of data can be reduced.Feedback from content developers and tool vendors is required toevaluate this node and its usability and data reduction capabilities.NurbsTextureSurfaceNurbsTextureSurface {field SFInt32 uDimension 0 # [0, ∞)field SFInt32 vDimension 0 # [0, ∞)field MFFloat uKnot [] # (-∞,∞)field MFFloat vKnot [] # (-∞,∞)field SFInt32 uOrder 3 # [2, ∞)field SFInt32 vOrder 3 # [2, ∞)exposedField MFVec2f controlPoint [] # (-∞,∞)exposedField MFFloat weight [] # (0, ∞)}The NurbsTextureSurface node is a NURBS surface existing inthe parametric domain of its surface host specifying the mappingof the texture onto the surface. The tessellation process generates2D texture coordinates, which means additional computationaleffort in a frame-by-frame tessellation. If theNurbsTextureSurface is undefined, texture coordinates arecomputed by the client on the basis of parametric step sizewithout any performance penalty. Conventional vertex parametersdo not apply on NURBS because triangles are only available afterpolygonization, but the conventional texture transform may beused.TrimmedSurfaceTrimmedSurface {eventIn MFNode addTrimmingContoureventIn MFNode removeTrimmingContourexposedField MFNode trimmingContour []exposedField SFNode surfaceNULL}The TrimmedSurface node defines a NURBS surface that istrimmed by a set of trimming loops. The surface field containsthe NurbsSurface that shall be trimmed. The trimmingContourfield, if specified, shall contain a set of Contour2D nodes. Thecontours specify the area to trim out following the trimming rulealigned to the Open Inventor definition [Wer94]. A area inside aloop is discarded if the loop is defined in a clockwise direction. Ifthe loop is defined in a counterclockwise direction the area insideis retained and outside is discarded. The outermost contour mustbe defined in a counterclockwise direction. The contours may notbe self-intersecting or intersect other contours.Contour2DContour2D {eventIn MFNode addChildreneventIn MFNode removeChildrenexposedField MFNode children []field SFVec3f bboxCenter 0 0 0 # (-∞,∞)field SFVec3f bboxSize -1 -1 -1 # (0, ∞)or -1,-1,-1}The Contour2D node groups a set of curve segments to acomposite contour. The children have to form a closed loop withthe first point of the first child repeated as the last point of the lastchild and the last point of a segmet repeated as the first point ofthe consecutive one. The segments must be of the type
NurbsCurve2D or Polyline2D and must be enumerated in thechild field in consecutive order according to the topology of thecontour.NurbsCurve2DNurbsCurve2D {field MFFloat knot []field SFInt32 order 3exposedField MFVec2f controlPoint []exposedField MFFloat weight []exposedField SFInt32 tessellation 0}suitable tessellation bound simply based on the desiredsmoothness. In addition, this value can be used to weight thepolygon budget of objects. Essential objects are given a hightessellation value to ensure a smooth surface; less importantobjects get a lower tessellation value because some coarseness istolerable.The NurbsCurve2D node defines a trimming segment that is partof a trimming contour in the u-v domain of the surface. If theNurbsCurve2D forms a closed contour, it may be used as aContour2D node.Polyline2DPolyline2D {exposedField MFVec2f point []}The Polyline2D node defines a linear curve segment as a part of atrimming contour in the u-v domain of a surface.3. IMPLEMENTATIONOur implementation in the VRML browser blaxxun Contact [bla2,web] proves the usage of NURBS in the VRML domain. Allproposed nodes except the NurbsTextureSurface have beensuccessfully implemented. In favour of fast and stable processinga uniform tessellation was applied as recommended in [KML96].Various rendering pipelines fullfill the requirements of differentplatforms (Figure 2). As a reference implementation we used theOpenGL tessellator located in the glu-library. The NURBSsurface parameters are directly handed over to the correspondingOpenGL functions. This method is easy to implement, butperformance is low.To use the built in rendering pipline in our client, we polygonizeNURBS models and store the resulting mesh data. If no dynamictessellation is required, the performance penalty is avoidedalltogether. For low-end CPUs or complex models, this methodcan be used to tessellate NURBS surfaces in a preprocessing step.In case of dynamic tessellation (view-depended rendering) theintroduction of thresholds for the tessellation values minimizes thecomputational load. If the tessellation value is altered by morethan 10% the vertex cache is flushed and a new tessellation cycleis invoked.Current chip architectures like the Intel ISSE or the AMD3DNow! allow to parallelize the computations involved in thepolygonization. An ISSE optimized tessellation with additionallyoptimized lighting and transformation showed best results. Thispipeline exploits the fact that CVs are invariant undertransformations. Transform is sped up by applying the costlymatrix multiplication to the small amount of CVs. After thetessellation process the transformed vertices are lit.In the current implementation stage no step size computation isperformed. As a first step we encourage the content author to set aFigure 2: pipelines for tessellation and renderingView dependent renderingThe implementation is targeted to dynamic tessellation whichallows view-dependend rendering. Like the classical LOD,NURBS objects can be scaled down according to the viewer’sdistance from the object. We have introduced a quality factordescribing the rendering quality by means of triangles per screensize of the object. This value is comparable with the screen basedtolerance shown in section 1, because both values specify theresolution of an object. In contrast to the screen based tolerancethe computation is very simple but is not directly related to thecurvature of the objecttriangles(scale)Quality =bbox(dist)Withtriangles ( scale)= ( uTess + 1) * scale*(vTess + 1) * scale* 2Quality:triangles(scale):bbox(dist):Describes rendering quality of an objectNumber of triangles of an objectDiameter of the bounding box in screen spaceThe quality factor is specified by the tessellation values in VRML.If the quality is assumed to be constant the scale value alters withthe distance of the viewer to the object. An additional feedbackloop can scale the quality factor according to the CPU speedreflecting in the frame rate. The algorithm keeps the framerateconstant by scaling the NURBS content at any given CPU speed.Of course, this implies that the whole scene has to be designed forscaling: There has to be reasonable space for upscaling anddownscaling the tessellation and thus the appearance of an objectif moving away from the target platform. However, scalability isnot unlimited: In the average scene NURBS content is scaleddown very fast with CPU frequency since certain portions of theoverall computational effort do not decrease. The drawbacks ofCPU based scaling are that the authors lose control over theappearance of the object since the client itself continuously altersthe object’s resolution. Proper lower bounds have to be defined to
Page 1 and 2: NURBS in VRMLHolger Grahn, Thomas V
Page 3: 2. PROPOSED NODESNurbsSurfaceNurbsS
Page 7 and 8: Figure 4 The Knight NURBS avatar co
Page 9: REFERENCES[AES91] S.S. Abi-Ezzi, L.

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