Surface modeling is a fundamental feature of any 3D geometric modeler. As you know, Open CASCADE offers a set of elementary surfaces (planar, conical, spherical, etc), Bezier and B-Spline, revolved, extruded and offset surfaces. There is also a trimmed surface which trims an underlying surface in parameter space.

Open CASCADE implements a subset of STEP (

ISO standard 10303, part 42) for geometrical and topological entities, though with some minor deviations.

The surface object only contains a final geometrical representation and does not provide any information on how it was created. This differentiates it, for instance, from ACIS which uses a notion of so called procedural surfaces which may contain both a construction technique and an optional final approximation. For instance, a skin surface comes with description of a set of section curves the surface was 'skinned' through and resulting NURBS approximation. This leads to increase in number of entity types to be supported by the modeler and likely complexity of modeling algorithms that use them. (This also makes me suffer developing extra classes to represent all this variety in the

CAD Exchanger translator and to translate them into Open CASCADE. I can successfully re-import all SAT files exported from Open CASCADE but not all possible SAT types yet). By the way, if there are readers who are familiar with ACIS their comments would be valuable to check how OCC capabilities compare with those of ACIS.

Open CASCADE favors different approach where knowledge of the performed modeling algorithms is stored elsewhere (e.g. in OCAF using function drivers). The B-Rep model only contains a result of an operation and thus is more compact.

Another point to make is that OCC offers algorithms both at geometry level (dealing with Geom_Surface and/or Geom_Curve objects) and topology level (TopoDS_Shape subclasses). The latter may use the former but this dual API is not always provided. Some algorithms are only available at the geometry level and some are only at topology. (If you are not certain about this distinction please make sure you re-read a

series of posts earlier this year).

Let's see what modeling techniques you can use with Open CASCADE. I bet there is no point in going through description of construction techniques of elementary surfaces. Documentation and header files are just enough for that. Let's rather check what kind of advanced stuff OCC has.

**Ruled surfaces**Ruled surface is constructed by connecting two curves (i.e. points along them) with lines. Particular case of a ruled surface is plane (as it can be built on two parallel lines). If you take two parallel circles then a ruled surface will be a cylinder or a cone.

Here is how it may look in general case:

Last spring, when we were in Spain and visiting Sagrada Familia in Barcelona (the central city cathedral, which is an on-going construction for several decades), there was an exhibition of Antoni Gaudi's construction techniques. Gaudi was an architect and he reused many techniques from nature. Among those there was a use of ruled surfaces – see some photos

here or even read a paper '

Gaudi and CAD'.

You can create a ruled surface at geometry level as follows:

Handle(Geom_Curve) aCrv1 = ...;

Handle(Geom_Curve) aCrv2 = ...;

Handle(Geom_Surface) aSurf = GeomFill::Surface (aCrv1, aCrv2);

If you dealing at topology level you can create either a face using two edges or a shell using two wires. You need to use BRepFill:

TopoDS_Edge anEdge1 = ...;

TopoDS_Edge anEdge2 = ...;

TopoDS_Face aFace = BRepFill::Face (anEdge1, anEdge2);

TopoDS_Wire aWire1 = ...;

TopoDS_Wire aWire2 = ...;

TopoDS_Face aShell = BRepFill::Shell (aWire1, aWire2);

Here is a shell of two faces lying on ruled surfaces:

When using BRepFill::Shell(), wires must contain the same number of edges. If not you may need to re-approximate the edges. For instance you can reuse ShapeAlgo_Container::HomoWires() or create some similar algorithm, or re-approximate a wire using BRepAdaptor_CompCurve adaptor and Approx_Curve3d. The latter will produce a single B-Spline curve from a wire, which you can later use with GeomFill or create a TopoDS_Edge from of it to use BRepFill.

*To be continued...*