Recognizing the construction methods of (piecewise) polyno-tems support, Sat data files in the case of Acis, and the mial or rational curves and surfaces is of great importance, e.g., Archive data format in Ideas. In contrast to these two for geometrical data exchange between two different modeling systems, Advanced Visualizer allows one to create an Obj systems. We formulate intrinsic conditions that are parameterfile that contains a polygonal approximation model of the ization independent whenever possible. These conditions can freeform shape, with no way of retrieving the history and detect: (i) whether a curve segment is a line, a circle, or a planar origin of the surfaces. 3Design [22], another product from curve; (ii) whether a surface patch is a plane, a sphere, a Wavefront Technologies that is integrated in Alias and cylinder, or a cone; and (iii) whether a surface is constructed Wavefront, can save geometry in Obj files as well as in as a surface of revolution/extrusion, a ruled/developable sur-Geo files where only the final model is saved, giving up face, or a generalized cylinder. ยฉ 1997 Academic Press the entire history of the model. Nevertheless, the geometry is saved in a precise form. That is, in a Geo file, the geome-
1. Introduction
try of a circle will be exactly represented but the origin and the fact that a surface has started as a cone might Geometric data are frequently exchanged between difbe lost. ferent solid modeling systems [18]. The ability to automati-While Acis is a self-contained kernel that does not dically recognize the way a surface is constructed is of great rectly support other geometric data file formats, Ideas importance in practice. A sphere can be represented in allow one, for example, to export and import geometry many different ways depending on the modeling system. using the IGES [14] data file format. Unfortunately, the That is, in one modeling system it may be represented as history is no longer saved when Ideas exports a model into a quadratic NURBS surface where in another system, it an IGES file. A trimmed surface originated as a sphere or may be represented as a procedural type in terms of its a cylinder is only saved as a trimmed NURBS surface center and radius. In a third modeling system, the same and information on the origin of this trimmed surface is sphere may be described as a surface of revolution, specicompletely lost, even when the IGES file is imported back fying the axis of revolution and a half circle as the crossinto the Ideas solid modeler. The IGES file format is quite section of the constructor. common in contemporary modeling environments. It is Consider Acis [1] from Spatial Technology, Ideas [13] quite interesting then, that while IGES allows one to prefrom SDRC, and Advanced Visualizer [21] from Wavescribe the form of a freeform rational B-spline surface as front Technologies. All three modeling systems are well a cone, a right circular cylinder, a torus, etc., a trimmed established and support freeform piecewise polynomial surface must assume a parametric form and the origin of representations. These three modeling systems also allow the surface as a primitive is no longer preserved. one to construct procedural primitives such as cones and
The knowledge that is lost in a specific surface geometry spheres, prescribing their centers, radii, etc. Moreover, transfer makes it difficult to consistently handle this geomewhile Boolean operations can result in a trimmed surface try. Two types of cones might exist in a modeling system. representation, Acis and Ideas can keep the knowledge A cone constructed locally will be treated as a full-fledged on the origin of the surface as the complete history of the model is known. Moreover, this complete knowledge is primitive, whereas a NURBS surface in the shape of a 417