Abstract: A system and method for approximating parametric curves may subdivide curves using a minimum number of subdivisions while meeting a given error tolerance. The method may include determining a subdivision point such that the maximum chord error on one side of the point is equal to the maximum chord error on the other side of the point, the chord error being the distance between the curve and a linear approximation thereof. These techniques may be applied recursively to sub-portions defined by the subdivision point if the maximum error is greater than a pre-determined error tolerance. The pre-determined error tolerance may be a default tolerance, or may be application-specific or user-configurable, in various embodiments. By subdividing a curve into fewer segments than conventional methods, the system and methods described herein may allow an alternate representation of the curve to be generated that includes less data than one generated using conventional methods.

Abstract: A method, system, and computer-readable storage medium are disclosed for tessellating a trimmed parametric surface comprising a parametric surface and a trim curve. The parametric surface may be tessellated to produce a set of polygons approximating the parametric surface. A first polygon of the set of polygons in which a first point on the trim curve is located may be determined. A second point on the trim curve may be projected into a plane, wherein the plane is determined by the first polygon. A set of one or more additional polygons of the set of polygons may be projected into the plane. A second polygon of the set of one or more additional polygons in which the second point on the trim curve is located may be determined.

Abstract: A digital representation having a data structure with tessellated data defining an object in terms of triangles is compressed by analyzing the tessellated data to identify neighboring triangles, identifying stripes comprising series of neighboring triangles, redefining a given triangle with respect to a preceding triangle in the stripe in terms of a vertex of the given triangle that is not on a common edge with the preceding triangle. Digital values of the compressed digital representation for a triangle are fed back to the digital representation and are used for triangles processed subsequently. The third vertex can be defined in terms of a vector from a predetermined position with respect to the common edge.

Abstract: A computer-implemented method can provide compression of a digital representation of an object. The digital representation can include a graphical data structure with graphical data defining the object in terms of a definition of respective faces of the object. Each face can be defined in terms of a surface for the face and each edge of the face on that surface. The method can include, for respective faces of the object, accessing the definition of the face in the graphical data structure, generating a compressed definition of the face and replacing the definition of the face in the graphical data structure by the compressed definition of the face.

Abstract: A digital representation having a data structure with tessellated data defining an object in terms of triangles is compressed by analyzing the tessellated data to identify neighboring triangles, identifying stripes comprising series of neighboring triangles, redefining a given triangle with respect to a preceding triangle in the stripe in terms of a vertex of the given triangle that is not on a common edge with the preceding triangle. Digital values of the compressed digital representation for a triangle are fed back to the digital representation and are used for triangles processed subsequently. The third vertex can be defined in terms of a vector from a predetermined position with respect to the common edge.