Abstract: A shape defined partially be a Bezier curve is rendered through a GPU-implemented technique which determines for various screen points which side of the curve the points lie on. This is done in the particular case of cubic Bezier curves for shapes defined by the Bézier control points of the curves. The type of the curve is identified through an analysis of an inflection point polynomial based on the curve. The curve is then projected to a canonical implicit form in a canonical texture space, allowing computation to be efficiently performed on a simple canonical form of the curve.

Abstract: Improved triangle management in triangular meshes uses a data structure having two fields to store data for each triangle in the triangular mesh. The first field is a set of three vertices for the triangle and the second field is a set of three edges, each edge corresponding to one of the three vertices. Each of the three edges is an identification of a next or subsequent edge that is encountered when performing a traversal (e.g., in a counterclockwise direction) about the corresponding vertex. According to one aspect, three operators are defined to assist in management of the triangular mesh. These operators are a make edge operator, a splice operator, and a swap operator, and are selectively invoked to both add triangles to the triangular mesh and remove triangles from the triangular mesh.

Abstract: Rendering an outline font. Rendering an outline font by adding Bezier control points to further define a contour of an outline font and applying an in or out test to determine if a pixel falls within the contour of an outline font.

Abstract: A system and process for computer modeling of an object involving first capturing images of the object that collectively depict all the object's surfaces which are to be modeled. A series of 3D reconstructions are then derived from the images. Each of the reconstructions represent a portion of the object's surfaces. Noise elimination techniques are employed to reduce the number of extraneous reconstruction points. The individual 3D reconstructions are then registered to a common coordinate system to produce an overall 3D reconstruction of the object's surfaces. A surface representation of the object is extracted from the overall 3D reconstruction using robust surface extraction techniques, and if desired, a texture map for the surface representation of the object can be computed using the previously captured images to produce a photorealistic model of the object.

Abstract: A system and method for modeling smooth free-form shapes using B-splines over irregular meshes, in a simple and efficient manner, to generate a display of aesthetically pleasing shapes is disclosed. A low degree parametric polynomial representation is generated. As a result, techniques for surface-surface or ray-surface intersection are faster and more robust than possible with existing techniques. In accordance with the present invention, an input mesh M.sup.0 is initially simplified by isolating irregularities and constraining geometry. First, the input mesh M.sup.0 is subjected to general refinement, whereby a new mesh M.sup.1 is constructed, which in turn is subjected to constrained refinement, whereby another new mesh M.sup.2 is constructed. After the general and constrained refinement steps, the mesh M.sup.2 is broken up into a set of "quad-nets" corresponding to each of its vertices. Finally, these quad nets are used as local geometry, over which, 4 cubic Bezier triangles are constructed.