Abstract: The invention provides techniques for wrapping a two-dimensional texture conformally onto a surface of a three dimensional virtual object within an arbitrarily-shaped, user-defined region. The techniques provide minimum distortion and allow interactive manipulation of the mapped texture. The techniques feature an energy minimization scheme in which distances between points on the surface of the three-dimensional virtual object serve as set lengths for springs connecting points of a planar mesh. The planar mesh is adjusted to minimize spring energy, and then used to define a patch upon which a two-dimensional texture is superimposed. Points on the surface of the virtual object are then mapped to corresponding points of the texture. The invention also features a haptic/graphical user interface element that allows a user to interactively and intuitively adjust texture mapped within the arbitrary, user-defined region.

Abstract: Methods of modeling a three-dimensional surface structure include partitioning three-dimensional object data into regions of a Morse complex and generating a feature skeleton having a plurality of smooth edges and a plurality of vertices separating the regions of the Morse complex. Operations are also performed to thicken the feature skeleton by replacing the plurality of smooth edges with corresponding pairs of curves that locate longitudinal boundaries of transitions between primary regions of the feature skeleton. The thickening operations may also include replacing each of the plurality of vertices with a corresponding loop of edges, using setback-type vertex blends.

Abstract: Methods, apparatus and computer program products provide efficient techniques for reconstructing surfaces from data point sets. These techniques include reconstructing surfaces from sets of scanned data points that have preferably undergone preprocessing operations to improve their quality by, for example, reducing noise and removing outliers. These techniques include reconstructing a dense and locally two-dimensionally distributed 3D point set (e.g., point cloud) by merging stars in two-dimensional weighted Delaunay triangulations within estimated tangent planes. The techniques include determining a plurality of stars from a plurality of points pi in a 3D point set S that at least partially describes the 3D surface, by projecting the plurality of points pi onto planes Ti that are each estimated to be tangent about a respective one of the plurality of points pi. The plurality of stars are then merged into a digital model of the 3D surface.

Abstract: Embodiments automatically generate an accurate network of watertight NURBS patches from polygonal models of objects while automatically detecting and preserving character lines thereon. These embodiments generate from an initial triangulation of the surface, a hierarchy of progressively coarser triangulations of the surface by performing a sequence of edge contractions using a greedy algorithm that selects edge contractions by their numerical properties. Operations are also performed to connect the triangulations in the hierarchy using homeomorphisms that preserve the topology of the initial triangulation in the coarsest triangulation. A desired quadrangulation of the surface can then be generated by homeomorphically mapping edges of a coarsest triangulation in the hierarchy back to the initial triangulation. This quadrangulation is topologically consistent with the initial triangulation and is defined by a plurality of quadrangular patches.

Abstract: Methods, apparatus and computer program products can generate light weight but highly realistic and accurate colored models of three-dimensional colored objects. The colored model may be generated from a second plurality of points that define a coarse digital representation of the surface and at least one texture map containing information derived from a first plurality of colored points that define a fine digital representation of the surface. This derivation is achieved by mapping points within the texture map to the fine digital representation of the three-dimensional surface. Colored scan data may be used to construct the fine digital representation as a triangulated surface (i.e., triangulation) using a wrapping operation.

Abstract: A method of automatic conversion of a physical object into a three-dimensional digital model. The method acquires a set of measured data points on the surface of a physical model. From the measured data points, the method reconstructs a digital model of the physical object using a Delaunay complex of the points, a flow strcuture of the simplicies in the Delaunay complex and retracting the Delaunay complex into a digital model of the physical object using the flow structure. The method then outputs the digital model of the physical object.

Abstract: A method of geometric morphing between a first object having a first shape and a second object having a second shape. The method includes the steps of generating a first Delaunay complex corresponding to the first shape and a second Delaunay complex corresponding to the second shape and generating a plurality of intermediary Delaunay complexes defined by a continuous family of mixed shapes corresponding to a mixing of the first shape and the second shape. The method further includes the steps of constructing a first skin corresponding to the first Delaunay complex and a second skin corresponding to the second Delaunay complex and constructing a plurality of intermediary skins corresponding to the plurality of intermediary Delaunay complexes. The first skin, second skin and plurality of intermediary skins may be visually displayed on an output device.