Geomagic

About: Geomagic is a based out in . It is known for research contribution in the topics: Surface (mathematics) & Vertex (computer graphics). The organization has 18 authors who have published 31 publications receiving 1093 citations. The organization is also known as: Geomagic Inc. & Geomagic Capture.

Sliver exudation

Abstract: A sliver is a tetrahedron whose four vertices lie close to a plane and whose projection to that plane is a convex quadrilateral with no short edge. Slivers are notoriously common in 3-dimensional Delaunay triangulations even for well-spaced point sets. We show that if the Delaunay triangulation has the ratio property introduced in [15] then there is an assignment of weights so the weighted Delaunay triangulation contains no slivers. We also give an algorithm to compute such a weight assignment.

Methods, apparatus and computer program products that reconstruct surfaces from data point sets

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 p i in a 3D point set S that at least partially describes the 3D surface, by projecting the plurality of points p i onto planes T i that are each estimated to be tangent about a respective one of the plurality of points p i . The plurality of stars are then merged into a digital model of the 3D surface.

Surface Reconstruction by Wrapping Finite Sets in Space

Abstract: Given a finite point set in ℝ3, the surface reconstruction problem asks for a surface that passes through many but not necessarily all points. We describe an unambiguous definition of such a surface in geometric and topological terms,and sketch a fast algorithm for constructing it. Our solution overcomes past limitations to special point distributions and heuristic design decisions.

Apparatus and methods for wrapping texture onto the surface of a virtual object

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.

Automatic extraction of surface structures in digital shape reconstruction

Abstract: One of the most challenging goals in digital shape reconstruction is to create high-quality surface models from measured data with a minimal amount of user assistance. We present techniques to meet the requirements of mechanical engineering CAD/CAM/CAE. The reconstructed models are composed of a hierarchy of surfaces, including primary surfaces, connecting features, (e.g. fillets) and vertex blends, and obey a well-defined topological structure. First, combinatorially robust segmentation techniques borrowed from Morse theory are presented. This is followed by computing a ''feature skeleton'' on the mesh that determines the primary regions of the object. The final surface structure comprises the optimally located boundaries of the connecting features and setback type vertex blends, which are faithfully aligned with the actual geometry of the object. This CAD-like surface structure is sufficient for high-quality surface approximations. A few representative objects reconstructed by Geomagic systems illustrate the efficiency and quality of the approach.