Automated geometric representation of discrete point sets

摘要

A system and method of creating a smooth analytical representation of a geometry using a discrete set of points. A meshfree representation of the geometry is generated. The representation includes a set of points. A starting point and an edge length range are then used to generate a set of vertices from the set of points. The vertices are used to generate a coarse mesh, which, in turn, is used to generate a Reproducing Kernel Element Method (RKEM) representation of the geometry. The points of the meshfree representation that were not included in the set of vertices are then applied to the RKEM representation. The quality of the RKEM representation is assessed and compared to a predetermined standard. Additional sets of vertices from the meshfree representation are generated repeatedly and all remaining operations are repeated until the quality of the RKEM at least meets the predetermined standard. This provides a smooth, analytical RKEM representation of the geometry.

主权项

1. A method of creating a smooth analytical representation of a geometry, comprising:
generating a meshfree representation of the geometry, the meshfree representation having a set of points; generating a set of vertices from the set of points of the meshfree representation using a starting point and a range of edge length; generating a coarse mesh using the set of vertices; generating a Reproducing Kernel Element Method (RKEM) representation of the geometry using the course mesh; applying the remaining points of the meshfree representation not included in the set of vertices to the RKEM representation of the geometry; assessing the quality of the RKEM representation of the geometry against a predetermined standard; and repeatedly generating an additional set of vertices from the meshfree representation and repeating all remaining operations until the quality of the RKEM representation of the geometry at least meets the predetermined standard; wherein generating a meshfree representation of the geometry comprises:
providing a surface triangularization of the geometry, the surface triangularization having a set of points and triangular faces connecting the set of points;modifying the surface triangularization's set of points to create a modified outer surface point set;identifying an outward directed normal vector at each surface point in the modified outer surface point set;generating a plurality of offset points, wherein the plurality of offset points are offset towards the interior of the modified outer surface point set along the outward directed normal vector by the amount of a specified wall thickness to create an interior surface point set;determining if any two points in the interior surface point set are closer than a predetermined distance; andreplacing any two points determined to be closer than the predetermined distance with a third point, the third point having the average position of the two points;whereby the modified outer surface point set combined with the interior surface point set is the meshfree representation of the geometry.