Modeling and 3D object reconstruction by implicitly defined surfaces with sharp features

Abstract

We propose a new method for describing sharp features (i.e., edges and vertices) of implicitly defined surfaces. We consider an initial implicitly defined surface, which is represented as the zero set of a C 1 smooth scalar field with non-vanishing gradients. In order to represent sharp edges and vertices, this surface is augmented by adding new types of implicit representations, called edge descriptors and vertex descriptors. They are defined with the help of the distance field of edge curves. In our implementation, we use circular splines to describe these edge curves, since they support a fast and non-iterative closest point computation.After adding the edge and vertex descriptors to the initial scalar field, the zero set of the augmented function contains the sharp features. We apply the new representation to surface modelling by implicitly defined surfaces with sharp features and to object reconstruction. In the latter case we describe an algorithm for detecting the sharp curves and vertices of a shape which is given by an unorganized point cloud, which are then approximated by circular splines, in order to define the edge and vertex descriptors.

Surface Reconstruction of Defective Point Clouds Based on Dual Off-Set Gradient Functions

“…Smoothing (Ravikrishna et al 2004), refitting (e.g. (Chandrajit et al 1995;Shen et al 2005;Shen et al 2009 (Carr et al 2001;Greg & James 2002), multi-level partition of unity (MPU) method (Yutaka et al 2003), products of univariate B-splines (Song & Jüttler 2009) and tri-cubic B-spline basis functions (Esteve et al 2008) on voxelization. However they either need the consistent normals as aided information or the point clouds with fewer defective samples.…”

“…The methods in (Esteve et al 2005) proposes DMS operation on volumetric grids to fill holes by detecting the incursions to the interior of the surface and approximates them with a bounded maximum distance. It is an improvement of (Song & Jüttler 2009), but a post process has to be introduced to the low density data zones. The typical implicit methods mentioned above are summarized in Table 1 Rather than constructing final surface directly, it is much easier to confirm the off-set surfaces of point clouds.…”

Moving particle semi-implicit method for fluid simulation with implicitly defined deforming obstacles

“…In the third approach, users can obtain approximated implicit form of existing polygonal shape models. Although implicit form typically assumes smoothness of the surfaces, some methods enables implicit expression of sharp edges and corners [21,22].…”

An unstructured immersed finite element method for nonlinear solid mechanics

“…In [38] the operations of surface reconstruction by means of marching cubes and the distance function computation are combined in order to generate a so-called directed distance field allowing for a better resolution of surface features. On the other hand, enriched distance functions are presented in [39] where additional edge and vertex descriptors augment the distance geometry representation. Although both approaches are promising concepts in the context of immersed finite element methods, they are not further considered in this work.…”