Triangulation of Stratified Objects

On the Triangulation of Stratified Sets and Singular Varieties

We show that every compact stratified set in the sense of Thom can be triangulated as a simplicial complex. The proof uses that author's description of a stratified set as the geometric realisation of a certain type of diagram of smooth fibre bundles and smooth imbeddings, and the triangulability of smooth fibre bundles. As a consequence, we obtain proofs of the classical triangulation theorems...

Stratified Ontologies: the Case of Physical Objects

This phenomenon is quite common: the examples above have been taken from existing toplevel ontologies used in practice, and they are responsible, in our opinion, of many situations of tangleness, confusion, and lack of semantic rigour. We advocate in the present paper a design principle aimed to clarify such situations and produce more reusable and well-founded ontologies. It can be stated as f...

Adaptive Triangulation Of Objects Reconstructed From Multiple Range Images

When reconstructing objects from multiple range images one has to deal with the problem of large data sets. In our approach, the surface itself is implicitly defined by a signed distance function. The distance function is derived from the range images which are assumed to be already registered. A triangulated model is generated from a rough approximation of the object using the marching-cubes a...

Category of Polygroup Objects

Flying triangulation--an optical 3D sensor for the motion-robust acquisition of complex objects.

Three-dimensional (3D) shape acquisition is difficult if an all-around measurement of an object is desired or if a relative motion between object and sensor is unavoidable. An optical sensor principle is presented-we call it "flying triangulation"-that enables a motion-robust acquisition of 3D surface topography. It combines a simple handheld sensor with sophisticated registration algorithms. A...