Delaunay triangulation of arbitrarily shaped planar domains

An algorithm is presented for constructing a Domain Delaunay triangulation (DDT) of an arbitrarily shaped, multiply-connected (manifold or nonmanifold), planar domain. DDT preserves the boundary of the given region and has properties identical to those of the standard Delaunay triangulation. Construction of this triangulation involves operations (node refinement, triangulation extraction) that are based solely on properties of the standard Delaunay diagram. Examples are included that demonstrate the validity of the algorithm.  

Drawing curves onto a cloud of points for point-based modelling

Point-based geometric models are gaining popularity in both the computer graphics and CAD fields. A related design/modelling problem is the focus of the reported research: drawing curves onto digital surfaces represented by clouds of points. The problem is analyzed and solved, and a set of ‘design tools’ are proposed which allow the user/designer to efficiently perform ‘product development’ (alternative name: ‘detail design’) tasks which require efficient processing of a ‘digital surface’. The primary tool is a robust and efficient point projection algorithm combined with a smoothing technique for producing smooth ‘digital curves’ lying onto the cloud surface. The new design tools are tested on a real-life industrial example with very satisfactory results, which are thoroughly presented in the paper.  

Information models of layout constraints for product life-cycle management: a solid-modelling approach

Complex products and systems, like an aircraft, ship, or machinery plant, involve a large number of components which are arranged under spatial constraints/relationships in design space. Current practices approximate these relationships with simplified ‘dimensional constraints’ aiming at formulating the design problem as a system of (in)equalities to be solved automatically, e.g. by a geometric-constraint solver. This research proposes informationally-complete models for design-constraints based on an analysis of geometric and non-geometric properties of the related space volumes. Also, an Extended Product Model is proposed describing the system's structure and components as well as related procedures and constraints to be used as a system life-cycle model.  

Protrusion-oriented 3D mesh segmentation

In this paper, we present a segmentation algorithm which partitions a mesh based on the premise that a 3D object consists of a core body and its constituent protrusible parts. Our approach is based on prominent feature extraction and core approximation and segments the mesh into perceptually meaningful components. Based upon the aforementioned premise, we present a methodology to compute the prominent features of the mesh, to approximate the core of the mesh and finally to trace the partitioning boundaries which will be further refined using a minimum cut algorithm. Although the proposed methodology is aligned with a general framework introduced by Lin et al. (IEEE Trans. Multimedia 9(1):46–57, 2007), new approaches have been introduced for the implementation of distinct stages of the framework leading to improved efficiency and robustness. The evaluation of the proposed algorithm is addressed in a consistent framework wherein a comparison with the state of the art is performed.  

From sketch to solid: an algebraic cross-section criterion for the realizability of a wireframe sketch

An intermediate step in the construction of a polyhedron from a partial-view sketch is the derivation of a realizable wireframe sketch, i.e., a complete sketch which is guaranteed to be the projection of a polyhedron. This paper presents a robust realizability-test based on the classical “cross-section criterion” that was developed in a geometric “ruler-and-compass” framework.  

Extracting a polyhedron from a single-view sketch: Topological construction of a wireframe sketch with minimal hidden elements

An essential prerequisite to construct a manifold trihedral polyhedron from a given natural (or partial-view) sketch is solution of the “wireframe sketch from a single natural sketch (WSS)” problem, which is the subject of this paper. Published solutions view WSS as an “image-processing”/“computer vision” problem where emphasis is placed on analyzing the given input (natural sketch) using various heuristics. This paper proposes a new WSS method based on robust tools from graph theory, solid modeling and Euclidean geometry. Focus is placed on producing a minimal wireframe sketch that corresponds to a topologically correct polyhedron.