PDE-BASED MEDIAL AXIS EXTRACTION AND SHAPE MANIPULATION OF ARBITRARY MESHES

Shape skeletonization （i.e., medial axis extraction） is powerful in many visual computing applications, such as pattern recognition, object segmentation, registration, and animation. In this paper, the authors expand the use of diffusion equations combined with distance field information to approximate medial axes of arbitrary 3D differential properties. It offers an alternative solids represented by polygonal meshes based on their but natural way for medial axis extraction for commonly used 3D polygonal models. By solving the PDE along time axis, this system can not only quickly extract diffusion-based medial axes of input meshes, but also allow users to visualize the extraction process at each time step. In addition, the proposed model provides users a set of manipulation toolkits to sculpt extracted medial axes, then use diffusion-based techniques to recover corresponding deformed shapes according to the original input datasets. This skeleton-based shape manipulation offers a fast and easy way for animation and deformation of complicated mesh objects.

A novel methodology for complex part motion planning

A motion planning strategy. tor the assembly task of inserting a dissymmetrical T-snaped putt into a C-shaped slot is presented. The coarse motion planning strategy is expounded by geometric reasoning. A medial axis diagram decreases the unnecessary configuration states and optimizes the planning strategy. Due to the uncertainties, force sensing and force control is indispensable for motion planning. Combining the coarse motion planning strategy with fine motion planning strategy, the task of assembling a dissymmetrical T-shaped part can be completed successfully.

Permeability differences based on three-dimensional geometrical information of void spaces

In this study,the permeabilities of Berea and Otway sandstones were measured under different confining pressures,and porosity was investigated through mercury intrusion porosimetry(MIP).The total porosities of the Berea and Otway sandstones were approximately 17.4%and 25%,respectively.Pore size distributions of each sandstone were almost the same,but the pores in the Otway sandstone were slightly narrower.However,the permeability of the Otway sandstone was smaller than that of the Berea sandstone by one order of magnitude.Three-dimensional(3D)void geometry and geometrical properties of the void spaces relevant to flow were compared to obtain the relation between the permeability differences and porosities of the two sandstones.The 3D geometrical analysis using microfocus X-ray computed tomography(CT)was performed,and the pore geometries of both sandstones were compared using the 3D medial axis(3DMA)method.Pore and throat radii,pore coordination number,tortuosity,number of connecting paths,connecting path volume,and other factors were determined using 3DMA.The Otway sandstone was characterized by a small effective throat/pore radius ratio.Based on the fluid flow mechanism,the lower effective throat/pore radius ratio results in a lower permeability induced by the fluid energy loss,which means that the 3D geometrical shape of void spaces affects the permeability value.

Applying Rational Envelope curves for skinning purposes

Special curves in the Minkowski space such as Minkowski Pythagorean hodograph curves play an important role in computer-aided geometric design,and their usages are thoroughly studied in recent years.Bizzarri et al.(2016)introduced the class of Rational Envelope(RE)curves,and an interpolation method for G1 Hermite data was presented,where the resulting RE curve yielded a rational boundary for the represented domain.We now propose a new application area for RE curves:skinning of a discrete set of input circles.We show that if we do not choose the Hermite data correctly for interpolation,then the resulting RE curves are not suitable for skinning.We introduce a novel approach so that the obtained envelope curves touch each circle at previously defined points of contact.Thus,we overcome those problematic scenarios in which the location of touching points would not be appropriate for skinning purposes.A significant advantage of our proposed method lies in the efficiency of trimming offsets of boundaries,which is highly beneficial in computer numerical control machining.

Shape Recognition and Retrieval Based on Edit Distance and Dynamic Programming

An important aim in pattern recognition is to cluster the given shapes. This paper presents a shape recognition and retrieval algorithm. The algorithm first extracts the skeletal features using the medial axis transform. Then, the features are transformed into a string of symbols with the similarity among those symbols computed based on the edit distance. Finally, the shapes are identified using dynamic programming. Two public datasets are analyzed to demonstrate that the present approach is better than previous approaches.