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.     

Darstellung doppelbrechender Lipoidtropfen aus dem Serum

Summary (1) Doubly refracting lipoid droplets can be demonstrated in normal and pathological sera by means of alcohol ether extraction. This is not possible with ether extraction alone.(2) These lipoid droplets can be demonstrated only, or almost only, when they are precipitated out of alcohol or ether alcohol     

Oberflächenspannung und Schallgeschwindigkeit

Summary The preceding empirical relation was found between the surface tension of liquids, the specific weight of liquids, and the velocity of sound:=6.3 · 10^{–4 3/2}. In place of the vèocity of sound can be used, with suitable changes in the equation, the compressibility or, in the case of solid substances, the elasticity of the material in question. The range of validity of this relation is so large that it is possible by means of it to calculate the surface tension of solid substances and of gases.