Cube-Related Corner Coalesced Nets

Finite or periodic structures containing the cube motif can be synthesized and transformed into a variety of structures both at the theoretical and real, experimental level. The rhombellation topo-geometric operation may be used to transform the cube-shape into larger units and then build light (spongy) structures with larger voids. Hyper-clusters are polyhedral structures which nodes are polyhedral structures (the same or different ones). The paper presents some hypothetical spongy structures related to the cubic primitive pcu-net, with defects induced by cutting-off some atoms and/or bonds so that only corners are shared between two cubes. A diamondoid hyper-structure containing cube-coalesced corners was proposed for an eventual synthesis. The discussed structures are described in topological terms, particularly by sequential vertex connectivity and ring environment.

Remove Mesh Self-Intersections Based on Light Projection Algorithm

Offset in computer aided design and manufacturing (CAD/CAM) is a kind of important geometric operation, such as rapid prototyping technology, NC machining, the collision detection, etc. When offset distancedis greater than the minimum radius of curvature on the original surface, or part of the distance between parts of curved surface pieces, it causes self-intersection. Self-intersection makes distance between two models smaller than the offset distancer, leading to offset model local intersection or distortion. This paper proposes a method based on light projection algorithm to remove self-intersections and achieve good results. Firstly, set point coordinates on the original model as the light source locations and build the projection light according to adjacent plane vector weighted sum.Secondly, the projection light passes through the offset model. We extract the triangles on the outermost layer and load it into a list. Finally it is essential to filter the intersection points and construct triangle mesh. We use different discrete data models to do experiments and prove the validity and practicability of the algorithm.

EQUIVALENT L-SHAPES OF DOUBLE-LOOP NETWORKS FOR THE DEGENERATE CASE

Double-loop networks have been widely studied as architecture for local area networks. The L-shape is an important tool for studying the distance properties of double-loop networks. Two L-shapes are equivalent if the numbers of nodes k steps away from the origin are the same for every k. Hwang and Xu first studied equivalent L-shapes through a geometric operation called a 3-rectangle transformation. Rödseth gave an algebraic operation, which was found by Huang, Hwang and Liu to correspond to the 3-rectangle transformation. Recently, Chen and Hwang obtained all equivalent transformations for the nondegenerate case. In this paper, we do the same for the degenerate case.