Linear Octree Represented Tool Swept Volume Modeling on Complex Surface Machining

In this paper, a novel approach of linear octree is employed to represent discrete tools and build their swept volumes along machining trajectories. Firstly, a data structure of linear octree is defined as the base of geometrical transformations. The linear octree can be extended into leaf nodes in the deepest level for simplifying homogeneous transformations, and all leaf nodes in the deepest level can also be concentrated into a linear octree for saving storage capacity inversely. Secondly, tool trajectories are interpolated as short lines, and swept volumes between neighbor interpolation points are defined as the Minkowski sum of their cell sets at both locations. Thirdly, equations of the rotation matrix for local coordinate system, roll, pitch and yaw angles of tool orientations are established to define the global rotation motions. Finally, a case of discrete sphere tool and its swept volume modeling are studied to validate the proposed approach.

A Method of Three-Dimensional Modeling Based on Voxel Code

This article proposes a method of three-dimensional modeling based on voxel code, which can build three-dimensional model by means of cubic voxels and Voxel code. Voxel code is the one that records the formation of physical location of the voxels piled up in turn order in the body. The different Three-dimensional shape can be constructed according to different codes. In order to reduce the storage overhead of the code, the linear octree coding and decoding are given in recording voxel code. Combined with VTK (Visualization Toolkit) programming, some voxel models have been visualization. The modeling idea and method proposed in this paper have a positive significance for the promotion of the research and development of related science fields and have their theoretical and practical value.