An approach towards offsetting of object in non-manifold 3-D geometric modeling: [Essay Example], 561 words GradesFixer
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An Approach Towards Offsetting of Object in Non-manifold 3-d Geometric Modeling

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Introduction While NURBS is de facto standard for exact curve and surface, triangular mesh (T-mesh for short) is probably the most popular choice for approximate shape representation in many engineering applications including FE analysis, tool path generation, and reverse engineering, as well as computer graphics and approximate shape representation in many engineering applications, Tiller [15].

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It is often required to offset a T-mesh that consists of two major steps: Raw offsetting Raw offsetting is to obtain a T-mesh apart from the original mesh by the given distance and the resulting mesh may have regenerated into triangles. Regularization is the step to remove those abnormalities. We obtain a regular T-mesh, which is a 2-D manifold triangular mesh free from regenerated triangles. Computing offset model of a shape represented by a T-mesh can be used for toolpath generation and process planning of a sculptured surface such as mold & die, Choi [7].

Geometric operation between T-meshes [8] is very similar to T-mesh regularization as it finds segmentation between T-meshes and selectively collects portions as specified by the Cartesian operators. Hence, the algorithm described in this paper can be applied to geometric operation between T-meshes. The primary advantage is that in geometric operation problem the triangle set is already separated into two groups that make the segmentation search easier. Related work Several researchers have developed strategies for offsetting of planar environments. Offsetting modeling technology has significantly outgrown its original scope of computer-aided mechanical design and manufacturing automation. It plays an important role in many domains like medical imaging and therapy planning, architecture and construction, digital video-production for entertainment and advertising Arnold [1].

Although no publications on three-dimensional non-manifold offsetting were found in journals Lee [3], much research on offsetting operations on solids and sheets has been made and published, Masuda [4]. Since offsetting operations on nonmanifold objects encompass those on solids, sheets and wireframes, previous works on solid and sheet offsetting will be reviewed as related work instead. Solid modeling theory and technology are becoming increasingly well understood, and their commercial and industrial exploitation is progressing rapidly Requicha [11], Voelcker [12].

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However, the range of operations on solids supported by current modelers are very limited. Typically, solids represented in a modeler can be transformed by rigid motions which are straightforward and well known in computer graphics, Newman [13], Dam [14], and can be combined by Boolean operations, which are complex but important. Many researchers already proposed a 3D curve offsetting methods Shin [16] which has a wide variety of applications and seems to be a natural extension of 2D curve offsetting. However, there is no commonly accepted definition of 3D curve offsetting and fundamental operation in geometric modeling. Objective Research related with offsetting has been carried out for over three hundred years and it may be classified into two main categories (i) Offset geometry (ii) Offset topology The area of offset geometry deals with the exact or approximate methods for generating offset curves and surfaces, which are well surveyed by Pham’s [5].

The area of offset topology deals with the development of topological operations for generating offset solids or converting sheets into solids in geometric modeling systems. The purpose of this work is to develop a generic algorithm, to do an offset between planners and spherical 3D objects through segmentation and non-manifold operations with the help of 3D coordinate geometry.

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An approach towards offsetting of object in non-manifold 3-D geometric modeling. (2018, May 17). GradesFixer. Retrieved April 19, 2021, from
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