טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentEytan Liat
SubjectAutomatic Generation of CSG Representation for Two
Dimensional Objects
DepartmentDepartment of Mechanical Engineering
Supervisors Professor Anath Fischer
Professor Emeritus Moshe Shpitalni


Abstract

This research proposes a technique for converting boundary representation (B-Rep) models to constructive solid geometry (CSG) models and for optimizing CSG models in order to store, compress, display and transform information via the Internet. CSG and B-Rep models represent a solid object using two different concepts. A B-Rep model represents a solid object by its boundary surface, while a CSG model represents the interior of the solid object through a binary tree based on volumetric primitives on its leaves. Boundary models of real engineering objects are huge, and algorithms for compressing and displaying objects require intensive computations. Therefore, converting a B-Rep model to a CSG model is needed to reduce data and to subsequently represent it in the form of a multiresolution CSG model. However, converting a B-Rep model, which is unique, to a CSG model that can be represented by multiple representations for a given solid object is known to be a difficult problem.


The first part of this research presents a method that converts a B-Rep 2D geometric model into a CSG representation, and the second part proposes a method that converts the CSG model to a multiresolution CSG model.


First, a 2D B-Rep model is converted to a CSG model. There are several approaches for this conversion, such as half-space, decomposition and convex hull approaches. However, the half-space and decomposition methods are limited to union operations, while the convex hull approach is limited to convex primitives and subtraction operations.

The conversion approach proposed in this work overcomes these limitations and generates a CSG tree with basic primitives and union, subtraction and intersection operations, where the primitives can overlap each other. This conversion approach is based on graph theory and AI techniques.   


Next, a multiresolution CSG representation is defined and implemented. This multiresolution representation represents the CSG model at different levels of detail, depending on the required level. The data of the multiresolution representation can be saved in more than one file, thus possibly increasing the time response whem the model is transferred via the Internet or updated. There are several approaches for multiresolution representation, such as LOD and subdivision. However, these approaches work on an object’s boundary rather than its interior.


CSG multiresolution with the proposed approach generates a hierarchy of multiresolution CSG trees from the original CSG tree, where at each level the multiresolution CSG model is represented by a minimum number of CSG primitives. This approach can be also used for mixed multiresolution that focuses on a local part of the object, while the rest of it is shown in less detail.


The conversion of B-Rep models to multiresolution CSG trees is more efficient in time complexity  than conventional multiresolution methods. Implementations of this approach are shown on complex 2D objects.