Ph.D Thesis

Ph.D StudentMassarwa Fady
SubjectTrivariate volumes - Algorithms and Applications
DepartmentDepartment of Computer Science
Supervisor PROF. Gershon Elber
Full Thesis textFull thesis text - English Version


This work investiages algorithms and data structures for volumetric representation (V-reps) of 3D objects, representing the interior of the object in addition to its boundaries, extending the contemporary Boundary representation (B-rep) common scheme.  In recent years, there is a growing and emerging need for a volumetric representation of 3D objects.  Specifically, with the development of Iso-geometric Analysis (IGA) and advanced manufacturing technologies employing heterogeneous

materials, such as 3D-printing and additive manufacturing (AM) of functionally graded material.  We employ B-spline trivariate basis functions for the V-reps as follows:

We start by proposing a volumetric representation (V-rep) for geometric modeling that is based on trimmed B-spline trivariates and introduce its supporting volumetric modeling framework.  The framework includes various volumetric models (V-model) construction schemes from basic (non-singular) volumetric primitives to high level constructors, such as volumes of revolutions, as well as Boolean operations' support

for V-models. Further, this framework is also a seamless extension to existing boundary representations (B-reps) common in all contemporary geometric modeling systems, and allows a simple migration path of existing B-rep data, tools and algorithms.

Then, we propose an untrimming algorithm - an algorithm for converting trimmed B-spline surfaces and trivariates into a set of tensor product B-splines.  The untrimming algorithm can be utilized to simplify algorithms and applications using the proposed framework, such as the integration process for IGA.

Finally, we propose two algorithms for modeling of volumetric micro-structures using functional composition over V-reps. The first algorithm generates random microstructures with connectivity and smoothness guarantees, and the second algorithm can be used to construct micro-structures with bifurcations, that compensates for the non-isometric behavior of the V-rep trivariate.