טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentAzernikov Sergei
SubjectIsotropic and Anisotropic Reconstruction of Freeform
Surfaces and Volumes from Scattered Data
DepartmentDepartment of Mechanical Engineering
Supervisor Professor Anath Fischer


Abstract

Reverse Engineering (RE) has become an essential part of Computer-Aided Design (CAD), particularly when no 3D model is available, so that the physical object must be used to create a model for design. This research deals with the difficult problem of creating a 3D computerized model from a cloud of oints sampled from a physical object. The input data is large in scale and unorganized, and often includes noise and spurious points. Moreover, the sampled object may have arbitrary topology and sharp features. Despite rapidly evolving commercial RE modules, there is  still a gap between the proposed tools and industry demands, with efficiency and robustness the weak points of existing solutions. Consequently, the current research work seeks to develop automatic, efficient and robust RE methods to meet practical requirements.


First, we proposed a new volumetric approach to the surface reconstruction problem that uses digital topology and dual meshing for surface reconstruction from points. The object is represented as a set of hierarchical volume elements (voxels). This volumetric representation is constructed by an isotropic refinement of the voxels, which contain some portion of the input cloud of points. Then, the topology of the original object is recovered from the digital topology of the volumetric representation. This approach was proven efficient, fast and robust, and has recently been extended for non-manifold and non-orientable surfaces, which could not be reconstructed with previous methods.


Second, we developed a shape sensitive voxelization method for representing the surface and interior volume of the reconstructed object. To the best of our knowledge, this is the first attempt to introduce anisotropy into the surface reconstruction process. The embedding Euclidean space is curved according to the shape of the object to be meshed. Mathematically, this phenomenon is formulated as a Riemannian tensor field, induced by the object's shape operator. This field introduces directionality into the problem Domain, so that the problem becomes anisotropic. Warping a structured grid in the produced field provides adaptivity to the shape, while preserving the structured topology, allowing us to achieve much more efficient, adaptive approximations, than with the previous isotropic methods.

The proposed approach has proved useful for a wide variety of applications, such as reverse engineering and rapid prototyping, anisotropic meshing of implicit surfaces and medical imaging. Moreover, it was later extended for anisotropic hexahedral meshing of volumes, making it applicable for finite element analysis.