Anath Fischer

Parameterization and reconstruction from 3D scattered points based on neural network and PDE techniques

Reverse engineering ordinarily uses laser scanners since they can sample 3D data quickly and accurately relative to other systems. These laser scanner systems, however, yield an enormous amount of irregular and scattered digitized point data that requires intensive reconstruction processing. Reconstruction of freeform objects consists of two main stages: parameterization and surface fitting. Selection of an appropriate parameterization is essential for topology reconstruction as well as surface fitness. Current parameterization methods have topological problems that lead to undesired surface fitting results, such as noisy self-intersecting surfaces. Such problems are particularly common with concave shapes whose parametric grid is self-intersecting, resulting in a fitted surface that considerably twists and changes its original shape. In such cases, other parameterization approaches should be used in order to guarantee non-self-intersecting behavior. The parameterization method described in this paper is based on two stages: 2D initial parameterization; and 3D adaptive parameterization. Two methods were developed for the first stage: partial differential equation (PDE) parameterization and neural network self organizing maps (SOM) parameterization. The Gradient Descent Algorithm (GDA) and Random Surface Error Correction (RSEC), both of which are iterative surface fitting methods, were developed and implemented.

New B‐Spline Finite Element approach for geometrical design and mechanical analysis

In most existing CAD systems, geometrical design and mechanical analysis are operated as completely separate modules. Intensive interaction between these modules is, however, highly desired due to the iterative nature of a typical product development process. Formulating a new, unified approach to design and analysis that provides a high level of interaction is the main purpose of this research. The idea is to integrate a mechanically based geometrical design concept with the mechanical analysis module in a uniform B-Spline Finite Element (BSFE) environment. In this paper, the BSFE method is formulated and its validity and adequacy are verified for elastic linear rod and plate models. In particular, the feasibility of applying B-spline functions as base functions of the finite element method for design and analysis is demonstrated. Unique scheme attributes based on intrinsic properties of B-spline functions are investigated in detail. Method adequacy is demonstrated by comparing convergence characteristics, complexity and computational cost to the spectral element method.

Modeling micro-scaffold-based implants for bone tissue engineering

A new conceptual biomedical method is presented for designing scaffold-based bone implants and using these implants in treating deteriorated bones. These implants have micro-architectural bone structures that are capable of mimicking the stochastic micro-structure as in natural bone bio-mineral structures. Moreover, they can be adapted as specific tailor-made compatible bone-repair mediator implants to be used as effective substitutes for natural damaged bone fracture structures.

Integrated mechanically based CAE system using B-Spline finite elements

Abstract In a product development cycle interaction between design and analysis should be very intensive. However, currently existing Computer Aided Engineering systems substantially limit such interaction, since design and analysis are realized in them as two isolated modules. These limitations can be distinguished on two levels: the conceptual and the technical. On the conceptual level a gap exists according to the functionality of each module: the design module is based on purely geometric operations, while the analysis module is based on physical phenomena. On the technical level an environmental gap exists that is characterized by differences in mathematical representation and computational methods. This is partially dictated by the functionality of each module. As a result of these limitations, each iteration between design and analysis and vice versa requires remodeling of the object and conversion of its mathematical representation. In order to overcome these problems, a mechanical B-Spline finite element model is proposed in this work to be used for both geometric design and mechanical analysis. With this approach the target object is modeled as a physical entity from the very beginning of the geometric design stage. Furthermore, both modules utilize the same computational environment—B-Spline finite element, and the same representational environment—B-Spline representation. Therefore, design and analysis are tightly integrated into a completely unified system, and corresponding analysis operations can be performed simultaneously with the geometric design. Technically, this eliminates remodeling and conversion operations between the design and analysis stages of the product development cycle. Conceptually, this allows engineers to substantially shorten the product development cycle time, test many more design variants, tune the final product more finely according to its functionality and reduce the total product development cost. A few examples verifying feasibility and demonstrating performance of the proposed system are presented in the paper. These are developing sculptured surface objects based upon an elastic linear plate model and developing sculptured solid objects based upon an elastic linear solid model.

Three-dimensional surface reconstruction using meshing growing neural gas (MGNG)

The neural network method, a relatively new method in reverse engineering (RE), has the potential to reconstruct 3D models accurately and fast. A neural network (NN) is a set of interconnected neurons, in which each neuron is capable of making autonomous arithmetic and geometric calculations. Moreover, each neuron is affected by its surrounding neurons through the structure of the network.This work proposes a new approach that utilizes growing neural gas neural network (GNG NN) techniques to reconstruct a triangular manifold mesh. This method has the advantage of reconstructing the surface of an n-genus freeform object without a priori knowledge regarding the original object, its topology or its shape. The resulting mesh can be improved by extending the MGNG into an adaptive algorithm. The proposed method was also extended for micro-structure modeling. The feasibility of the proposed method is demonstrated on several examples of freeform objects with complex topologies.

3D hierarchical geometric modeling and multiscale FE analysis as a base for individualized medical diagnosis of bone structure

This paper describes a new alternative for individualized mechanical analysis of bone trabecular structure. This new method closes the gap between the classic homogenization approach that is applied to macro-scale models and the modern micro-finite element method that is applied directly to micro-scale high-resolution models. The method is based on multiresolution geometrical modeling that generates intermediate structural levels. A new method for estimating multiscale material properties has also been developed to facilitate reliable and efficient mechanical analysis. What makes this method unique is that it enables direct and interactive analysis of the model at every intermediate level. Such flexibility is of principal importance in the analysis of trabecular porous structure. The method enables physicians to zoom-in dynamically and focus on the volume of interest (VOI), thus paving the way for a large class of investigations into the mechanical behavior of bone structure. This is one of the very few methods in the field of computational bio-mechanics that applies mechanical analysis adaptively on large-scale high resolution models. The proposed computational multiscale FE method can serve as an infrastructure for a future comprehensive computerized system for diagnosis of bone structures. The aim of such a system is to assist physicians in diagnosis, prognosis, drug treatment simulation and monitoring. Such a system can provide a better understanding of the disease, and hence benefit patients by providing better and more individualized treatment and high quality healthcare. In this paper, we demonstrate the feasibility of our method on a high-resolution model of vertebra L3.

Adaptive reconstruction of freeform objects with 3D SOM neural network grids

Abstract There are several open problems that are viewed as a bottleneck in the reverse engineering process: (1) The topology is unknown; therefore, point connectivity relations are undefined. (2) The fitted surface must satisfy global and local shape preservation criteria, which are undefined explicitly. The reconstruction is based on parameterization and fitting stages. However, the above problems are influenced mainly by the parameterization. To overcome the above problems, the neural network self-organizing map (SOM) method is proposed for creating a 3D parametric grid. The main advantage of the SOM method is that it detects the orientation of the grid and the position of the sub-boundaries. Then through an adaptive process the neural network grid is converged to the sampled shape. The SOM method is applied directly on a 3D grid and avoids projection anomalies, which are common to other methods. For the surface fitting stage the random surface error correction fitting method, which is based on the SOM method, was developed and implemented.

Reconstruction of Freeform Objects with Arbitrary Topology Using Neural Networks and Subdivision Techniques

Abstract In reverse engineering, laser scanned data is reconstructed into a CAD model. This paper presents a new reconstruction approach that integrates neural networks with subdivision techniques. The neural network technique creates a triangular mesh that approximates the shape of an object and detects its topology, where the subdivision approach applies smooth surfaces onto this mesh. The advantage of this method is that the reconstruction can be applied on objects with arbitrary topology, and the final model can be integrated with traditional CAD systems using a NURBS representation that preserves continuity. The feasibility of the method is demonstrated on freeform objects with arbitrary topology.

Efficient surface reconstruction method for distributed CAD

Abstract This paper describes a new fast Reverse Engineering (RE) method for creating a 3D computerized model from an unorganized cloud of points. The proposed method is derived directly from the problems and difficulties currently associated with remote design over the Internet, such as accuracy, transmission time and representation at different levels of abstraction. With the proposed method, 3D models suitable for distributed design systems can be reconstructed in real time. The mesh reconstruction approach is based on aggregating very large scale 3D scanned data into a Hierarchical Space Decomposition Model (HSDM) , realized by the Octree data structure. Then, a Connectivity Graph (CG) is extracted and filled with facets. The HSDM can represent both the boundary surface and the interior volume of an object. Based on the proposed volumetric model, the surface reconstruction process becomes robust and stable with respect to sampling noise. Moreover, the data received from different surface/volume sampling devices can be handled naturally. The hierarchical structure of the proposed volumetric model enables data reduction , while preserving significant geometrical features and object topology. As a result, reconstruction and transmission over the network are efficient. Furthermore, the hierarchical representation provides a capability for extracting models at desired levels of detail , thus enabling designers to collaborate at any product development stage: draft or detailed design.

Cutting 3D freeform objects with genus-n into single boundary surfaces using topological graphs

In reverse engineering, surface reconstruction methods for freeform objects are based mainly on geometrical criteria, while topological factors are neglected. Current methods use a bottom-up approach based on local parameterization to reconstruct the object from points to a dense mesh and finally to smooth connected patches. This type of reconstruction, however, can have topological problems that might lead to parameterization difficulties, noisy surface behavior and texture anomalies. Such problems are particularly common with concave objects and shapes with complex topology of genus-n. To avoid the above problems, a new global topological approach for cutting objects with genus-n was developed and implemented. The proposed process is based on two main stages: (1) computing iso-curves on the mesh and extracting the topological graph, and (2) cutting the mesh according to the curve cutting guidelines that are calculated from the topological graph. The resulting mesh is a single boundary mesh and therefore can be flattened onto a disk. The time complexity of the algorithm is O(n log(n)). To demonstrate the feasibility of the cutting process, the mesh was also flattened. The flattened mesh can then be used for global parameterization, surface fitting and texture mapping. The robustness of the cutting process is demonstrated on several examples using sculptured freeform objects with genus-n.