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Variable Voxel Computing Method Variable Voxel Computing Method Innovative Approaches to Reduce the Computing Load in Voxel-based Solid Modeling and New Representation Methods Sezgi Yalçınkaya1, Burak Delikanlı2 1,2Istanbul Technical University 1,2{yalcinkayas18|burak.delikanli}@itu.edu.tr The concept of ``voxel'' refers to a volumetric element or volumetric pixel and corresponds to the smallest piece that can be computed in solid and complex model analysis. The voxel-based solid modeling commonly used by geometry-based CAD (Computer-Aided Design) applications. Whilst other geometry-based modeling methods, it uses pixels as the smallest unit instead of dots or vectors. However, the size of the data contained in the smallest unit causes problems such as computing load and representation inaccuracies. This study fundamentally aims to find a fast and effective method for voxel-based solid modeling. While doing that it presents a new visualization algorithm. During the research, the transformation of a geometric model into voxels, then the reproduction of these voxels, and finally, the representation method were practiced and compared. In this process, three complex models were developed and compared by their complexity, their voxelization time, and the amount of time that spend during the formation. As a result, the study proposes new representation methods for voxel-based solid modeling. Keywords: Voxel-based Modeling, Solid Models, Representation Methods, Computing Load INTRODUCTION Aided Design (CAD), Computer-Aided Manufactur- Nowadays, computers are not just machines that col- ing (CAM), and Computer-Aided Engineering (CAE) lect, distribute, and visualize data but they are in applications existing and developing in the industry. a completely different position. Meanwhile, it has Accurate visual representation of geometric models been used as a production planning, control, and dis- through computers has become a problem for math- tribution center in fields such as industry and busi- ematicians, designers, manufacturers, and engineers ness, as modeling and representation tools in the as well as software developers. fields of architecture and art, and as a production Geometric modeling represents a collection of and simulation tool in the fields of engineering. Dif- methods that can be used in computer-based appli- ferent model representations are used in Computer- cations to synthesize, representation, and analysis of D1.T4.S2. MAKING THROUGH CODE –BUILT BY DATA AND THE ARCHITECTURAL ILLUSTRATION - Volume 1 - eCAADe 38 | 663 shape and other geometric information (Agarwal and plications, findings, outcomes, and evaluations were Waggenspack 1992). Modeling systems that we used discussed. in CAD, CAM, or CAE applications are usually geo- metrical model-based. There are three different cat- SOLID MODELS AND VOXEL-BASED MOD- egories of geometric modeling methods: wireframe ELING or line, surface, and solid modeling (Al-Ahmari et al. 2016). These modeling methods have advantages Solid Models A three-dimensional model is a computational repre- and disadvantages compared with each other, and sentation of any object that is intended to be trans- these criteria determine which method will be used ferred, by referring volumetric data in x, y, and z coor- in the representation. While solid modeling is the dinates. Modeling is a way of production of a model most comprehensive modeling method in represent- by using some modeling software packages (e.g Pro- ing a shape, it has disadvantages compared to wire- E, CATIA) or three-dimensional scanning tools (CAT, frame and surface models due to excess of the com- MRI, etc.) to produce a row model in the three- puting load. However, solid modeling includes vol- dimensional space environment. Constructive Solid ume information as well as edges and surfaces to rep- Geometry, Boundary Representation, Feature-based resent a shape. Solid models can be considered the modeling can be listed as examples of modeling best way to represent a shape, but the multiplicity of types. Representation of the solid models usually operations limits their use. represented by the surfaced based modeling soft- Solid modeling is widely used in medical model- ware.“The surface-based modeling method has the ing as well as in the fields of engineering and design. advantage of being more efficient interns of capac- The number of information contained in the repre- ity and (sometimes) productivity on the computation sentation of the models in these areas increases the because an object can be defined easier by the sur- preference of solid models. The increasing complex- face than volume elements.” (Toennics and Tronnier, ity of the assembly process and the number of parts 2010). Therefore, this modeling method is fast and and components increases the need for efficient solid practical and is considered sufficient for many mod- modeling methods in production and design. Also, els. However, Surface models are lack of volumetric production-oriented applications in this area are of knowledge and cannot be easily prepared for volu- great significance. This study aims to find solutions metric analysis and imaging. For this reason, it car- to reduce the computing load by analyzing the repre- ries great importance to express the differentiation of sentation methods of solid modeling and proposing volumetric density differences, and these occupancy innovative approaches. In addition, the frame of solid vacancy rates in complex models are transferred well, modeling is examined and the voxel-based model- easily, and quickly. There are different schemes to ing method is explained. Then, analyzes are made represent three-dimensional models. These are Sur- on the computing algorithms created with the new face models, Lattice models - networks and Polygon approaches proposed. For this approach three dif- (directional models), decomposition-based (Octrees, ferent models were selected and developed in a vir- BSP), and voxel-based representation schemes. tual field then they were compared and discussed ac- cording to their responses to those algorithms. Their reactions to transformation into voxel models were shown in the charts. Their transformation speed and their reaction to execute their model conversion to another volumetric model were examined in detail. Finally, in the conclusion section, possible future ap- 664 | eCAADe 38 - D1.T4.S2. MAKING THROUGH CODE –BUILT BY DATA AND THE ARCHITECTURAL ILLUSTRATION - Volume 1 Figure 1 of voxel models can also be applied.“It is expected A Modular Volume: that voxel-based modeling will be used extensively The Bemis Cubical in future in areas like CAD/CAM/CAE, medical imag- Modular Concept ing, scientific simulations and visualizations, anima- (Russel, A.L., 2012). tions, and non-engineering modeling, virtual reality systems, and teleoperations and controls, etc. Some manufacturing-related problems can be better ana- lyzed using voxel-based modeling than conventional surface-based systems. ”(Patil and Ravi, 2005) Re- lated problems can be analyzed better than conven- Voxel-Based Modeling tional surface-based systems by using voxel-based The voxel is the name given to the three-dimensional modeling. The focus of this study on this system, elements that are the smallest part of an object in the which also offers a new visualization algorithm, is to third dimension. When modeling volumetrically, ev- create a new volumetric modeling method for en- ery regular or irregular element in any object can be gineering / non-engineering components. A voxel- considered as an element of the voxel collection. The based model representation scheme was developed simplest and most commonly used notation is cubic together for this purpose. voxels which are aligned with the coordinate axes at a uniform grid. Volume visualization in complex ge- REPRESENTATION METHODS ometries and the analysis of large data sets is a very The preparation of the representation of a model is rapidly evolving field for computer graphics.“Volume very important in terms of finding the correct expres- visualization systems are used to create high-quality sion for that model. Volume graphics and volume displays from scalar and vector datasets defined on models have developed considerably over the past multidimensional grids, usually for the purpose of decade thanks to technological diversity. Represen- gaining insight into a scientific problem.”(Patil and tation methods which were prepared by making cer- Ravi, 2005). The term voxel also used by volumet- tain extraction operations from solid models, analyz- ric modeling. However, the Voxels used in CAD im- ing the volumes by breaking them into pieces over plementation are slightly different, as they are usu- their occupancy and gaps or three-dimensional mod- ally based on the volumetric occupancy and space els created by drawing certain boundaries of two- state of the voxel only in the given object. It is not dimensional shapes help the models to represent true to say that this is new for voxel-based model- and transfer the true meaning. ing methods, and we have been using this model- Figure 2 ing method for a long time under different head- Volume ings. We can see modular representation theories in Representation some architectural representations of Albert Farwell Methods Bemis in the 1930s (Figure 1). Later on, these repre- sentation theories were not frequently used as repre- sentation methods due to the lack of large memory and processing capacity required for computers to use voxel models with sufficient resolution. But now computers, along
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