Polygonal modelling is a 3D modelling approach that utilizes edges, vertices and faces to form models. Modellers start with simple shapes and add details to build on them. They alter the shapes by adjusting the coordinates of one or more vertices. A polygonal model is called faceted as polygonal faces determine its shape.
Polygonal or polyhedral modelling fits best where visualization matters more than precision. It's extensively used by video game designers and animation studios. Assets in video games form whole worlds for gamers. Features of these assets are built using polygonal modelling.
Computers take less time to render polygonal models. So, polygonal modelling software run well on browsers. For higher precision, advanced 3D models such as NURBS are suitable. However, NURBs can't be 3D printed unless they are converted to polygons. Many industrial applications easily handle polygonal model representations.
Can you describe the basic elements of polygonal modelling?
Faces of polygons combine to form polygonal meshes. One can deform meshes. That is, one may move, twist or turn meshes to create 3D objects using deformation tools in the software. The number of polygons in a mesh makes its polycount.
Polygon density in the meshes is its resolution. Higher resolution indicates better detailing. Good 3D models contain high-resolution meshes where fine-detailing matters and low-resolution meshes where detailing isn't important.
How are polygonal meshes generated?
Polygonal mesh generation (aka meshing) is of two types: Manual and Automatic. In manual meshing, the positions of vertices are edited one by one. In automatic meshing, values are fed into the software. The software automatically constructs meshes based on the specified values. The automatic method enables the rapid creation of 3D objects in games, movies and VR.
There are many ways to produce polygonal meshes. Forming primitives from standard shapes is one way. Meshes can also be drawn by interpolating edges or points of other objects. Converting existing solid models and stretching custom-made meshes into fresh meshes are two other options.
What are free edges, manifold edges and non-manifold edges?
A free edge in a mesh is an edge that doesn't fully merge with the edge of its neighbouring element. The nodes of meshes with free edges won't be accurately connected. Such edges within the geometry will affect the overall output. Therefore, unwanted free meshes should be removed.
How would you classify the polygonal meshing process based on grid structure?
A grid structure works on the principle of Finite Element Analysis (FEA). An FEA node can be thought of as the vertex of a polygon in polygonal modelling. An FEA element shall represent an edge, a shape and a solid in three different dimensions.
- Structured meshing displays a definite pattern in the arrangement of nodes or elements. The size of each element in it is nearly the same. It enables easy access to the coordinates of these elements. It's applicable to uniform grids made of rectangles, ellipses and spheres that make regular grids.
- Unstructured meshing is arbitrary and forms irregular geometric shapes. The connectivity between elements is not uniform. So, unstructured meshes do not follow a definite pattern. It requires that the connectivity between elements is well-defined and properly stored. The axes of these elements are unaligned (non-orthogonal).
How are mesh generation algorithms written for polygonal modelling?
Let's take the Delaunay triangulation method for instance. According to it, the surface domain elements are discretized into non-overlapping triangles. The nodes are so created that the angles between them when triangulated are the least. The circumcircle drawn about each triangle cannot accommodate an additional triangle within it.
Delaunay triangulation is applied through several algorithms. Boyer-Watson algorithm is one of them. It's an incremental algorithm that adds one node at a time in a given triangulation. If the new point falls within the circumcircle of a triangle, the triangle is removed. Using the new point a fresh triangle is formed.
How does one fix the polygon count for models?
Polygon count or polycount gives a measure of visual quality. Detailing needs a high number of polygons. It gives a photorealistic effect. But high polycount impacts efficiency. It may take more time to load and render. When a model takes more time to download, we may run out of patience. Real-time rendering delays cause a video or animation to stop and start. So, a good polygonal model is a combination of high visual quality and low polycount.
The threshold number to call a polygon count high is subjective. For mobile devices, anywhere between 300 to 1500 polygons is good. Desktops can comfortably accommodate 1500 to 4000 polygons without affecting performance.
These polycount numbers vary depending on the CPU configuration and other hardware capabilities. Advanced rendering capabilities smoothly handle anywhere between 10k to 40k polygons. Global mobile markets are vying to produce CPUs that can render 100k to 1 million polygons for an immersive 3D experience.
What are some beginner pitfalls to polygonal modelling?
Irregular meshes: As beginners, we may miss triangles and create self-intersecting surfaces. Or we may leave holes on mesh surfaces or fill in with backward triangles. Irregular meshes will affect the model's overall appearance. Eyeball checks and use of mesh generation software will help us avoid mesh-related errors.
Incorrect measurements: It may distort the model's proportionality and ruin the output. It's best to train our eyes to compare images and estimate the difference in depths. Comparing our model with the reference piece on the image viewer tool will tell us the difference.
Too many subdivisions early in the modelling: It will disable us from making changes without tampering with the measurements. So, we may end up creating uneven surfaces. Instead, it's better to start with fewer polygons and add to them as we build the model.
Topology error: We may get the edge structure and mesh distributions wrong. We need to equip ourselves by learning how to use mesh tools. It's important to learn where to use triangles, quads and higher polygons. Duplicates are to be watched out for. Understanding the flow of edges is vital.
Geoffrey Colin Shepherd furthers Thomas Bradwardine's 14th-century work on non-convex polygons. He extends polygon formation to the imaginary plane. It paves the way for the construction of complex polygons. In polygonal modelling, complex polygons have circuitous boundaries. A polygon with a hole inside is one example.
- 3D-Ace. 2021. "Polygon And Spline Modelling: Know The Difference." Blog, 3D-Ace, October 21. Accessed 2023-01-12.
- Allison, Chloe. 2020. "Meshing in FEA: Structured vs Unstructured meshes." Blog, Onscale, April 01. Accessed 2023-01-12.
- Autodesk. 2016. "Polygonal Modeling." Autodesk inc., May 11. Accessed 2022-10-20.
- Autodesk. 2017. "Connectivity problems in mesh, about." Autodesk, November 07. Accessed 2023-01-19.
- Autodesk. 2020. "About Creating 3D Meshes." Autodesk Inc., March 30. Accessed 2023-01-12.
- Baumgart, Bruce G. 1972. "Winged Edge Polyhedron Representation." Standord Artificial Intelligence Project Memo AIM-179, Stanford University, October. Accessed 2023-01-13.
- Bourke, Paul. 1997. "Surface (polygonal) Simplification." July. Accessed 2023-01-17.
- Cairnhill Metrology. 2023. "Polygonal Model." Cairnhill. Accessed 2023-01-12.
- Crowder, Ashley. 2020. "Do Polygon Counts Really Matter For 3D Web & Mobile AR?" Blog, Vntana, August 5. Updated 2021-07-16. Accessed 2023-01-13.
- Dan. 2021. "Learning 3D - Part I: Simple geometry." Tutorial, Sketchfab Help Center, Sketchfab, June 17. Accessed 2022-10-20.
- Demeuse, Jason. 2013. "Introduction To Polygonal Modeling And Three.js." Smashing Magazine, September 17. Accessed 2022-10-21.
- Denham, Thomas. 2019. "What is UV Mapping & Unwrapping?" Concept Art Empire. February 05 Accessed 2023-01-12.
- Dr J. 2023. "NURBS vs Polygons: Do you know the differences?" 3dbiology. Accessed 2023-01-12.
- Fowlery, Deborah R., Hans Meinhardtz, and Przemyslaw Prusinkiewiczy. 1992. "Modeling seashells." From Proceedings of SIGGRAPH ’92 (Chicago, Illinois, July 26–31, 1992), In Computer Graphics, 26, 2, (July 1992), ACM SIGGRAPH, New York, pp. 379–387, ACM SIGGRAPH, July. Accessed 2023-01-13.
- Galetzka, Michael, and Patrick Glauner. 2017. "A Simple and Correct Even-Odd Algorithm for the Point-in-Polygon Problem for Complex Polygons." 12th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2017), vol. 1: GRAPP, SCITEPRESS – Science and Technology Publications, Lda., pp. 175-178. doi: 10.5220/0006040801750178. Accessed 2023-01-17.
- Hager, Izabela, Anna Golonka, and Roman Putanowicz. 2016. "3D printing of buildings and building components as the future of sustainable construction?" International Conference on Ecology and new Building materials and products, Procedia Engineering 151, ICEBMP 2016. doi: 10.1016/j.proeng.2016.07.357. Accessed 2023-01-19.
- Hiester, H.R., Matthew D. Piggott, P.E. Farrell, and P. A. Allison. 2014. "Assessment of spurious mixing in adaptive mesh simulations of the two-dimensional lock-exchange." Ocean Modelling, 73(2014), pp. 30–44. Elsevier, January. doi: 10.1016/j.ocemod.2013.10.003. Accessed 2023-01-13.
- Isenberg, Tobias. 2004. "Capturing the Essence of Shape of Polygonal Meshes." Dissertation, Faculty of Computer Science the Otto von Guericke University Magdeburg, April 16. Accessed 2023-01-13.
- Kronrod, Boris, and Craig Gotsman. 2000. "Efficient Coding of Non-Triangular Mesh Connectivity." IEEE Comput. Soc the Eighth Pacific Conference on Computer Graphics and Applications - Hong Kong, China (3-5 Oct. 2000), Computer Science Department Technion- Israel Institute of Technology. doi: 10.1109/PCCGA.2000.883946. Accessed 2023-01-19.
- Live2D Inc. 2021. "Automatic Mesh generator." Live2D Inc, May 13. Accessed 2023-01-12.
- MAPSystems. 2023. "Low And High Polygon 3D Modeling Techniques." Mapsystems. Accessed 2023-01-12.
- Malkevitch, Joe. 2021. "In Praise of Collaboration." Feature Column, Math Voices, American Mathematical Society, March 31. Accessed 2023-01-13.
- Manufactur3D. 2021. "How to Avoid Common Pitfalls in 3D Modelling." Manufactur3D Magazine, December 12. Accessed 2022-10-21.
- Martínez, Jonàs, Núria Pla, and Marc Vigo. 2013. "Skeletal representations of orthogonal shapes." Graphical Models, 75(4), pp. 189–207, Department of Languages and Computer Systems. Polytechnic University of Catalonia, Spain, April 08. doi: 10.1016/j.gmod.2013.03.005. Accessed 2023-01-18.
- Materialise nv. 2018. "What's the Maximum Polygon Count for My 3D File?" Materialise nv. Accessed 2023-01-13.
- Miky, Yehia, Ahmed Alshouny, and Abdullah Kamel. 2022. "A combined contour lines iteration algorithm and Delaunay triangulation for terrain modeling enhancement." Informa UK Limited, May 26. doi: 10.1080/10095020.2022.2070553. Accessed 2023-01-13.
- Mobsby, Niall. 2020. "Non-Manifold Edges: Facts & Fixes." All3DP, February 01. Accessed 2023-01-19.
- Nakahashi, K, T Fujita, and Yasushi Ito. 2006. "From one-month CFD to one-day CFD - Efforts for reducing time and cost of CFD." Yasushi Ito, New Developments in Computational Fluid Dynamics, pp. 68–80. January. doi: 10.1007/3-540-31261-7_7. Accessed 2023-01-13.
- Nash, Charlie, Yaroslav Ganin, S. M. Ali Eslami, and Peter W. Battaglia. 2020. "PolyGen: An Autoregressive Generative Model of 3D Meshes." arxiv, February 23. Accessed 2023-01-12.
- Neperud, Bryan, John Lowther, and Ching-Kuang Shene. 2007. "Visualizing and animating the winged-edge data structure." Computers & Graphics, Elsevier B.V., vol. 31, no. 6, pp. 877-886. doi: 10.1016/j.cag.2007.08.009. Accessed 2023-01-16.
- Nordsletten, D., and N.P. Smith. 2007. "Triangulation of p-Order Parametric Surfaces." Journal of Scientific Computing, Springer Science+Business Media, LLC, vol. 34, no. 3, pp. 308-335, November 08. doi: 10.1007/s10915-007-9167-3. Accessed 2023-01-18.
- Norman, Jeremy M. 2022. "The First 3D Rendered Movie." History of Information, December 20. Accessed 2023-01-13.
- Polasek, Tomas, David Hrusa, Bedrich Benes, and Martin Cadik. 2021. "ICTree: Automatic Perceptual Metrics for Tree Models." ACM Trans. Graph., Vol. 40, No. 6, Article 230, ACM Trans, December. doi: 10.1145/3478513.3480519. Accessed 2023-01-13.
- Prescient Technologies. 2022. "What is Mesh and what are the types of Meshing." Prescient Technologies. Accessed 2023-01-12.
- Prescient Technologies. 2022a. "Mesh Generation Algorithms." Prescient Technologies. Accessed 2023-01-13.
- ProGlobalBusinessSolutions. 2022. "The Fundamentals of Polygon 3D Modeling technique." ProGlobalBusinessSolutions, October 6. Updated Accessed 2022-10-21.
- Rana, Devi. 2020. "Mesh Generation & CFD Steps." Cadsys25. Accessed 2023-01-12.
- Simscale. 2021. "What is a Mesh?" Simscale, September 02. Accessed 2023-01-13.
- Skill-Lync. 2022. "How to Resolve A Free Edge in ANSA?" Blog, Skill-Lync, September 26. Accessed 2023-01-19.
- Skotny, Łukasz. 2019. "What are Nodes and Elements in Finite Element Analysis?" Blog, FEA Fundamentals, Enterfea, January 24. Accessed 2023-01-19.
- Slick, Justin. 2020. "59 What Is 3D Modeling?" Lifewire is part of the Dotdash Meredith publishing family., Lifewire, September 24. Accessed 2022-10-12.
- Slick, Justin. 2021. "Common Pitfalls of Beginning Modelers." Lifewire, May 22. Accessed 2022-10-21.
- Spatial Team. 2019. "The Main Benefits and Disadvantages of Polygonal Modeling." Blog, Dassault Systèmes, Spatial Corp, December 17. Accessed 2023-01-12.
- Stepp, Emerson. 2022. "Polycount? Understanding model efficiency." Blog, linkedin, March 02. Accessed 2023-01-13.
- Unity3d. 2017. "Modeling Characters For Optimal Performance." 5.5-001G 2017-03-29, Unity Technologies. Accessed 2023-01-13.
- Varotsis, Alkaios Bournias. 2021. "Meshing in FEA, CFD & Manufacturing." Blog, nTopology, Inc, June 08. Accessed 2023-01-12.
- Vatresia, Arie, Ferzha Putra Utama, and Nirwana Nirwana. 2022. "Spatial zonation system with Voronoi diagram and Delaunay triangulation to improve management education." Vol. 17, No. 1, February 2023, pp. 93~101, Journal of Education and Learning (EduLearn), September 23. doi: 10.11591/edulearn.v17i1.20548. Accessed 2023-01-13.
- Vendelskis, Sarunas. 2022. "What is the difference between High Poly and Low Poly models in 3D modeling?" Blog, Modelry, September 01. Accessed 2023-01-13.
- VisCircle. 2019. "Guide for beginners: What is the Painter`s Algorithm?" VisCircle GmbH. March 19. Updated 2021-06-22. Accessed 2023-01-13.
- Wacom. 2022. "Three common 3D modeling mistakes and how to avoid them." Wacom. Accessed 2022-10-21.
- caddesignhelp. 2022. "What is the difference between low-poly and high-poly 3D models?" CADdesignhelp, March 08. Accessed 2023-01-13.
- Isenberg, Tobias, Bert Freudenberg, Nick Halper, Stefan Schlechtweg, and Thomas Strothotte. 2003. "A Developer’s Guide to Silhouette Algorithms for Polygonal Models." IEEE Computer Society, August. Accessed 2023-01-13.
- Russo, Mario. 2006. "Polygonal modeling : basic and advanced techniques." Wordware Pub., Plano, Texas.
- Daniele, Todd. 2012. "Poly-Modeling with 3ds Max." Taylor & Francis, New York.
- Kerich, Chris. 2019. "Polygonal Modeling: The Aestheticization of Identity." Digital Games Research Association. Accessed 2023-01-13.
- Computer Graphics Development
- 3D Modelling
- NURBS Modelling
- 3D Rendering
- Computer-Aided Design
- Video Game Development
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