Visual Computing Geometric Modelling 1 INFO410 & INFO350 S2 2015 Tavita Su’a INFORMATION SCIENCE

Lecture Overview Definition Sample Application Areas Geometric Model Techniques Wireframe Modelling Surface Modelling Solid Modelling Potential Exam questions

Definition is a branch of applied mathematics and computational geometry that studies methods and algorithms for the mathematical description of shapes It is concerned with the computer compatible and mathematical representation of the geometry of an object Requires visual representation and mathematical representation

Definition Is this object 2D or 3D?

Why is Geometric Modelling needed? Design Analysis – simulate physical behaviour on the computer Finite element analysis for stress, vibration, thermal and optimization Less expensive than building a physical model Can be used directly in manufacturing, generating tool path for Computer Numerical Control (CNC) Can be used for presentations and marketing purposes

Geographic Information Systems Sample Applications Areas Geographic Information Systems And Spatial Databases Computer Graphics CAD

Sample Applications Medical Imaging Manufacturing Design Video Games

Geometric Object Information necessary for defining geometric object can be divided into two categories: Geometric information – definition of the coordinates and dimensions of an object and its entities Topological Information – the connectivity and associativity of the object entities; it determines the relational information between object entities

Geometry vs Topology

Geometric Representation Properties When looking at geometric object representations we should pay attention If it is: Complete – if it allows a point to be classified as being inside, outside or on the object boundary Valid – it is possible to build a physical model on it e.g. it does not contain free edges or faces Unambiguous – it can only be interpreted only in one way

Wireframe Modelling Developed in 1960s and referred to as a “stick figure” or “edge representation” Model consists entirely of points, lines, arcs, circles, conics and curves A wireframe object is not recorded as a solid Simplest and thus the fastest modelling technique in terms of speed and processing power

Wireframe Modelling Ambiguous or ? Complex models are difficult to interpret

Surface Modelling Developed in the end of the 1960s as the extension of wireframe modelling. Defines not only the edges, but also its surfaces Objects are defined by their bounding faces Surface model represents the skin of an object, these skins have no thickness or material type

Surface Modelling Can be used for both open and closed surfaces Renders model for better visualization Can be used to design and analyse complex surfaces (free-form) Surface properties such as roughness and colour can be assigned

Solid Modelling Introduced in the 1970s A complete and unambiguous representation of a precisely enclosed and filled volume Common Approaches: Boundary Representation (B-Rep) Constructive Solid Geometry (CSG) Parametric Modelling Spatial decomposition representations Cell decomposition Voxel representation

Constructive Solid Geometry Defines a model in terms of combining basic and generated solid shapes Objects represented as a combination of simpler solid objects (primitives) Uses Boolean operations to construct a model

CSG – Boolean Operations Union Intersection Subtract/Cut

CSG Example To Create this object: Identify which primitives are required Identify required Boolean operations Record operations in a CSG tree

Union CSG Example Cut Cut

CSG Continued Data structure implies the geometric shape Eg. Object is not defined by a set of edges or faces but by the instruction: union primitive1 with primitive2 Procedural data is stored in a CSG tree Simple and easy to manage Can grow to be cumbersome for complex shapes Non-uniqueness of solid models databases can store different instructions to reconstruct the same object

Parametric Modelling Concept Parametric is a term used to describe a dimension’s ability to change the shape of model geometry if the dimension value is modified. Feature-based is a term used to describe the various components of a model. For example, a part can consists of various types of features such as holes, grooves, fillets, and chamfers. Parametric modelers are featured-based, parametric, solid modeling design programs: SolidWorks, Pro-Engineer, Unigraphics (CSG and parametric) etc.

Potential Exam Questions How is a CSG model defined, and how does it differ from other solid modelling techniques? What is the benefit of constructing a wireframe model? Why is parametric representation preferred over implicit and explicit forms of a mathematical definition in geometric modelling?

Resources https://en.wikipedia.org/wiki/Geometric_modeling http://www.engr.uvic.ca/~mech410/old/2_Lecture_Notes/5_Geometric_Modeling.pdfhttp://www.engr.uvic.ca/~mech410/old/2_Lecture_Notes/5_Geometric_Modeling.pdf http://graphics.cs.ucdavis.edu/~joy/GeometricModelingLectures/ https://www.youtube.com/watch?v=0IgOapAtauM

References http://www.epension.am/__vfs/__system_images/backgrounds/1.jpg http://www.ewh.ieee.org/soc/es/Aug1996/030/cd/en495w03/subtopic/cad1.htm http://www2.imm.dtu.dk/projects/MeshMed/gfx/heart_zhang.png https://upload.wikimedia.org/wikipedia/commons/7/77/Polygon_face.jpg https://suburbanexperiment.files.wordpress.com/2011/11/box.jpg http://enggcharts.org/category/COMP%20GRAPHIC.jpg http://www1.eafit.edu.co/cadcamcae/warped_Marching_Cubes.png http://designer.mech.yzu.edu.tw/articlesystem/article/compressedfile/(2010-11-25)%20Solid%20modeling%20techniques%20and%20boundary%20representation.files/image008.gif https://upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Necker_cube.svg/2000px-Necker_cube.svg.png http://www.esru.strath.ac.uk/Consultancy/Ex6_besancon/theatre_page/ESP_wire_frame.gif https://upload.wikimedia.org/wikipedia/commons/4/4a/Gaussian_curvature.PNG http://i.ytimg.com/vi/n2iSagbexsg/maxresdefault.jpg