Geometric Modelling 1Tavita Su’a

INFO410 & INFO350 S2 2015

INFORMATIONSCIENCE

Visual Computing

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Lecture Overview Definition Sample Application Areas Geometric Model Techniques

Wireframe Modelling Surface Modelling Solid Modelling

Potential Exam questions

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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

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Definition

Is this object 2D or 3D?

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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

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Sample Applications Areas

Computer GraphicsGeographic Information

SystemsAnd Spatial Databases

CAD

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Sample Applications

Medical Imaging Manufacturing Design Video Games

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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

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Geometry vs Topology

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Geometric Representation Properties

When looking at geometric object representations we should pay attentionIf 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

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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

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Wireframe ModellingAmbiguous

Complex models are difficult to interpret

or ?

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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

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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

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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

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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

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CSG – Boolean Operations

Union Intersection

Subtract/Cut

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CSG Example

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

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CSG ExampleUnion

Cut

Cut

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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

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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.

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Potential Exam Questions

1. How is a CSG model defined, and how does it differ from other solid modelling techniques?

2. What is the benefit of constructing a wireframe model?

3. Why is parametric representation preferred over implicit and explicit forms of a mathematical definition in geometric modelling?

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Resources

https://en.wikipedia.org/wiki/Geometric_modelinghttp://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.pdfhttp://graphics.cs.ucdavis.edu/~joy/GeometricModelingLectures/https://www.youtube.com/watch?v=0IgOapAtauM http://graphics.cs.ucdavis.edu/~joy/GeometricModelingLectures/

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

References