Geometric Modelling 1 Tavita Su’a INFO410 & INFO350 S2 2015 INFORMATION SCIENCE Visual Computing.
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Transcript of Geometric Modelling 1 Tavita Su’a INFO410 & INFO350 S2 2015 INFORMATION SCIENCE Visual Computing.
Geometric Modelling 1Tavita Su’a
INFO410 & INFO350 S2 2015
INFORMATIONSCIENCE
Visual Computing
INFO410 S2 2015 GEOMETRIC MODELLING 1 (Tavita Su’a) SLIDE 2INFORMATION SCIENCE
Lecture Overview Definition Sample Application Areas Geometric Model Techniques
Wireframe Modelling Surface Modelling Solid Modelling
Potential Exam questions
INFO410 S2 2015 GEOMETRIC MODELLING 1 (Tavita Su’a) SLIDE 3INFORMATION SCIENCE
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
INFO410 S2 2015 GEOMETRIC MODELLING 1 (Tavita Su’a) SLIDE 4INFORMATION SCIENCE
Definition
Is this object 2D or 3D?
INFO410 S2 2015 GEOMETRIC MODELLING 1 (Tavita Su’a) SLIDE 5INFORMATION SCIENCE
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
INFO410 S2 2015 GEOMETRIC MODELLING 1 (Tavita Su’a) SLIDE 6INFORMATION SCIENCE
Sample Applications Areas
Computer GraphicsGeographic Information
SystemsAnd Spatial Databases
CAD
INFO410 S2 2015 GEOMETRIC MODELLING 1 (Tavita Su’a) SLIDE 7INFORMATION SCIENCE
Sample Applications
Medical Imaging Manufacturing Design Video Games
INFO410 S2 2015 GEOMETRIC MODELLING 1 (Tavita Su’a) SLIDE 8INFORMATION SCIENCE
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
INFO410 S2 2015 GEOMETRIC MODELLING 1 (Tavita Su’a) SLIDE 9INFORMATION SCIENCE
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
INFO410 S2 2015 GEOMETRIC MODELLING 1 (Tavita Su’a) SLIDE 11INFORMATION SCIENCE
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
INFO410 S2 2015 GEOMETRIC MODELLING 1 (Tavita Su’a) SLIDE 12INFORMATION SCIENCE
Wireframe ModellingAmbiguous
Complex models are difficult to interpret
or ?
INFO410 S2 2015 GEOMETRIC MODELLING 1 (Tavita Su’a) SLIDE 13INFORMATION SCIENCE
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
INFO410 S2 2015 GEOMETRIC MODELLING 1 (Tavita Su’a) SLIDE 14INFORMATION SCIENCE
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
INFO410 S2 2015 GEOMETRIC MODELLING 1 (Tavita Su’a) SLIDE 15INFORMATION SCIENCE
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
INFO410 S2 2015 GEOMETRIC MODELLING 1 (Tavita Su’a) SLIDE 16INFORMATION SCIENCE
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
INFO410 S2 2015 GEOMETRIC MODELLING 1 (Tavita Su’a) SLIDE 17INFORMATION SCIENCE
CSG – Boolean Operations
Union Intersection
Subtract/Cut
INFO410 S2 2015 GEOMETRIC MODELLING 1 (Tavita Su’a) SLIDE 18INFORMATION SCIENCE
CSG Example
To Create this object: Identify which primitives are required Identify required Boolean operations Record operations in a CSG tree
INFO410 S2 2015 GEOMETRIC MODELLING 1 (Tavita Su’a) SLIDE 19INFORMATION SCIENCE
CSG ExampleUnion
Cut
Cut
INFO410 S2 2015 GEOMETRIC MODELLING 1 (Tavita Su’a) SLIDE 20INFORMATION SCIENCE
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
INFO410 S2 2015 GEOMETRIC MODELLING 1 (Tavita Su’a) SLIDE 21INFORMATION SCIENCE
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.
INFO410 S2 2015 GEOMETRIC MODELLING 1 (Tavita Su’a) SLIDE 22INFORMATION SCIENCE
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?
INFO410 S2 2015 GEOMETRIC MODELLING 1 (Tavita Su’a) SLIDE 23INFORMATION SCIENCE
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/
INFO410 S2 2015 GEOMETRIC MODELLING 1 (Tavita Su’a) SLIDE 24INFORMATION SCIENCE
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