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

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

3. 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

4. Definition
Is this object 2D or 3D?

5. 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

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

7. Sample Applications
Medical Imaging
Manufacturing Design
Video Games

8. 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

9. Geometry vs Topology

10. 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

11. 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

12. Wireframe Modelling Ambiguous or ?
Complex models are difficult to interpret

13. 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

14. 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

15. 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

16. 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

17. CSG – Boolean Operations
Union
Intersection
Subtract/Cut

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

19. Union
CSG Example
Cut
Cut

20. 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

21. 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.

22. 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?

23. Resources https://en.wikipedia.org/wiki/Geometric_modeling

24. References