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Computer Aided Engineering
Applications
1A.Geometric Modeling1.1 Geometric modelling methods
Engi 6928 - Fall 2014
1.1 Geometric modelling methods
1.2 Data representation
1.3 Modeling functions
1.4 Structure of a CAD system
1.Geometric modeling1.Geometric modeling
• Geometric modeling attempts to replace a
physical model with a mathematical description
capturing its geometry.
• This mathematical description should assist in
different tasks in the design process. Ex:
manipulation, deforming, adding removing
material, similar to a physical model.
Clay model [9] CAD model [10]
1.1 Geometric modelling methods1.1 Geometric modelling methods
• A Geometric modeling system determines how the product geometry is represented. Evolved over four geometric modelling systems :
1. Wireframe modeling
– Keeps only Vertices and Edges– Keeps only Vertices and Edges
– Representation is ambiguous
– No surface or mass information
extractable
– Not ideal for CAM CAE tasksAmbiguous representations of
the same wire frame [1]
1.1 Geometric modelling methods1.1 Geometric modelling methods
2. Surface modeling
• Carries information of surfaces
• Additionally carries surface connectivity information
• Good for surface machining, surface shading
• Hard to form fully closed (water tight) models.• Hard to form fully closed (water tight) models.
• Allows surface normal verification, curvature analysis
Surfaces and boundaries [4] Surface normal analysis [5]
1.1 Geometric modelling methods1.1 Geometric modelling methods
3. Solid modeling
• Only geometries of closed volumes are kept
• Solid information can be derived (e.g. mass,
centre of gravity, etc.)
• Carries complete info for CAM CAE tasks. Ex: Finite
element meshing, NC machiningelement meshing, NC machining
• Complicated data structures in modern systems
Solid model [4]
1.1 Geometric modelling methods1.1 Geometric modelling methods
4. Non Manifold modeling
• Manifold modelling creates closed volumes.
• This is only required by the final solid design.
• The design process greatly benefits from allowing
Non manifold models (hybrid solid, surfaces, and
wireframes). wireframes).
• Non manifold modeling captures the evolution of
a design.
Non manifold geometries [1]
1.2 Data representation1.2 Data representation
There are different ways the software manages
the geometric data of solids.
1. CSG – Constructive Solid Geometry
– Positioned Primitives and Boolean operations are
used to generate a solidused to generate a solid
Boolean operations [1]
Primitives
1.2 Data representation 1.2 Data representation -- CSGCSG
• Allows easy parametric edits
in the CGS tree
• The tree structure becomes
complex due to limited
operations
Editing the diameter of the primitive [1]
Long tree structures [2]
1.2 Data representation 1.2 Data representation -- CSGCSG
• No information of boundary surfaces and
edges. Therefore simple operations like a
chamfer is quite involved.
• Simple extrusions require multiple
decompositions in to primitive shapesdecompositions in to primitive shapes
The edge corresponding to the
chamfer is not available in the
CGS tree [1]
Extrusion and decomposition [2]
1.2 Data representation 1.2 Data representation –– BB--RepRep
2. B-Rep – Boundary representation
– Carries geometric information. i.e . Points, Curves,
Surfaces
– Carries topological (connectivity) information i.e.
Vertices, Edges, Faces, ShellsVertices, Edges, Faces, Shells
B-Rep data structure [2] CSG vs. B-Rep [2]
1.2 Data representation 1.2 Data representation –– BB--RepRep
• Curve and surface geometries can be non
planar. (quadratic, circular etc.)
• Curve and surface geometries not required for
the planar case.
Example B-Rep data structure table for a polygon [1]
1.2 Data representation 1.2 Data representation –– BB--RepRep
• To handle Inner boundaries and outer
boundaries of faces a bridge edge is used.
• Inner boundaries and outer boundaries of
solids are kept as separate shells.
Inner boundary
A hollow cube
Outer boundaryInner boundary
Bridge edge to handle inner boundaries [1]
1.2 Data representation1.2 Data representation--ExerciseExercise
• B-rep for a simple cube
B-Rep data structure [2] Edges and vertices of a cube [2]
1.2 Data representation 1.2 Data representation -- OctreeOctree
3. Decomposition model
[6]
The Stanford bunny [8]
[6][6]
쀀!
1.3 Modelling functions1.3 Modelling functions
• The data structure is at the heart of the CAD
system.
• The user simply calls on modeling functions
(extrude, sweep etc..) which modifies this data
structure.structure.
Geometric modelling
kernel
Layered modeling kernel [2]
1.3 Modelling functions1.3 Modelling functions
• Sweeping [1]
• Skinning [1]
1.3 Modelling functions1.3 Modelling functions
• Edge rounding, Vertex rounding [1]
• Lifting [1] – Lift a portion of a full face
1.3 Modelling functions 1.3 Modelling functions
• Boundary modeling
– Add, delete or modify lower entities of a solid.
(Vertices, edges, surfaces)
Vertex modification [1]
Edge replacement [1]Surface replacement [2]
1.3 Modelling functions 1.3 Modelling functions
• Parametric modeling
• The geometry of the models are linked to constraints
and parameters.
• Allows generating many derivative designs.
• Change of parameters rebuilds the model by solving
the geometric constraints and equations for the new the geometric constraints and equations for the new
parameters.
•Parameters
•Constraints
A B-Rep data structure linked to parameters [2]
1.3 Modelling functions 1.3 Modelling functions
• Feature based modeling
– CGS like editable history tree, composed of
elementary shape units (features <- not primitives).
– The designer can capture the desired
manufacturing process sequence in the tree. Ex:
chamfer, drill a hole, cut a slot, etc.chamfer, drill a hole, cut a slot, etc.
– The design is limited to the available features.
CAD feature tree
1.4 CAD system structure1.4 CAD system structure
• Modern CAD system structure [2]
• GUIs
•Modelling devices (keyboard ,mouse)
•Proprietary files
•Standard product data exchange files
•OpenGL
•DirectX•CAE apps
•Design apps
1.4 CAD system structure1.4 CAD system structure
• Geometric modeling kernel
The working engine of a CAD system. Performs the
essential mathematics and data representation for
different operations.
• Current software are mainly based on two kernels:• Current software are mainly based on two kernels:
– ACIS - AutoCAD
– Parasolids –Solidworks, Abaqus, Ansys, NX
1.4 CAD system structure1.4 CAD system structure
• Databases (output files)- Are the files created by a
CAD system to store the data.
• The output file structure greatly resembles the
data structure adopted by the modelling kernels.
• Standard product data exchange files are used to • Standard product data exchange files are used to
allow the CAD data to be easily transferred
between applications.
– STL (Stereo Lithography)
– IGES (Initial Graphics Exchange specification)
– STEP (ISO 10303)
STL filesSTL files
• STL files – decomposes the solid to a set of
polygon surfaces. Composing of triangular faces.
• Used mainly for stereo lithography 3D printing
• Used to generate meshes from point cloud data.
• A detailed comparison of other different types will
be made during the next part of the course.
Point clouds, STL surfaces, and Smooth surfaces [7]
ExerciseExercise
• Visualize the resulting STL file of a cube
STL file of a cubeThe cube
ReferencesReferences
[1] K. Lee, Principles of CAD/CAM/CAE systems. Addison-Wesley, 1999, p. 582.
[2] I. Stroud and H. Nagy, Solid Modelling and CAD Systems: How to Survive a CAD
System. Springer Science & Business Media, 2011, p. 711.
[3] I. Zeid, Mastering CAD/CAM. McGraw-Hill Higher Education, 2005, p. 962.
[4] X. Xu, Integrating Advanced Computer-aided Design, Manufacturing, and
Numerical Control: Principles and Implementations. IGI Global Snippet, 2009, p.
397.
[5] http://www.studiorola.com/tutorials/miscellaneous/basic-tips-for-preparing-files-[5] http://www.studiorola.com/tutorials/miscellaneous/basic-tips-for-preparing-files-
for-rapid-prototyping/
[6] A. Hornung, K. M. Wurm, M. Bennewitz, C. Stachniss, and W. Burgard, “OctoMap:
an efficient probabilistic 3D mapping framework based on octrees,” Autonomous
Robots, vol. 34, no. 3, pp. 189-206, Feb. 2013.
[7] http://www.cs.mun.ca/~omeruvia/philosophy/philosophy.html
[8] http://http.developer.nvidia.com/GPUGems2/gpugems2_chapter37.html
[9] http://www.machine-language.com/
[10] http://www.creativecrash.com/3d-model/bicycle-helmet