2 Geometric Modelling
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Transcript of 2 Geometric Modelling
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1.2 Geometric modelling
How do you represent thegeometry of 3D objects?
Dr. Benny Raphael
Assistant Professor, Departmentof Building, NUS
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Outline
Motivation
Mathematical representations of simplesurfaces and solids
Representation of complex solids
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Influencing factors
Computers have become faster and cheaper
Building are being constructed on more difficultsites and in more complex situations
Aim for paperless integrated design process
Fabrication capabilities (CAM) have increased
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Frank Gehry Experience MusicProject, Seattle
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Bahai Temple - Delhi
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How can we model these buildings
geometric modeling provides tools for
spatial representation of engineeringobjects
the objective is to create valid,computational representations of surfacesand solids
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Approaches to geometric modelling
Points, lines, planes
Surfaces
Solids
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Criteria for EvaluatingRepresentations
How accurate is the representation
What shapes can be represented
Whether the representation is unique
Is the representation compact and efficient
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Mathematical representation ofSurfaces
A surface is represented by an equation
involving two parameters
A cylindrical surface of Height H, Radius Rx = R cos(t)
y = R sin(t)
z = t1
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Mathematical representation ofsolids
A solid is represented by an equation
involving three parameters
A solid cylinder is represented byx = t2 cos(t)
y = t2 sin(t)
z = t1
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Representing solids
Primitive instancing
Mesh
Sweep
Boundary Decomposition models
Constructive solid geometry
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Solid Primitives
represent objects using parameterized
solids, e.g. block
cylinder
cone
sphere
wedge torus
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Primitive Instancing
Represent complex objects using
parameterized primitives
Example:Doors, windows, walls, roofs
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Mesh
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Sweep
Extrusion (translation sweep)
Rotation
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Boundary methodsA 3D object is represented by lists of
vertices, edges and faces
A tetrahedron consists of
4 faces
Each face has 3 edges
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Decomposition Quadtrees
Octrees
11
1 1 1 1
1 1 1 1
1 1
0 0
0 0
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Constructive Solid GeometrySolids are represented by a tree of simple
primitives combined using boolean setoperators
Union
Subtraction
Intersection
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Solid element operation
-(subtraction)
=
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Solid element operations
Intersection
=
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SummaryA number of techniques for modelling 3D
object geometry were covered. You mightfind some of these techniques in your 3DCAD software.
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ReferenceFundamentals of computer aided
engineering, B.Raphael and I.F.C. Smith,Chapter 11