2 geometric modelling

8/2/2019 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

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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

2 geometric modelling

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