Parametric Design using Digital Project

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Parametric Design using Digital Project

• 05 Solid Modeling

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Solid

• Adjective
• Not soft or yielding
• Not hollow
• Unadulterated or unmixed
• Of strong and secure construction
• Noun
• Something solid
• A three dimensional geometric figure of object
• A substance that resists moderate stress and
  deformation, unlike a liquid or a gas

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Some history

• Early 70s
• ROMULUS, Parasolid, ACIS
• the Compac system U of Berlin, U of Ruhr
• Bruns Euclid system France
• Englis Euclid system Switzerland
• TIPS-1, GeoMap Japan
• Shapes
• Synthavision
• GLIDE, PADL

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Solid model

• Create only complete representation of solid
  objects
• Unambiguous representations representation of
  solid

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Mathematical properties

• Rigidity
• Finiteness
• Solidity
• Closure under Boolean operation
• Finite describability
• Boundary determinism

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Types of solid models

• Decomposition models
• Constructive models
• Boundary models
• Non manifold models

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Decomposition model

• Represent a point set as a collection of simple
  objects from a fixed collection of primitive
  object types, combined with a single gluing
  operation

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Types of decomposition model

• Exhaustive enumeration
• Voxel
• Cellular decomposition
• FEM (Finite Element Meshes) for FEA
• Space subdivision
• Octree representation

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FEM
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Quadtree
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Octree
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Constructive model

• Represent a point set as combination of primitive
  point sets. Each of the primitives is represented
  as an instance of primitive solid type with
  set-theoretic operation (union, intersection, set
  difference)

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Types of constructive models

• Half-space model
• CSG model

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Half-space model
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CSG model

• Primitives

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CSG model

• CSG tree

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CSG model

• CSG tree

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CSG model

• CSG tree

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CSG model
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CSG model
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CSG model
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CSG model
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Boundary model

• Represent a point set in terms of its boundary.
• Boundary of solid surfaces
• Boundary of surface faces
• Boundary of face curve

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Boundary model
edge
face
vertex
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B-Rep graph
Topology
Geometry
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Topology / Geometry
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Tessellation/triangulation
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Nonmanifold model
B
A
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CAD systems
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CAD systems