lecture 11 solid representations
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MAE 455 Computer-Aided Design and Drafting
Solid Model
Representations
How does the computer store
solid models?
MAE 455 Computer-Aided Design and Drafting 2
Types of Solid Modeling
Representations
• Boundary Representation (B-Rep)
• Construction History Representation
• Decomposition Representations
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Simplified B-Rep
Includes point coordinates
Includes surface equation
Solid Body
Shell
Face
Edge
Vertice
Edge Loop
Includes curve equation
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Construction History
• In a construction history, the sequence of modeling operations and their dependencies are recorded. UUUU –
Cylinder(4)
Block(1) Block(2)
Unite(3)
Subtract(5)
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Construction History
(a) Flat list
Solid Model
• Block(1)
• Block(2)
• Unite(3)
• Cylinder(4)
• Subtract(5)
(b) Hierarchical list
Solid Model
• Subtract(5)
• Cylinder(4)
• Unite(3)
• Block(2)
• Block(1)
• This information can be displayed in two ways:
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Decomposition
Representations
• Voxel Representation
• Octree Representation
• Cellular Decomposition
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Voxel Representation
In this representation a cubic volume is
divided into a three dimensional grid of
smaller cubes, known as voxels (volume
elements).
From K. Lee, “Principles of CAD/CAM/CAE Systems,” Addison-Wesley, 1999
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Octree Representation
• Similar to the voxel
representation, except
that the structure is
hierarchical, rather than
using an array.
• A larger cube is divided
into 8 smaller cubes only
if the larger cube contains
points both inside and
outside the solid being
approximated.
Figure from K. Lee, “Principles of CAD/CAM/CAE Systems,” Addison-Wesley, 1999
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MAE 455 Computer-Aided Design and Drafting 9
Cell Representation
• In this representation, the cells can have
any shape (don’t have to be cubes).
• Finite Elements are one example.
From K. Lee, “Principles of CAD/CAM/CAE Systems,” Addison-Wesley, 1999
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How Solid Boolean Operators Are Implemented
1. Split edges at intersections.
2. Determine whether each edge is inside, outside, or on the boundary of the other solid.
3. Recombine edges according to the type of the Boolean operation.Union A U B: keep “on A, out B” and “out A, on B”Subtraction A – B: keep “on A, out B” and “in A, on B”Intersection A ∩ B: keep “in A, on B” and “on A, in B”
Figure from K. Lee, “Principles of CAD/CAM/CAE Systems,” Addison-Wesley
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MAE 455 Computer-Aided Design and Drafting 11
Non-manifold Solids
• Many modeling errors occur from inadvertently trying to
create non-manifold solids in a modeling operation.
• In a manifold solid, every point on a surface is locally
two-dimensional. (A bug traveling on the surface can always move
forward, backward, left, and right.)
• Here are some problematic non-manifold models:
Figure from K. Lee, “Principles of CAD/CAM/CAE Systems,” Addison-Wesley