SOLID MODEL REPRESENTATIONS How does the computer store solid models? MAE 455– Computer-Aided Drafting and Design Nice picture from web used without permission.
SOLID MODEL REPRESENTATIONS
How does the computer store solid models?
MAE 455– Computer-Aided Drafting and Design
Nice picture from web used without permission.
SOLID GEOMETRY CAN BE STORED AS:
1. BOUNDARY REPRESENTATION (B-REP)
2. CONSTRUCTIVE SOLID GEOMETRY (CSG)
3. DECOMPOSITION REPRESENTATION
Boundary Representation
Faces
Edges
Vertices
Edge Loops
More Detailed Version of B-Rep
Includes point coordinates
Includes surface equation
Solid Body
Shell
Face
Edge
Vertice
Edge Loop
Includes curve equation
Constructive Solid Geometry
Block(1) Block(2)
U
Unite(3)
Cylinder(4)
–Subtract(5)
(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 2 ways:
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Decomposition Representations
■ Voxel Representation
■ Octree Representation
■ Cellular Decomposition
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Voxel RepresentationIn 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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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 Boolean Operations Are Implemented1. 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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Nonmanifold Solids■ Modeling errors may occur from inadvertently trying to create
nonmanifold 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 nonmanifold models:
Figure from K. Lee, “Principles of CAD/CAM/CAE Systems,” Addison-Wesley