Solid Model Representations - West Virginia...

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SOLID MODEL REPRESENTATIONS How does the computer store solid models? MAE 455– Computer-Aided Drafting and Design Nice picture from web used without permission.

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Page 1: Solid Model Representations - West Virginia Universitycommunity.wvu.edu/~bpbettig/MAE455/Lecture_11_solid_representations.pdfMAE 455 Computer-Aided Design and Drafting 7 Voxel Representation

SOLID MODEL REPRESENTATIONS

How does the computer store solid models?

MAE 455– Computer-Aided Drafting and Design

Nice picture from web used without permission.

Page 2: Solid Model Representations - West Virginia Universitycommunity.wvu.edu/~bpbettig/MAE455/Lecture_11_solid_representations.pdfMAE 455 Computer-Aided Design and Drafting 7 Voxel Representation

SOLID GEOMETRY CAN BE STORED AS:

1. BOUNDARY REPRESENTATION (B-REP)

2. CONSTRUCTIVE SOLID GEOMETRY (CSG)

3. DECOMPOSITION REPRESENTATION

Page 3: Solid Model Representations - West Virginia Universitycommunity.wvu.edu/~bpbettig/MAE455/Lecture_11_solid_representations.pdfMAE 455 Computer-Aided Design and Drafting 7 Voxel Representation

Boundary Representation

Faces

Edges

Vertices

Edge Loops

Page 4: Solid Model Representations - West Virginia Universitycommunity.wvu.edu/~bpbettig/MAE455/Lecture_11_solid_representations.pdfMAE 455 Computer-Aided Design and Drafting 7 Voxel Representation

More Detailed Version of B-Rep

Includes point coordinates

Includes surface equation

Solid Body

Shell

Face

Edge

Vertice

Edge Loop

Includes curve equation

Page 5: Solid Model Representations - West Virginia Universitycommunity.wvu.edu/~bpbettig/MAE455/Lecture_11_solid_representations.pdfMAE 455 Computer-Aided Design and Drafting 7 Voxel Representation

Constructive Solid Geometry

Block(1) Block(2)

U

Unite(3)

Cylinder(4)

–Subtract(5)

Page 6: Solid Model Representations - West Virginia Universitycommunity.wvu.edu/~bpbettig/MAE455/Lecture_11_solid_representations.pdfMAE 455 Computer-Aided Design and Drafting 7 Voxel Representation

(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

Page 10: Solid Model Representations - West Virginia Universitycommunity.wvu.edu/~bpbettig/MAE455/Lecture_11_solid_representations.pdfMAE 455 Computer-Aided Design and Drafting 7 Voxel Representation

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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