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Solid Modeling. 고려대학교 그래픽스 연구실. Solid Modeling. Represent Solid Interiors of Objects Surface may not be described explicitly. Motivation. Some Acquisition Methods Generate Solids Example: CAT scan. Motivation. Some Applications Require Solids Example: CAD/CAM. Motivation.

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Solid modeling

Solid Modeling

고려대학교 그래픽스 연구실

cgvr.korea.ac.kr


Solid modeling1
Solid Modeling

  • Represent Solid Interiors of Objects

    • Surface may not be described explicitly

cgvr.korea.ac.kr


Motivation
Motivation

  • Some Acquisition Methods Generate Solids

    • Example: CAT scan

cgvr.korea.ac.kr


Motivation1
Motivation

  • Some Applications Require Solids

    • Example: CAD/CAM

cgvr.korea.ac.kr


Motivation2
Motivation

  • Some Algorithms Require Solids

    • Example: ray tracing with refraction

cgvr.korea.ac.kr


Solid modeling representation
Solid Modeling Representation

  • Voxels

  • Quadtrees & Octrees

  • Binary Space Partitions

  • Constructive Solid Geometry

cgvr.korea.ac.kr


Voxels
Voxels

  • Partition Space into Uniform Grid

    • Grid cells are called a voxels (like pixels)

  • Store Properties of Solid Object with Each Voxel

    • Occupancy

    • Color

    • Density

    • Temperature

    • Etc.

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Voxel acquisition
Voxel Acquisition

  • Scanning Devices

    • MRI

    • CAT

  • Simulation

    • FEM

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Voxel storage
Voxel Storage

  • O(n3) Storage for n x n x n Grid

    • 1 billion voxels for 1000 x 1000 x 1000

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Voxel boolean operations
Voxel Boolean Operations

  • Compare Objects Voxel by Voxel

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Voxel display
Voxel Display

  • Isosurface Rendering

    • Render surfaces bounding volumetric regions of constant value (e.g., density)

cgvr.korea.ac.kr


Voxel display1
Voxel Display

  • Slicing

    • Draw 2D image resulting from intersecting voxels with a plane

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Voxel display2
Voxel Display

  • Ray Casting

    • Integrate density along rays through pixels

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Voxels1
Voxels

  • Advantages

    • Simple, intuitive, unambiguous

    • Same complexity for all objects

    • Natural acquisition for some applications

    • Trivial boolean operations

  • Disadvantages

    • Approximate

    • Large storage requirements

    • Expensive display

cgvr.korea.ac.kr


Solid modeling representation1
Solid Modeling Representation

  • Voxels

  • Quadtrees & Octrees

  • Binary Space Partitions

  • Constructive Solid Geometry

cgvr.korea.ac.kr


Quadtrees octrees
Quadtrees & Octrees

  • Refine Resolution of Voxels Hierarchically

    • More concise and efficient for non-uniform objects

Quadtree

Uniform Voxel

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Quadtree boolean operations
Quadtree Boolean Operations

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Solid modeling representation2
Solid Modeling Representation

  • Voxels

  • Quadtrees & Octrees

  • Binary Space Partitions

  • Constructive Solid Geometry

cgvr.korea.ac.kr


Binary space partitions bsps
Binary Space Partitions (BSPs)

  • Recursive Partition of Space by Planes

    • Mark leaf cells as inside or outside object

1

a

b

1

g

g

a

a

6

c

2

f

f

3

d

3

5

e

e

7

e

4

d

c

4

d

c

b

b

f

5

2

6

7

Object

Binary Spatial Partition

BSP Tree

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Bsp fundamentals
BSP Fundamentals

  • Single Geometric Operation

    • Partition a convex region by a hyperplane

  • Single Combinatorial Operation

    • Two child nodes added as leaf nodes

cgvr.korea.ac.kr


Bsp display
BSP Display

  • Visibility Ordering

    • Determine on which side of plane the viewer lies

      • Near-subtree -> polygons on split -> far-subtree

Partitioning Tree

A

o2

A

B

o4

B

C

o1

C

o1

o2

o3

o4

o3

3rd

4th

1st

2nd

Viewer

Viewer

cgvr.korea.ac.kr


Solid modeling representation3
Solid Modeling Representation

  • Voxels

  • Quadtrees & Octrees

  • Binary Space Partitions

  • Constructive Solid Geometry

cgvr.korea.ac.kr


Constructive solid geometry csg
Constructive Solid Geometry (CSG)

  • Represent Solid Object as Hierarchy of Boolean Operations

    • Union

    • Intersection

    • Difference

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Csg acquisition
CSG Acquisition

  • Interactive Modeling Programs

    • CAD/CAM

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Csg display analysis
CSG Display & Analysis

  • Ray Casting

Union

Circle

Box

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Summary
Summary

Voxels

Octree

BSP

CSG

Accurate

No

No

Some

Some

Concise

No

No

No

Yes

Affine Invariant

No

No

Yes

Yes

Easy Acquisition

Some

Some

No

Some

Guaranteed Validity

Yes

Yes

Yes

No

Efficient Boolean Operations

Yes

Yes

Yes

Yes

Efficient Display

No

No

Yes

No

cgvr.korea.ac.kr


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