Solid modeling
This presentation is the property of its rightful owner.
Sponsored Links
1 / 26

Solid Modeling PowerPoint PPT Presentation


  • 73 Views
  • Uploaded on
  • Presentation posted in: General

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.

Download Presentation

Solid Modeling

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


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.

cgvr.korea.ac.kr


Voxel acquisition

Voxel Acquisition

  • Scanning Devices

    • MRI

    • CAT

  • Simulation

    • FEM

cgvr.korea.ac.kr


Voxel storage

Voxel Storage

  • O(n3) Storage for n x n x n Grid

    • 1 billion voxels for 1000 x 1000 x 1000

cgvr.korea.ac.kr


Voxel boolean operations

Voxel Boolean Operations

  • Compare Objects Voxel by Voxel

cgvr.korea.ac.kr


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

cgvr.korea.ac.kr


Voxel display2

Voxel Display

  • Ray Casting

    • Integrate density along rays through pixels

cgvr.korea.ac.kr


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

cgvr.korea.ac.kr


Quadtree boolean operations

Quadtree Boolean Operations

cgvr.korea.ac.kr


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

cgvr.korea.ac.kr


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

cgvr.korea.ac.kr


Csg acquisition

CSG Acquisition

  • Interactive Modeling Programs

    • CAD/CAM

cgvr.korea.ac.kr


Csg display analysis

CSG Display & Analysis

  • Ray Casting

Union

Circle

Box

cgvr.korea.ac.kr


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


  • Login