- 92 Views
- Uploaded on
- Presentation posted in: General

Solid Modeling

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 - - - - - - - - - - - - - - - - - - - - - - - - - -

Solid Modeling

고려대학교 그래픽스 연구실

cgvr.korea.ac.kr

- Represent Solid Interiors of Objects
- Surface may not be described explicitly

cgvr.korea.ac.kr

- Some Acquisition Methods Generate Solids
- Example: CAT scan

cgvr.korea.ac.kr

- Some Applications Require Solids
- Example: CAD/CAM

cgvr.korea.ac.kr

- Some Algorithms Require Solids
- Example: ray tracing with refraction

cgvr.korea.ac.kr

- Voxels
- Quadtrees & Octrees
- Binary Space Partitions
- Constructive Solid Geometry

cgvr.korea.ac.kr

- 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

- Scanning Devices
- MRI
- CAT

- Simulation
- FEM

cgvr.korea.ac.kr

- O(n3) Storage for n x n x n Grid
- 1 billion voxels for 1000 x 1000 x 1000

cgvr.korea.ac.kr

- Compare Objects Voxel by Voxel

cgvr.korea.ac.kr

- Isosurface Rendering
- Render surfaces bounding volumetric regions of constant value (e.g., density)

cgvr.korea.ac.kr

- Slicing
- Draw 2D image resulting from intersecting voxels with a plane

cgvr.korea.ac.kr

- Ray Casting
- Integrate density along rays through pixels

cgvr.korea.ac.kr

- 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

- Voxels
- Quadtrees & Octrees
- Binary Space Partitions
- Constructive Solid Geometry

cgvr.korea.ac.kr

- Refine Resolution of Voxels Hierarchically
- More concise and efficient for non-uniform objects

Quadtree

Uniform Voxel

cgvr.korea.ac.kr

cgvr.korea.ac.kr

- Voxels
- Quadtrees & Octrees
- Binary Space Partitions
- Constructive Solid Geometry

cgvr.korea.ac.kr

- 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

- Single Geometric Operation
- Partition a convex region by a hyperplane

- Single Combinatorial Operation
- Two child nodes added as leaf nodes

cgvr.korea.ac.kr

- Visibility Ordering
- Determine on which side of plane the viewer lies
- Near-subtree -> polygons on split -> far-subtree

- Determine on which side of plane the viewer lies

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

- Voxels
- Quadtrees & Octrees
- Binary Space Partitions
- Constructive Solid Geometry

cgvr.korea.ac.kr

- Represent Solid Object as Hierarchy of Boolean Operations
- Union
- Intersection
- Difference

cgvr.korea.ac.kr

- Interactive Modeling Programs
- CAD/CAM

cgvr.korea.ac.kr

- Ray Casting

Union

Circle

Box

cgvr.korea.ac.kr

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