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### Modeling

Aaron Bloomfield

CS 445: Introduction to Graphics

Fall 2006

(Slide set originally by Greg Humphreys)

Outline

- Acquisition
- Seashells
- Fractals
- Volumes
- Constructive Solid Geometry
- Modeling Programs

Model Construction

- Interactive modeling tools
- CAD programs
- Subdivision surface editors :)
- Scanning tools
- CAT, MRI, laser, magnetic, robotic arm, etc.
- Computer vision
- Stereo, motion, etc.

Interactive Modeling Tools

- User constructs objects with drawing program
- Menu commands, direct manipulation, etc.
- CSG, parametric surfaces, quadrics, etc.

Cosmoworlds, SGI

Model Construction

- Interactive modeling tools
- CAD programs
- Subdivision surface editors :)
- Scanning tools
- Laser, magnetic, robotic arm, etc.
- Computer vision
- Stereo, motion, etc.

Scanning tools

- Acquire geometry of objects with active sensors
- CAT/MRI
- Laser range scanner
- Magnetic sensor
- Robotic arm
- etc.

Lorensen

Stanford Graphics Laboratory

(Xc,Yc)

Scanning tools- Acquire geometry of objects with active sensors
- CAT/MRI
- Laser range scanner
- Magnetic sensor
- Robotic arm
- etc.

Color

Depth

Scanning tools

- Acquire geometry of objects with active sensors
- CAT/MRI
- Laser range scanner
- Magnetic sensor
- Robotic arm
- etc.

Scanning tools

- Acquire geometry of objects with active sensors
- CAT/MRI
- Laser range scanner
- Magnetic sensor
- Robotic arm
- etc.

Computer Vision

- Infer 3D geometry from images
- Stereo
- Motion
- Constraints
- etc.

Computer Vision

- Infer 3D geometry from images
- Stereo
- Motion
- Constraints
- etc.

Procedural Modeling

- Goal:
- Describe 3D models algorithmically
- Best for models resulting from ...
- Repeating processes
- Self-similar processes
- Random processes
- Advantages:
- Automatic generation
- Concise representation
- Parameterized classes of models

Outline

- Acquisition
- Seashells
- Fractals
- Volumes
- Constructive Solid Geometry
- Modeling Programs

Example: Seashells

- Create 3D polygonal surface models of seashells

“Modeling Seashells,”

Deborah Fowler, Hans Meinhardt,

and Przemyslaw Prusinkiewicz,

Computer Graphics (SIGGRAPH 92),

Chicago, Illinois, July, 1992, p 379-387.

Fowler et al. Figure 7

Example: Seashells

- Sweep generating curve around helico-spiral axis

Helico-spiral definition:

Fowler et al. Figure 1

Example: Seashells

- Model is parameterized:
- Helico-spiral: z0, lz, r0, lr, Nq, Dq
- Generating curve: shape, Nc, lc

Fowler et al. Figure 1

Example: Seashells

- Generate different shells by varying parameters

Different helico-spirals

Fowler et al. Figure 2

Example: Seashells

- Generate different shells by varying parameters

Different generating curves

Fowler et al. Figure 3

Example: Seashells

Generate many interesting shells

with a simple procedural model!

Fowler et al. Figures 4,5,7

Outline

- Acquisition
- Seashells
- Fractals
- Volumes
- Constructive Solid Geometry
- Modeling Programs

Fractals

- Useful for describing natural 3D phenomenon
- Terrain
- Plants
- Clouds
- Water
- Feathers
- Fur
- etc.

H&B Figure 10.80

Fractal Generation

- Deterministically self-similar fractals
- Parts are scaled copies of original
- Statistically self-similar fractals
- Parts have same statistical properties as original

Deterministic Fractal Generation

- General procedure:
- Initiator: start with a shape
- Generator: replace subparts with scaled copy of original

H&B Figure 10.68

Fractal Generation

- Deterministically self-similar fractals
- Parts are scaled copies of original
- Statistically self-similar fractals
- Parts have same statistical properties as original

Statistical Fractal Generation

- General procedure:
- Initiator: start with a shape
- Generator: replace subparts with a self-similar random pattern

Random Midpoint Displacement

Outline

- Acquisition
- Seashells
- Fractals
- Volumes
- Constructive Solid Geometry
- Modeling Programs

Solid Modeling

- Represent solid interiors of objects
- Surface may not be described explicitly

SUNY Stony Brook

Visible Human

(National Library of Medicine)

Solid Modeling Representations

- What makes a good solid representation?
- Accurate
- Concise
- Affine invariant
- Easy acquisition
- Guaranteed validity
- Efficient boolean operations
- Efficient display

Lorensen

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.

FvDFH Figure 12.20

Voxel Storage

- O(n3) storage for nxnxn grid
- 1 billion voxels for 1000x1000x1000

Voxel Display

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

Isosurface Visualization

Princeton University

Voxel Display

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

Visible Human

(National Library of Medicine)

Voxels

- Advantages
- Simple, intuitive, unambiguous
- Same complexity for all objects
- Natural acquisition for some applications
- Trivial boolean operations
- Disadvantages
- Approximate
- Not affine invariant
- Large storage requirements
- Expensive display

Quadtrees & Octrees

- Refine resolution of voxels hierarchically
- More concise and efficient for non-uniform objects

Uniform Voxels

Quadtree

FvDFH Figure 12.21

Quadtree Display

- Extend voxel methods
- Slicing
- Isosurface extraction
- Ray casting

Finding neighbor cell requires traversal of hierarchy (O(1))

FvDFH Figure 12.25

Outline

- Acquisition
- Seashells
- Fractals
- Volumes
- Constructive Solid Geometry
- Modeling Programs

Constructive Solid Geometry (CSG)

- Represent solid object as hierarchy of boolean operations
- Union
- Intersection
- Difference

FvDFH Figure 12.27

CSG Boolean Operations

- Create a new CSG node joining subtrees
- Union
- Intersection
- Difference

FvDFH Figure 12.27

Outline

- Acquisition
- Seashells
- Fractals
- Volumes
- Constructive Solid Geometry
- Modeling Programs

Popular rendering programs

- 3D Studio Max ($3.5k)
- Made by Autodesk (makers of CAD programs)
- Runs only on Windows (Win32 and Win64)
- Movies made w/Max: Incredibles, X-Men, Star Wars III, etc.
- Maya ($2k or $6k)
- Made by Alias
- Originally by SGI
- Bought by Autodesk in Oct 2006
- Runs on Windows, Linux
- Blender (free!)
- Others are less well known and less used

3D Studio Max

- http://en.wikipedia.org/wiki/Image:3dsmax8Screenshot.jpg

Maya

- http://en.wikipedia.org/wiki/Image:Autodesk_Maya_8.0_win32.png

Blender

- http://en.wikipedia.org/wiki/Image:Blender_node_screen_242a.jpg

Comparison of renderers

- http://wiki.cgsociety.org/index.php/Comparison_of_3d_tools
- And a better formatted version…

Elephant’s Dream

- Downloadable at http://orange.blender.org/
- An open movie
- Meaning you can download the Blender files that were used to make it
- Made using only open-source software
- Blender, GIMP, CinePaint, Inkscape, etc.
- Length is 11 minutes (including 90 sec of credits)
- That’s 19,800 frames
- Took a 2.1 TFLOPS supercomputer cluster 125 days to render
- Used Bowie State’s XSeed supercomputer
- Took 9 minutes and 2.8 Gb per frame
- An “average” high-end PC has only a “few” GFLOPS (not TFLOPS!)
- So if you had a 3 Ghz computer w/4 Gb of RAM, it would take over 200 years to render!
- Or 3 days per frame
- Assuming a 3 Gz computer can do 3 TFLOPS (a generous assumption)

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