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

Interactive Modeling Tools

Example: Mechanical CAD
H&B Figure 9.9

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

Scanning tools

Acquire geometry of objects with active sensors

CAT/MRI


Laser range scanner
Magnetic sensor

Robotic arm
 etc.
Xp (Xc,Yc)

Laser Range Scanning

Example: 70 scans

Volumetric reconstruction
Stanford Graphics Laboratory

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.

Computer Vision

Infer 3D geometry from images

Stereo


Motion
Constraints
 etc.
Debevec96

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

Connect adjacent points to form polygonal mesh
Fowler et al. Figure 6

Example: Seashells

Model is parameterized:


Helico-spiral: z
0
, l z
, r
0
, l r
, N q
, Dq
Generating curve: shape, N c
, l c
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

Defining property:

Self-similar with infinite resolution
Mandelbrot Set H&B Figure 10.100

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

Deterministic Fractal Generation

Apply generator repeatedly
Koch Curve
H&B Figure 10.69

Deterministic Fractal Generation

Useful for creating interesting shapes!
Mandelbrot Figure X

Deterministic Fractal Generation

Useful for creating interesting shapes!
Mandelbrot Figure 46

Deterministic Fractal Generation

Useful for creating interesting shapes!
H&B Figures 75 & 109

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

Statistical Fractal Generation

Example: terrain
H&B Figure 10.83b

Statistical Fractal Generation

Useful for creating mountains
H&B Figure 10.83a

Statistical Fractal Generation

Useful for creating 3D plants
H&B Figure 10.82

Statistical Fractal Generation

Useful for creating 3D plants
H&B Figure 10.79

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)

Motivation 1

Some acquisition methods generate solids

Example: CAT scan
Stanford University

Motivation 2

Some applications require solids

Example: CAD/CAM
Intergraph Corporation

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 Acquisition

Scanning devices

MRI

CAT

Simulation

FEM
Stanford University
SUNY Stony Brook

Voxel Storage

O(n 3 ) storage for nxnxn grid

1 billion voxels for 1000x1000x1000

Voxel Boolean Operations

Compare objects voxel by voxel

Trivial

=

=

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)

Voxel Display

Ray casting

Integrate density along rays through pixels
Engine Block
Stanford University

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 Boolean Operations
A B
A

B A

B
FvDFH Figure 12.24

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 Acquisition

Interactive modeling programs

CAD/CAM
H&B Figure 9.9

CSG Boolean Operations

Create a new CSG node joining subtrees

Union


Intersection
Difference
FvDFH Figure 12.27

CSG Display & Analysis

Ray casting
Union
Circle Box

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:3dsmax8Screen shot.jpg

Maya
 http://en.wikipedia.org/wiki/Image:Autodesk_Maya
_8.0_win32.png

Blender
 http://en.wikipedia.org/wiki/Image:Blender_node_s creen_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)