Modeling

1
Modeling

• Aaron Bloomfield
• CS 445 Introduction to Graphics
• Fall 2006
• (Slide set originally by Greg Humphreys)

2
Outline

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

3
Model Construction

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

4
Interactive Modeling Tools

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

Cosmoworlds, SGI
5
Interactive Modeling Tools

• Example Mechanical CAD

HB Figure 9.9
6
Model Construction

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

7
Scanning tools

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

Stanford Graphics Laboratory
Lorensen
8
Scanning tools

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

Color
Depth
9
Laser Range Scanning

• Example 70 scans
• Volumetric reconstruction

Stanford Graphics Laboratory
10
Scanning tools

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

11
Scanning tools

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

12
Computer Vision

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

13
Computer Vision

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

14
Computer Vision

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

Debevec96
15
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

16
Outline

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

17
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
18
Example Seashells

• Sweep generating curve around helico-spiral axis

Helico-spiral definition
Fowler et al. Figure 1
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Example Seashells

• Connect adjacent points to form polygonal mesh

Fowler et al. Figure 6
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Example Seashells

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

Fowler et al. Figure 1
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Example Seashells

• Generate different shells by varying parameters

Different helico-spirals
Fowler et al. Figure 2
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Example Seashells

• Generate different shells by varying parameters

Different generating curves
Fowler et al. Figure 3
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Example Seashells
Generate many interesting shells with a simple
procedural model!
Fowler et al. Figures 4,5,7
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Outline

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

25
Fractals

• Defining property
• Self-similar with infinite resolution

HB Figure 10.100
Mandelbrot Set
26
Fractals

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

HB Figure 10.80
27
Fractal Generation

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

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Deterministic Fractal Generation

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

HB Figure 10.68
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Deterministic Fractal Generation

• Apply generator repeatedly

Koch Curve
HB Figure 10.69
30
Deterministic Fractal Generation

• Useful for creating interesting shapes!

Mandelbrot Figure X
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Deterministic Fractal Generation

• Useful for creating interesting shapes!

Mandelbrot Figure 46
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Deterministic Fractal Generation

• Useful for creating interesting shapes!

HB Figures 75 109
33
Fractal Generation

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

34
Statistical Fractal Generation

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

Random Midpoint Displacement
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Statistical Fractal Generation

• Example terrain

HB Figure 10.83b
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Statistical Fractal Generation

• Useful for creating mountains

HB Figure 10.83a
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Statistical Fractal Generation

• Useful for creating 3D plants

HB Figure 10.82
38
Statistical Fractal Generation

• Useful for creating 3D plants

HB Figure 10.79
39
Outline

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

40
Solid Modeling

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

SUNY Stony Brook
Visible Human (National Library of Medicine)
41
Motivation 1

• Some acquisition methods generate solids
• Example CAT scan

Stanford University
42
Motivation 2

• Some applications require solids
• Example CAD/CAM

Intergraph Corporation
43
Solid Modeling Representations

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

Lorensen
44
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
45
Voxel Acquisition

• Scanning devices
• MRI
• CAT
• Simulation
• FEM

Stanford University
SUNY Stony Brook
46
Voxel Storage

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

47
Voxel Boolean Operations

• Compare objects voxel by voxel
• Trivial

?

?

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Voxel Display

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

Isosurface Visualization Princeton University
49
Voxel Display

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

Visible Human (National Library of Medicine)
50
Voxel Display

• Ray casting
• Integrate density along rays through pixels

Engine Block Stanford University
51
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

52
Quadtrees Octrees

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

Uniform Voxels
Quadtree
FvDFH Figure 12.21
53
Quadtree Boolean Operations
A
B
A ? B
A ? B
FvDFH Figure 12.24
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Quadtree Display

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

Finding neighbor cell requires traversal of
hierarchy (O(1))
FvDFH Figure 12.25
55
Outline

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

56
Constructive Solid Geometry (CSG)

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

FvDFH Figure 12.27
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CSG Acquisition

• Interactive modeling programs
• CAD/CAM

HB Figure 9.9
58
CSG Boolean Operations

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

FvDFH Figure 12.27
59
CSG Display Analysis

• Ray casting

Union
Box
Circle
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Outline

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

61
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

62
3D Studio Max

• http//en.wikipedia.org/wiki/Image3dsmax8Screensh
  ot.jpg

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Maya

• http//en.wikipedia.org/wiki/ImageAutodesk_Maya_8
  .0_win32.png

64
Blender

• http//en.wikipedia.org/wiki/ImageBlender_node_sc
  reen_242a.jpg

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Comparison of renderers

• http//wiki.cgsociety.org/index.php/Comparison_of_
  3d_tools
• And a better formatted version

66
Elephants 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)
• Thats 19,800 frames
• Took a 2.1 TFLOPS supercomputer cluster 125 days
  to render
• Used Bowie States 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)