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Geometry Synthesis. Mathias Ricken Rice Undergraduate Scholar Program November 11, 2003. Overview. Computer-Generated Geometry Uses Creation Previous Work Landscapes Mazes Problems Geometry Synthesis Parametric synthesis Synthesis by analogy. Computer-Generated Geometry. 1.

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geometry synthesis

Geometry Synthesis

Mathias Ricken

Rice Undergraduate Scholar Program

November 11, 2003

overview
Overview
  • Computer-Generated Geometry
    • Uses
    • Creation
  • Previous Work
    • Landscapes
    • Mazes
    • Problems
  • Geometry Synthesis
    • Parametric synthesis
    • Synthesis by analogy
creating geometry
Creating Geometry
  • Hand-Crafted
    • Computer games

1 Man-Year for 40 hours of game play 2

  • Automation
    • Lower costs
    • Better training
    • Higher replay value
landscapes6
Landscapes
  • Height Map
    • Matrix of numbers
      • e.g. one per square foot
    • Numbers

 Elevation

  • Filters
    • Smoothen or roughen landscape
    • Add rivers and lakes
mazes8
Mazes
  • Recursive Backtracking
    • Regular grid
    • 2-Dimensional
  • Creates perfect mazes
    • All cells connected in exactly one way
    • No loops

algorithm explained in extra slides

problems
Problems
  • Landscapes
    • Large scale, but low detail
    • Only natural, not artificial
  • Mazes
    • 2-dimensional
    • Small scale
    • Not reminiscent of human architecture
proposed project
Proposed Project
  • Create meaningful geometry
    • Similar to human architecture
    • 3-dimensional
    • High detail
  • Algorithms
    • Parametric synthesis
    • Synthesis by analogy
parametric synthesis
Parametric Synthesis
  • Create a network of rooms and corridors
    • Generalization of DungeonMaker algorithm 4
  • Tunnelers, agents (“robots”)
    • Randomly
  • Probabilities controlled by parameters
  • change direction
  • create rooms
  • create branches
parametric synthesis13
Parametric Synthesis
  • Generalize
    • 3D, not 2D
    • Not grid-based

4

  • Examples of Parameters
    • Frequencies
    • Dimensions
    • Angles
    • Alignment
synthesis by analogy
Synthesis by Analogy
  • Automatically enhance bare geometry created by parametric synthesis
    • Use design templates
    • Add colors, patterns, details

5

texture synthesis by analogy
Texture Synthesis by Analogy
  • Given small texture, create arbitrarily large similar texture
    • Few visual flaws
  • Similar to a jigsaw puzzle
    • Look at the surrounding pieces (neighborhood) and pick best match
    • Does not have to be perfect fit
    • Pieces can be used more than once or not at all
texture synthesis by analogy16
Texture Synthesis by Analogy

Template

Synthesis Target

  • Randomly pick first color
  • Move left to right, top to bottom
  • Pick neighborhood that matches best
texture synthesis by analogy17
Texture Synthesis by Analogy

Template

Synthesis Target

  • Randomly pick first color
  • Move left to right, top to bottom
  • Pick neighborhood that matches best
texture synthesis by analogy18
Texture Synthesis by Analogy
  • Large features require large neighborhood

Source

5 x 5

7 x 7

9 x 9

6

geometry synthesis by analogy
Geometry Synthesis by Analogy
  • Geometry can be represented by matrix
    • Distance to next surface
    • Implicit representation
    • Positiveinside
    • Negative  outside
    • Zero  surface
  • Convert geometry into matrix
  • Apply synthesis by analogy to it

7

geometry synthesis by analogy20
Geometry Synthesis by Analogy
  • Previous research in two dimensions

8

  • Generalize from 2D to 3D
  • Improve speed
editor
Editor
  • Build application
    • Graphical user interface
    • 3D display
    • Support all synthesis steps

9

notes
Notes

[1] Lord of the Rings. New Line Cinema.

Beasts. Comp 460, Rice University.

Midfield Terminal Complex. Southwest Florida International Airport.

Dynamic Flight Simulator. Naval Warfare Center, Westminster, Penn. United States Navy.

[2] Rollings, A., and Morris, D. Game Architecture and Design.

[3] Terragen. Planetside Software. http://www.planetside.co.uk/terragen/

[4] DungeonMaker. Dr. P. Henningsen. http://dungeonmaker.sourceforge.net/

notes23
Notes

[5] Illustration. Hive Assault. Comp 460, Rice University.

[6] Wei, Li-Yi. Texture Synthesis by Fixed Neighborhood Searching. Ph.D. thesis.

[7] Implicit Modeling Editor. Scott Schaefer, Rice University.

[8] Actual synthesis result. Geometry Synthesis by Analogy. Mathias Ricken, Rice University (unpublished).

[9] Illustration.

extra slides
Extra Slides
  • Recursive Backtracking
recursive backtracking
Recursive Backtracking

Unvisited neighbor to the north. Tear down wall!

  • Square grid
  • Start in one cell
  • Pick a neighboring cell that has never been reached before and tear down the wall to it
    • Remember previous cell
    • If no unvisited neighboring cell, backtrack

No more unvisited neighbors, backtrack!

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