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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 l.jpg

Geometry Synthesis

Mathias Ricken

Rice Undergraduate Scholar Program

November 11, 2003


Overview l.jpg
Overview

  • Computer-Generated Geometry

    • Uses

    • Creation

  • Previous Work

    • Landscapes

    • Mazes

    • Problems

  • Geometry Synthesis

    • Parametric synthesis

    • Synthesis by analogy



Creating geometry l.jpg
Creating Geometry

  • Hand-Crafted

    • Computer games

      1 Man-Year for 40 hours of game play 2

  • Automation

    • Lower costs

    • Better training

    • Higher replay value



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Landscapes

  • Height Map

    • Matrix of numbers

      • e.g. one per square foot

    • Numbers

       Elevation

  • Filters

    • Smoothen or roughen landscape

    • Add rivers and lakes



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Mazes

  • Recursive Backtracking

    • Regular grid

    • 2-Dimensional

  • Creates perfect mazes

    • All cells connected in exactly one way

    • No loops

algorithm explained in extra slides


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Problems

  • Landscapes

    • Large scale, but low detail

    • Only natural, not artificial

  • Mazes

    • 2-dimensional

    • Small scale

    • Not reminiscent of human architecture


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Proposed Project

  • Create meaningful geometry

    • Similar to human architecture

    • 3-dimensional

    • High detail

  • Algorithms

    • Parametric synthesis

    • Synthesis by analogy


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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



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Parametric Synthesis

  • Generalize

    • 3D, not 2D

    • Not grid-based

4

  • Examples of Parameters

    • Frequencies

    • Dimensions

    • Angles

    • Alignment


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Synthesis by Analogy

  • Automatically enhance bare geometry created by parametric synthesis

    • Use design templates

    • Add colors, patterns, details

5


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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


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Texture Synthesis by Analogy

Template

Synthesis Target

  • Randomly pick first color

  • Move left to right, top to bottom

  • Pick neighborhood that matches best


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Texture Synthesis by Analogy

Template

Synthesis Target

  • Randomly pick first color

  • Move left to right, top to bottom

  • Pick neighborhood that matches best


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Texture Synthesis by Analogy

  • Large features require large neighborhood

Source

5 x 5

7 x 7

9 x 9

6


Geometry synthesis by analogy l.jpg
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


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Geometry Synthesis by Analogy

  • Previous research in two dimensions

8

  • Generalize from 2D to 3D

  • Improve speed


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Editor

  • Build application

    • Graphical user interface

    • 3D display

    • Support all synthesis steps

9


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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/


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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.


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Extra Slides

  • Recursive Backtracking


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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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