geometry synthesis mathias ricken rice undergraduate scholar program november 11, 2003

Geometry Synthesis

Mathias Ricken

Rice Undergraduate Scholar Program

November 11, 2003

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OverviewComputer-Generated Geometry

Uses Creation

Previous Work Landscapes Mazes Problems

Geometry Synthesis Parametric synthesis Synthesis by analogy

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Computer-Generated Geometry1

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Creating GeometryHand-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

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Landscapes

Filters Smoothen or roughen landscape Add rivers and lakes

Height Map Matrix of numbers

e.g. one per square foot Numbers

Elevation

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Mazes

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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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ProblemsLandscapes

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

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Generalize 3D, not 2D Not grid-based

Examples of Parameters Frequencies Dimensions Angles Alignment

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Parametric Synthesis

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Synthesis by Analogy

Automatically enhance bare geometry created by parametric synthesis Use design templates Add colors, patterns, details

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Texture Synthesis by AnalogyGiven 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 AnalogyTemplate Synthesis Target

1. Randomly pick first color

2. Move left to right, top to bottom

3. Pick neighborhood that matches best

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Texture Synthesis by AnalogyTemplate Synthesis Target

1. Randomly pick first color

2. Move left to right, top to bottom

3. 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

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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 matrixApply synthesis by analogy to it

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Geometry Synthesis by AnalogyPrevious research in two dimensions

Generalize from 2D to 3D

Improve speed

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Editor

Build application Graphical user interface 3D display Support all synthesis steps

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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 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!

Unvisited neighbor to the

north. Tear down wall!