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# Geometry Synthesis - PowerPoint PPT Presentation

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

Mathias Ricken

November 11, 2003

• Computer-Generated Geometry

• Uses

• Creation

• Previous Work

• Landscapes

• Mazes

• Problems

• Geometry Synthesis

• Parametric synthesis

• Synthesis by analogy

• Hand-Crafted

• Computer games

1 Man-Year for 40 hours of game play 2

• Automation

• Lower costs

• Better training

• Higher replay value

• Height Map

• Matrix of numbers

• e.g. one per square foot

• Numbers

 Elevation

• Filters

• Smoothen or roughen landscape

• Recursive Backtracking

• Regular grid

• 2-Dimensional

• Creates perfect mazes

• All cells connected in exactly one way

• No loops

algorithm explained in extra slides

• Landscapes

• Large scale, but low detail

• Only natural, not artificial

• Mazes

• 2-dimensional

• Small scale

• Not reminiscent of human architecture

• Create meaningful geometry

• Similar to human architecture

• 3-dimensional

• High detail

• Algorithms

• Parametric synthesis

• Synthesis by analogy

• 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

• Generalize

• 3D, not 2D

• Not grid-based

4

• Examples of Parameters

• Frequencies

• Dimensions

• Angles

• Alignment

• Automatically enhance bare geometry created by parametric synthesis

• Use design templates

5

• 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

Template

Synthesis Target

• Randomly pick first color

• Move left to right, top to bottom

• Pick neighborhood that matches best

Template

Synthesis Target

• Randomly pick first color

• Move left to right, top to bottom

• Pick neighborhood that matches best

• Large features require large neighborhood

Source

5 x 5

7 x 7

9 x 9

6

• 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

• Previous research in two dimensions

8

• Generalize from 2D to 3D

• Improve speed

• Build application

• Graphical user interface

• 3D display

• Support all synthesis steps

9

[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/

[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.

• 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!