More modelling

Ruth Aylett

Overview

The great outdoors: fractals– L-systems

City Models– Procedural generation of models

How to make models..

Interactive modeling– Human with a software modeling tool

Scanning– Model geometry is scanned from a real world example using

a laser scanner or similar device

Computer vision– Scanned from real world example using multiple

photographic cameras (or video sequences)

Procedural modeling– Model constructed by automatic procedure that may

make use of randomness for variety

The great outdoors

Water, fire, rain, snow– Particle system: see later lecture– Included in some games engines like UT

Trees– Use fractals: Lindenmayer systems (L-

systems) are method of choice

Fractals

Geometry similar/identical at differentscales

Often generated from simple rules Frequent in Nature

– Zoom in on jagged coast• Still jagged however close you get

– Tree branches that branch

L-systems

A type of fractal– Invented in 1968 by Aristid Lindenmayer to model

biological growth• ‘The algorithmic beauty of plants’• http://algorithmicbotany.org/papers/#abop

Constructed from line segments using rulesspecified in drawing commands– Start with an initial string– Axiom, transformation rules are applied a specified

number of times– Produce the final command string– Which is used to draw the image

How it works

L-systems are parallel rewriting systems. L-systems consist of:

– an alphabet (V)– an axiom (a non-empty “seed” string V+)– Production rules of the form:

V => V* (predecessor => successor)

Rules replace predecessors with successors. Identity production rule is the default.

L-system example

Alphabet:{a, b}

Axiom (“seed”):b

Production rules:a => abb => a

A variant of the Koch curve which uses only right-angles.– variables : F– constants : + −– start : F– rules : (F → F+F−F−F+F)

Here, F means "draw forward", + means "turn left 90°", and -means "turn right 90°"

n = 0: F

n = 1: F+F-F-F+F

Example: the Koch Curve

n = 2: F+F-F-F+F+F+F-F-F+F-F+F-F-F+F-F+F-F-

F+F+F+F-F-F+F

n = 3:F+F-F-F+F+F+F-F-F+F-F+F-F-F+F-F+F-F-F+F+F+F-F-F+F+ F+F-F-F+F+F+F-F-F+F-F+F-F-F+F-F+F-F-F+F+F+F-F-F+F- F+F-F-F+F+F+F-F-F+F-F+F-F-F+F-F+F-F-F+F+F+F-F-F+F- F+F-F-F+F+F+F-F-F+F-F+F-F-F+F-F+F-F-F+F+F+F-F-F+F+ F+F-F-F+F+F+F-F-F+F-F+F-F-F+F-F+F-F-F+F+F+F-F-F+F

A fractal plant variables : X F

– constants : + −– start : X– rules : (X → F-[[X]+X]+F[+FX]-X),(F → FF)– angle : 25º

Here,– F means "draw forward",– - means "turn left 25º", and– + means "turn right 25º".– X does not correspond to any drawing action and is used to

control the evolution of the curve.– [ corresponds to saving the current values for position and

angle, which are restored when the corresponding ] isexecuted

Using L-systems

Modelling software available– See

http://www.vterrain.org/Plants/plantsw.html for a list of some

– E.g shareware xfrog plant modeller• http://www.vterrain.org/Plants/Xfrog/index.htm

l

Procedural models of cities

Different levels of structure– Street network (only some cities are purely

grids)– ‘Lots’: 2D spaces where buildings can go– Buildings– Low-level geometry

Active Research Area– Procedural Modeling of Cities [Parish and Müller, 2001]

– Procedural Modeling of Buildings [Haegler et al. 2006]

Streets

Modified L-systems

Global goals:– Desired type of street pattern (entered by user)

Local constraints:– Streets must join up; no closed loops etc

PredecessorIdealSuccessor

GlobalGoals

Local

Constraints

City Engine examples

See www.procedural.comOrganic, radial, raster

Organic main, rasterlocal

Radial main, radiallocal

Division into Lots

Road network divided into city blocks andthen building footprints

Buildings Shape grammars (1972)

– Symbols represent shapes– Manipulation rules represent operations on

shapes• EG: insert (replace one shape with another); split

(along a plane); scale, translate, rotate;

– See http://en.wikipedia.org/wiki/Shape_grammar Plus a rule engine to run the rules

Applying a shape grammar

Form: LHS -> RHS– LHS: condition = shape + marker– RHS: LHS shape transformation + new marker

position

Grammar– 1 start rule; n transformation rules; 1 termination

rule (e.g. remove the marker)

Process:– Working memory holds current state– LHS rules triggered by matching– Conflict resolution if more than one

Façade addition to extrudedshape

Examples

Palladian villas– William Mitchell (1990)– 69 rules– fired during eight stages.

City Engine videos– Commercial engine

Open source: Shape Grammar Interpreter• http://sourceforge.net/projects/sginterpreter/

Applications

Mainly in games– City Engine a recent startup

Considerable resistance by real-worlddesigners– Possibly too little user control

Development of plugins for 3dmodelling packages