More modelling. Ruth Aylett

Transcription

1 More modelling Ruth Aylett

2 Overview The great outdoors: fractals L-systems City Models Procedural generation of models

3 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

4 The great outdoors Water, fire, rain, snow Particle system: see later lecture Included in some games engines like UT Trees Use fractals: Lindenmayer systems (Lsystems) are method of choice

5 Fractals Geometry similar/identical at different scales Often generated from simple rules Frequent in Nature Zoom in on jagged coast Still jagged however close you get Tree branches that branch

6 L-systems A type of fractal Invented in 1968 by Aristid Lindenmayer to model biological growth The algorithmic beauty of plants Constructed from line segments using rules specified 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

7 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.

8 L-system example Alphabet: {a, b} Axiom ( seed ): b Production rules: a => ab b => a

9 Example: the Koch Curve 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

10 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

11 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

12 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 ] is executed

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14 Using L-systems Modelling software available See ml for a list of some E.g shareware xfrog plant modeller l

15 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

16 Active Research Area Procedural Modeling of Cities [Parish and Müller, 2001] Procedural Modeling of Buildings [Haegler et al. 2006]

17 Streets Modified L-systems Predecessor Ideal Successor Global Goals Local Constraints Global goals: Desired type of street pattern (entered by user) Local constraints: Streets must join up; no closed loops etc

18 City Engine examples See Organic, radial, raster Organic main, raster local Radial main, radial local

19 Division into Lots Road network divided into city blocks and then building footprints

20 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 Plus a rule engine to run the rules

21 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

22 Façade addition to extruded shape

23 Examples Palladian villas William Mitchell (1990) 69 rules fired during eight stages. City Engine videos Commercial engine Open source: Shape Grammar Interpreter

24 Applications Mainly in games City Engine a recent startup Considerable resistance by real-world designers Possibly too little user control Development of plugins for 3d modelling packages