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Geometric Modelling

Computer GraphicsCOMP 770 (236)Spring 2007

Instructor: Brandon Lloyd

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■ Modeling methods■ Surface representations■ Procedural modeling

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Modelling methodology

■ Explicit° Hand modification of the

underlying representation° CSG° Sweeps° Deformations

■ Procedural° L-Systems

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Constructive Solid Geometry

■ Combine simple solid objects into complex ones through set theoretic operations

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Union Difference Intersection

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Constructive Solid Geometry

http://en.wikipedia.org/wiki/Constructive_solid_geometry

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Sweeps

http://groups.csail.mit.edu/graphics/classes/6.837/F98/talecture/

■ Formed by sweeping a generating shape along a path° Surfaces of revolution° Extrusions

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Free-form deformation

■ Surround object in a lattice

■ Freeze lattice coordinates of surface points

■ Manipulate lattice to deform object

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Free-Form Deformations

Yoon and Kim 2006

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Representations

■ Boundary representations (B-reps)° represent only the surface of an

object° “shells”° e.g. polygon meshes,

parameteric patches

■ Solid representations° have clear inside and outside° e.g. implicit functions

http://cadd.web.cern.ch/cadd/cad_geant_int/thesis/node23.html

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Representations

■ Explicit° Polygonal mesh° Point-based° Parametric patches° Subdivision surfaces° Spatial subdivision

■ Others° Distance fields° Medial axis° Metaballs

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Polygons

■ May or may not have connectivity

■ Fast to draw

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Points

■ Typical output from a range finder

■ No topology■ Adaptive sampling

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Parmeteric Patches

■ Compact■ Smooth surface

representation■ Good control■ Special care is

needed to maintain continuity

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Subdivision surfaces

■ Compact ■ More flexible than patches■ Refine to required

level-of-detail

DeRose98

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Spatial subdivision

■ Explicit representation of the interior of an object

■ Uses ° visibility ° simplification

UniformUniform

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Distance fields

■ Store the distance to the surface at each point° Good for collision detection° Can “implicitize” a b-rep

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Medial axis

■ Compact■ Uses

° Classification° Deformation

http://www.fegs.co.uk/motech.html

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Metaballs

■ Define potential field around each point

■ Set a threshold for the surface

■ Extract the surface for polygonal rendering° Marching cubes

http://www.inf.ufrgs.br/~nedel/projects/vh.html

http://www.corelmag.com

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Marching Cubes

■ Extracts an isosurface from a regular grid■ Looks for sign changes between grid

points and creates a surface between them

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Procedural modelling

■ Advantages° Can be used to generate models that could never be

generated by hand° Compact representations

■ Disadvantages° Sometime hard to get exactly what you want

(can be use to generate a starting point)

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L-Systems

■ Simple rules used to produce complex structures

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Plant ecosystems

■ Combines simulation with user specified parameters

Maps for controlling theplacement of nettle

Deussen et al. 1998

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Procedural Terrains

http://www.pandromeda.com

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Procedural Terrains

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Procedural Terrains

http://www.basinski-net.de/scapes6/pages/valley.htm

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Procedural cities

■ User specified parameters:° water° elevation° population density

■ L-systems generate roads

■ Buildings added to city blocks Parish and Müller 2001

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Procedural cities

Parish and Müller 2001

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Procedural Buildings

Müller et al 2006