1 Particle Systems - History Particle Systems 1982 Star Trek II: - - PDF document

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Advanced Modeling

Eduard Gröller, Thomas Theußl, Peter Rautek Institute of Computer Graphics and Algorithms Vienna University of Technology

Motivation

Real world phenomena Complex geometry Large deformations Topological changes Fuzzy objects Tedious or impossible to model with meshes Examples Smoke, fire Fluids Fur, hair, grass

Eduard Gröller, Thomas Theußl, Peter Rautek 1

[http://physbam.stanford.edu/~fedkiw/]

Motivation

Eduard Gröller, Thomas Theußl, Peter Rautek 2

[http://physbam.stanford.edu/~fedkiw/]

Motivation

Eduard Gröller, Thomas Theußl, Peter Rautek 3

[http://physbam.stanford.edu/~fedkiw/]

Overview

Particle systems Implicit modeling Soft objects Superquadrics Level sets Procedural modeling Sweeps Cellular texure generation Terrain simulation Vegetation simulation Structure-deforming transformations

Eduard Gröller, Thomas Theußl, Peter Rautek 4

Particle Systems

Modeling of objects changing over time Flowing Billowing Spattering Expanding Modeling of natural phenomena: Rain, snow, clouds Explosions, fireworks, smoke, fire Sprays, waterfalls, lumps of grass

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[Matthias Müller]

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Particle Systems - History 1982 Star Trek II: The Wrath of Khan

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“A particle system is a collection of many many minute particles that together represent a fuzzy object. Over a period of time, particles are generated into a system, move and change from within the system, and die from the system.”

William T. Reeves Particle Systems - A Technique for Modeling a Class of Fuzzy Objects ACM Transactions on Graphics, 1983

Particle Systems Certain number of particles is rendered Particle parameters change over time:

Location Speed Appearance

Particles die (lifetime) and are deleted

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Particle Systems (2)

Particle shapes may be spheres, boxes, or arbitrary models Size and shape may vary over time Motion may be controlled by external forces, e.g. gravity

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Particle Systems (3) Particles interfere with other particles

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Particle Systems: Bomb

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Particle Systems: Grass Clumps

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lifetime can be encoded by color: from green to yellow

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Implicit Modeling No fixed shape and topology Modeling of

Molecular structures Water droplets Melting objects Muscle shapes

Shape and topology change

In motion In proximity to other objects

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Implicit Modeling No seams Oriented surface (well defined inside and outside) Differentiable Closed Continuous

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Implicit Modeling Implicit equation e.g.,

• Vs. explicit equation e.g.,

Function Right side constant (typically a threshold T)

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T y x y x f     ) ( ) , (

2 2

  n

2d function intersection with T - plane result (the 2d model)

The surface of an implicit model is defined as the set of points that fulfill the implicit equation

d kx y   Implicit Modeling Level sets level curve, iso contour, contour line level surface, iso surface level hypersurface Changing the threshold   2   3   n

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change of topology

Soft Objects: Blobs Volume stays constant during movement Molecular bonding: As two molecules move away from each other, the surface shapes

Stretch Snap and finally Contract into spheres

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Definition of Blobby Objects Sum of Gaussian density functions centered at the k control points where T is a specified threshold, and ak and bk adjust the blobbiness of control point k

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

  

 k r a k

T e b z y x f

k k

) , , (

2

2 2 2 2

) ( ) ( ) (

k k k k

z z y y x x r       ) , , (

k k k k

z y x X 

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Definition of Blobby Objects Metaball model uses density functions, which drop off to 0 at a finite interval Soft object model uses same approach with a different density-distribution characteristic

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Superquadrics Generalization of quadric representation Additional parameters Increased flexibility for adjusting object shapes One additional parameter for curves and two parameters for surfaces

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Superellipse Exponent of x and y terms of a standard ellipse are allowed to be variable: Influence of s:

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1

/ 2 / 2

                 

s y s x

r y r x

Superellipsoid Exponent of x, y and z terms of a standard ellipsoid are allowed to be variable: Influence of s1 and s2:

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1

1 1 2 2 2

/ 2 / / 2 / 2

                                  

s z s s s y s x

r z r y r x

Procedural Modeling High geometric complexity Complex model does not exist as geometry

Set of production rules

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Demo

Procedural Modeling

Motivation One window in highest resolution ~7 million triangles Modeled with 126 KB (18 KB zipped)

• f code

Changing parameters yields very different models

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Sweeps Modeling of objects with symmetries:

Translational Rotational

Represented by

2D shape Sweep-path

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Translational Sweeps Control points of spline curve P(u) Generates the solid, whose surface is described by point function P(u,v)

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p1 p2 p0 p3 P(u) P(u,v)

Rotational Sweeps

 Spline curve P(u)  Rotated about given

rotation axis

 Sampled at given angles

yields the surface P(u,v)

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rotation axis

General Sweeps

 Spline curve P(u)  Moved along a sweep

path (e.g., spline)

 Animated sweep path

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[Kinetix 3D Studio MAX]

Sweeps - Pros and Cons Advantages:

Generates shapes that are hard to do

• therwise

Disadvantages:

Hard to render Difficult modeling

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Example

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Cellular Texture Generation A cellular particle system, that changes geometry

• f surface

cell state cell programs extracellular environments

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Cellular Texture Generation

Cell state: position, orientation, shape, chemical concentrations (reaction-diffusion) Cell programs: Go to surface, die if too far from surface, align, adhere to

• ther cells, divide until surface is covered, ...

Differential equations Extra cellular environment: neighbor orientation, concentration, ...

Eduard Gröller, Thomas Theußl, Peter Rautek 31 Eduard Gröller, Thomas Theußl, Peter Rautek 32

Cellular Texture Generation 2 Levels of Detail (LOD): Use fewer polygons for further distances Cellular Texture Generation 3 Cell: group of polygons with texture and transparency maps

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Cellular Texture Generation - Examples Handling of unusual topologies No problem with parameterization

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Cellular Texture Generation - Examples Reaction-diffusion determine pattern of bumps and thorns

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Cellular Texture Generation - Examples Cells (fur)

• riented

like their neighbors

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Cellular Texture Generation - Examples Cells (fur) similarly

• riented

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Modeling and Visualization of Knitwear Knitwear: simulation of thin 3D structure with instanced volume elements

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b a s i c e l e m e n t (R-loop) b a s i c e l e m e n t (L-loop)

Visualization of Knitwear Volume element: 2D cross-section swept + rotated along parametric curve

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x y p ( t ) g g’ g" b1 b2 p0 p1 p2 p3 p4 p5 p6 C 1 C 2 C 3 C 4 x y z z x p ( t ) y g

Visualization of Knitwear Rendering with raycasting

Surface tiled with volumetric elements Curved rays

Eduard Gröller, Thomas Theußl, Peter Rautek 40 x y z xm i n xmax v i e wing ray t

• p

f a c e bottom f a c e F u , v

i j c

P

entry c

P

e x i t

P

p entry

P

p e x i t

y z x ’ P p P p d P c ’ u w v P c d

Fu , v

i j

Knitwear - Examples

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Knitwear - Examples

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Knitwear - Examples

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Knitwear - Examples

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Terrain Simulation

 Fractals  Geographical Data  Simulations  Hybrids

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Terrain Simulation Terrain Simulation

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Terrain Simulation Terrain Simulation Terrain Simulation Realistic modeling and rendering of plant

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Scene Synthesis System

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Terrain

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Height map Hills through noise synthesis Stream through masking Water concentration (blue=high, yellow=low)

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Specification of Plant Populations

Space-occupancy

Explicit specification (counting plants, painting) Procedural generation (cellular automata, reaction-diffusion)

Individual based

Explicit specification (survey, interactive specification) Procedural generation (point pattern generation model)

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Self-thinning: Green: not dominated Red: dominated Yellow: old Distribution of eight species

Realistic Modeling and Rendering of Plants Complex models necessary for realistic appearance

Plant distribution by ecosystem simulation and/or manual setting Reduce geometric complexity by approximate instancing (similar plants, groups of plants or plant organs) Parametrized models of individual plants

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Plant Ecosystems - Examples

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Plant Ecosystems - Examples

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Plant Ecosystems - Examples

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Plant Ecosystems - Examples

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Plant Ecosystems - Examples

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Plant Ecosystems – Self Thinning

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Plant Ecosystems – Self Thinning

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Plant Ecosystems - Examples

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Plant Ecosystems - Examples

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Structure-Deforming Transformations Non-linear transformations

Tapering: non-linear scaling Twist: non-linear rotation Bend: also non-linear rotation

Eduard Gröller, Thomas Theußl, Peter Rautek 65

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Tapering Scale factor is a function:

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x x f x f x f x

z y x

                  ) ( ) ( ) (

Twist Angle of rotation is a function e.g., for rotation about z-axis

Eduard Gröller, Thomas Theußl, Peter Rautek 67

x x f x f x f x f x                     1 ) ( cos ) ( sin ) ( sin ) ( cos Bend Also non-linear rotation

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Example 1

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Example 2

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Other Topics not Covered Here Shape grammars Procedural architecture Fractals (see Fraktale VO WS)

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Thank you for your attention Questions?

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References

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