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

Motivation Real world phenomena Complex geometry Large deformations Advanced Modeling Topological changes Fuzzy objects Tedious or impossible to Eduard Gröller, Thomas Theußl, model with meshes Peter Rautek Examples Smoke, fire Institute of Computer Graphics and Algorithms Fluids Fur, hair, grass Vienna University of Technology [http://physbam.stanford.edu/~fedkiw/] Eduard Gröller, Thomas Theußl, Peter Rautek 1 Motivation Motivation [http://physbam.stanford.edu/~fedkiw/] [http://physbam.stanford.edu/~fedkiw/] 2 3 Eduard Gröller, Thomas Theußl, Peter Rautek Eduard Gröller, Thomas Theußl, Peter Rautek Overview Particle Systems Particle systems Modeling of objects changing over time Implicit modeling Flowing Soft objects Billowing Superquadrics Spattering Level sets Expanding Procedural modeling Modeling of natural phenomena: Sweeps Rain, snow, Cellular texure generation clouds Terrain simulation Explosions, Vegetation simulation fireworks, Structure-deforming transformations smoke, fire [Matthias Müller] Sprays, waterfalls, lumps of grass Eduard Gröller, Thomas Theußl, Peter Rautek 4 Eduard Gröller, Thomas Theußl, Peter Rautek 5 1

Particle Systems - History Particle Systems 1982 Star Trek II: The Wrath of Khan Certain number of particles is rendered Particle parameters change over time: Location Speed “A particle system is a collection of many many minute particles that Appearance together represent a fuzzy object. Over a period of time, particles are generated into a system, move and change from within the system, Particles die (lifetime) and and die from the system.” are deleted William T. Reeves Particle Systems - A Technique for Modeling a Class of Fuzzy Objects ACM Transactions on Graphics, 1983 Eduard Gröller, Thomas Theußl, Peter Rautek 6 Eduard Gröller, Thomas Theußl, Peter Rautek 7 Particle Systems (2) Particle Systems (3) Particle shapes Particles interfere with other particles may be spheres, boxes, or arbitrary models Size and shape may vary over time Motion may be controlled by external forces, e.g. gravity 8 9 Eduard Gröller, Thomas Theußl, Peter Rautek Eduard Gröller, Thomas Theußl, Peter Rautek Particle Systems: Bomb Particle Systems: Grass Clumps lifetime can be encoded by color: from green to yellow Eduard Gröller, Thomas Theußl, Peter Rautek 10 Eduard Gröller, Thomas Theußl, Peter Rautek 11 2

Implicit Modeling Implicit Modeling No fixed shape and topology No seams Modeling of Oriented surface (well defined inside and outside) Molecular structures Differentiable Water droplets Melting objects Closed Muscle shapes Continuous Shape and topology change In motion In proximity to other objects Eduard Gröller, Thomas Theußl, Peter Rautek 12 Eduard Gröller, Thomas Theußl, Peter Rautek 13 Implicit Modeling Implicit Modeling     2 2 Implicit equation e.g., f ( x , y ) ( x y ) T Level sets    2   Vs. explicit equation e.g., y kx d level curve, iso contour, contour line  3    n   level surface, iso surface Function  n   level hypersurface Right side constant (typically a threshold T) Changing the threshold result 2d function intersection with T - plane (the 2d model) The surface of an implicit model is defined as change of topology the set of points that fulfill the implicit equation 14 15 Eduard Gröller, Thomas Theußl, Peter Rautek Eduard Gröller, Thomas Theußl, Peter Rautek Soft Objects: Blobs Definition of Blobby Objects Volume stays constant Sum of Gaussian density functions centered X  during movement at the k control points ( x , y , z ) k k k k    2   a r f ( x , y , z ) b e T 0 k k k Molecular bonding: k where As two molecules move       2 2 2 2 away from each other, r ( x x ) ( y y ) ( z z ) k k k k the surface shapes T is a specified threshold, and a k and b k adjust Stretch the blobbiness of control point k Snap and finally Contract into spheres Eduard Gröller, Thomas Theußl, Peter Rautek 16 Eduard Gröller, Thomas Theußl, Peter Rautek 17 3

Definition of Blobby Objects Superquadrics Metaball model uses density functions, which Generalization of quadric representation drop off to 0 at a finite interval Additional parameters Soft object model uses same approach with a Increased flexibility for adjusting object different density-distribution characteristic shapes One additional parameter for curves and two parameters for surfaces Eduard Gröller, Thomas Theußl, Peter Rautek 18 Eduard Gröller, Thomas Theußl, Peter Rautek 19 Superellipse Superellipsoid Exponent of x and y terms of a standard Exponent of x, y and z terms of a standard ellipse are allowed to be variable: ellipsoid are allowed to be variable:   s / s 2 / s 2 1 2 / s   2 / s   2   2 1 x y z       2 / s        2 / s   1       x y             r  r  r 1     x y z     r  r  x y Influence of s : Influence of s 1 and s 2 : 20 21 Eduard Gröller, Thomas Theußl, Peter Rautek Eduard Gröller, Thomas Theußl, Peter Rautek Procedural Modeling Motivation One window in High geometric complexity highest resolution Complex model does not exist as geometry ~7 million triangles Set of production rules Modeled with 126 KB (18 KB zipped) of code Changing parameters yields very different models Demo Procedural Modeling Eduard Gröller, Thomas Theußl, Peter Rautek 22 Eduard Gröller, Thomas Theußl, Peter Rautek 23 4

Sweeps Translational Sweeps Modeling of objects with symmetries: p 1 p 2 Translational Control points of spline curve P(u) Rotational Represented by P(u) p 0 p 3 2D shape Generates the solid, whose surface is Sweep-path described by point P(u,v) function P(u,v) Eduard Gröller, Thomas Theußl, Peter Rautek 24 Eduard Gröller, Thomas Theußl, Peter Rautek 25 Rotational Sweeps General Sweeps rotation axis  Spline curve P(u)  Spline curve P(u)  Rotated about given  Moved along a sweep rotation axis path (e.g., spline) [Kinetix 3D Studio MAX]  Sampled at given angles  Animated sweep path yields the surface P(u,v) 26 27 Eduard Gröller, Thomas Theußl, Peter Rautek Eduard Gröller, Thomas Theußl, Peter Rautek Sweeps - Pros and Cons Example Advantages: Generates shapes that are hard to do otherwise Disadvantages: Hard to render Difficult modeling Eduard Gröller, Thomas Theußl, Peter Rautek 28 Eduard Gröller, Thomas Theußl, Peter Rautek 29 5

Cellular Texture Generation Cellular Texture Generation A cellular particle system, that changes geometry of surface cell state Cell state: position, orientation, shape, chemical concentrations (reaction-diffusion) cell programs Cell programs: extracellular Go to surface, die if too far from surface, align, adhere to environments other cells, divide until surface is covered, ... Differential equations Extra cellular environment: neighbor orientation, concentration, ... Eduard Gröller, Thomas Theußl, Peter Rautek 30 Eduard Gröller, Thomas Theußl, Peter Rautek 31 Cellular Texture Generation 2 Cellular Texture Generation 3 Levels of Detail (LOD): Use fewer polygons Cell: group of for further distances polygons with texture and transparency maps 32 33 Eduard Gröller, Thomas Theußl, Peter Rautek Eduard Gröller, Thomas Theußl, Peter Rautek Cellular Texture Generation - Examples Cellular Texture Generation - Examples Handling of unusual topologies Reaction-diffusion determine pattern of bumps and thorns No problem with parameterization Eduard Gröller, Thomas Theußl, Peter Rautek 34 Eduard Gröller, Thomas Theußl, Peter Rautek 35 6

Cellular Texture Generation - Examples Cellular Texture Generation - Examples Cells (fur) Cells (fur) oriented similarly like their oriented neighbors Eduard Gröller, Thomas Theußl, Peter Rautek 36 Eduard Gröller, Thomas Theußl, Peter Rautek 37 Modeling and Visualization of Knitwear Visualization of Knitwear Knitwear: simulation of thin 3D structure with Volume element: 2D cross-section swept + instanced volume elements rotated along parametric curve p1 p5 b a s i c e l e m e n t C 2 p3 C 3 (R-loop) y C 1 C 4 p0 p6 p2 p4 z x b a s i c e l e m e n t x y g (L-loop) g’ p ( t ) b1 b2 z g" y g p ( t ) x 38 39 Eduard Gröller, Thomas Theußl, Peter Rautek Eduard Gröller, Thomas Theußl, Peter Rautek Visualization of Knitwear Knitwear - Examples Rendering with raycasting Surface tiled with volumetric elements Curved rays v i e wing ray z t o p f a c e bottom f a c e y x xm i xmax n P p Fu z w P , v c i j e x i t d P p P ’ e x i t d p P c entry entry x v ’ u y P P P F u c p c , v i j Eduard Gröller, Thomas Theußl, Peter Rautek 40 Eduard Gröller, Thomas Theußl, Peter Rautek 41 7

Knitwear - Examples Knitwear - Examples Eduard Gröller, Thomas Theußl, Peter Rautek 42 Eduard Gröller, Thomas Theußl, Peter Rautek 43 Knitwear - Examples Terrain Simulation  Fractals  Geographical Data  Simulations  Hybrids 44 45 Eduard Gröller, Thomas Theußl, Peter Rautek Eduard Gröller, Thomas Theußl, Peter Rautek Terrain Simulation Terrain Simulation 8