2.11 Particle Systems
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- Loreen Mathews
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1 2.11 Particle Systems : Advanced Graphics - Chapter 2 152
2 Particle Systems Lagrangian method not mesh-based set of particles to model time-dependent phenomena such as snow fire smoke : Advanced Graphics - Chapter 2 153
3 Particle systems particles are characterized by mass, position, and velocity. forces determine the dynamic behavior particles can carry attributes for rendering like shape, color, transparency, : Advanced Graphics - Chapter 2 154
4 Particle quantities : Advanced Graphics - Chapter 2 155
5 Particle motion : Advanced Graphics - Chapter 2 156
6 Governing equations : Advanced Graphics - Chapter 2 157
7 Initial value problem : Advanced Graphics - Chapter 2 158
8 Initial value problem : Advanced Graphics - Chapter 2 159
9 Finite differences : Advanced Graphics - Chapter 2 160
10 Euler method : Advanced Graphics - Chapter 2 161
11 Accuracy and stability : Advanced Graphics - Chapter 2 162
12 Higher-order integration scheme : Advanced Graphics - Chapter 2 163
13 Video 750,000 particles : Advanced Graphics - Chapter 2 164
14 Particle interactions Up to now, particles did not interact with each other. Still, certain phenomena can be modeled quite realistically. If particle interaction is desired, one can apply the methods for spring-mass models, where the attracting and repelling forces between particles can, for example, be modeled using the Lennard-Jones function : Advanced Graphics - Chapter 2 165
15 2.12 Mesh-free Physics : Advanced Graphics - Chapter 2 166
16 Mesh-free physics The continuum mechanics that were introduced in the context of finite elements methods can also be applied to particle positions : Advanced Graphics - Chapter 2 167
17 Mesh-free physics : Advanced Graphics - Chapter 2 168
18 Mesh-free physics The only challenge is to accurately determine the derivative of the displacement vector. As no connectivity is given between particles, derivative computation is not straight forward, even if the displacement vectors of all nearby particles are known : Advanced Graphics - Chapter 2 169
19 Gradient approximation : Advanced Graphics - Chapter 2 170
20 Moving Least Squares In order to have the resulting function be an interpolation, choose weights 2 ( ) = k w t t, k = 1,2, : Advanced Graphics - Chapter 2 171
21 Rendering To render the results of an animation, isosurfaces are shown. The isosurfaces are rendered using, again, a moving least squares approximation : Advanced Graphics - Chapter 2 172
22 Results Elastic solid melts to fluid: : Advanced Graphics - Chapter 2 173
23 Fractures To handle fractures, use explicit surface representation in terms of surface splats. When cracks emerge, new surface splats are created. Sharp features (creases and corners) are represented implicitly by the intersection of two surface sheets following the idea of constructive solid geometry (CSG) : Advanced Graphics - Chapter 2 174
24 Results Highly plastic deformation, where fracture is incorporated when strain gets too high: : Advanced Graphics - Chapter 2 175
25 2.13 Summary : Advanced Graphics - Chapter 2 176
26 Morphing Mesh morphing Volume morphing Animation Motion capturing Physically-based animation Humans, animals, Spring models Hair, Cloth Continuum mechanics Deformable objects Finite elements Mesh-less Particle systems Smoke, fire, Euler (Lagrangian, semi-lagrangian) Fluids methods : Advanced Graphics - Chapter 2 177
27 X. GPU Programming : Advanced Graphics - Chapter X 1
28 X.1 GPU Architecture : Advanced Graphics - Chapter X 2
29 GPU Graphics Processing Unit Parallelized SIMD Architecture 112 processing cores on nvidia GeForce 9800GT (4 years ago) 512 processing cores on nvidia GeForce GTX 580 (2 years ago) 1536 processing cores on nvidia GeForce GTX 680 (newest) : Advanced Graphics - Chapter X 3
30 Restrictions Not a generalized vector processor Cannot read and write to same areas of memory Limited output capability Currently, expensive to output to arbitrary locations in memory Restricted memory size 1GB on nvidia GeForce 9800GT 1.5GB on nvidia GeForce GTX 580 2GB on nvidia GeForce GTX : Advanced Graphics - Chapter X 4
31 Notation Vertex A data structure for a point in a mesh, containing position, normal, texture coordinates, etc. Fragment A pixel, possibly sub-pixel, of a rasterized image Shaders Small programs run in the GPU at specific stages of the GPU pipeline : Advanced Graphics - Chapter X 5
32 Memory constructs Buffered Objects Uniform Registers/State Table Interpolated Registers Temporary Registers Textures : Advanced Graphics - Chapter X 6
33 Memory constructs Buffered Objects CPU Generated Streams of Data Limited Modifiability Example Vertex Data of a Mesh : Advanced Graphics - Chapter X 7
34 Memory constructs Uniform Registers/State Table Constant Data through the Pipeline Only Necessarily Constant for 1 Polygon 32 general purpose registers State Table Specific Registers Projection/Model View Matrices Lights and more : Advanced Graphics - Chapter X 8
35 Memory constructs Interpolated Registers Per Vertex Data of a Polygon Stores Information Interpolated Across Polygon 10 General Purpose Interpolated Registers : Advanced Graphics - Chapter X 9
36 Memory constructs Temporary Registers Standard Notion of Registers Temporary Registers for In Shader Calculations : Advanced Graphics - Chapter X 10
37 Memory constructs Textures Closest to Random Access Memory Expensive to Access Multiple Dependent Accesses Extremely Expensive : Advanced Graphics - Chapter X 11
38 GPU pipeline Program/ API Driver GPU Front End CPU GPU Bus Vertex Processing Primitive Assembly Rasterization & Interpolation Fragment Processing Raster Operations Framebuffer : Advanced Graphics - Chapter X 12
39 GPU pipeline Program/ API Program API Your Program Either OpenGL or DirectX Interface : Advanced Graphics - Chapter X 13
40 GPU pipeline Driver Driver Black-box Implementations are Company Secrets Largest Bottleneck in many GPU programs : Advanced Graphics - Chapter X 14
41 GPU pipeline GPU Front End GPU Front End Receives commands & data from driver PCI Express helps at this stage : Advanced Graphics - Chapter X 15
42 GPU pipeline Vertex Processing Vertex Processing Normally performs transformations Programmable vertex POSITION, NORMAL, BINORMAL*, TANGENT*, TEXCOORD[0-7], COLOR[0-1], PSIZE Vertex Processor shader textures data for rasterization POSITION PSIZE FOG data for interpolation TEXCOORD[0-7] COLOR[0-1] : Advanced Graphics - Chapter X 16
43 GPU pipeline Primitive Assembly Primitive Assembly Compiles Vertices into Points, Lines and/or Polygons Link elements and set rasterizer : Advanced Graphics - Chapter X 17
44 GPU pipeline Rasterization & Interpolation Rasterization For each fragment determine respective area of triangle (Barycentric Coordinates) or other primitive Interpolation Primitive Assembler data for rasterization Primitive Type PSIZE POSITION Rasterizer rasterized data DEPTH FOG Barycentric Coordinates TEXCOORD[0-7] COLOR[0-1] data for interpolation TEXCOORD[0-7] COLOR[0-1] Interpolator interpolated data : Advanced Graphics - Chapter X 18
45 GPU pipeline Fragment Processing Fragment Processing Programmable rasterized data DEPTH interpolated data TEXCOORD[0-7] COLOR[0-1] Fragment Processor shader data for raster ops DEPTH COLOR[0-3] textures : Advanced Graphics - Chapter X 19
46 GPU pipeline Raster Operations Depth Checking Check framebuffer to see if lesser depth already exists (Z- Buffer) Limited Programmability Blending Use alpha channel to combine colors already in the framebuffer Limited Programmability : Advanced Graphics - Chapter X 20
47 Example Program/ API Bus Driver GPU Front End Vertex Processing Code Snippet. glbegin(gl_triangles); gltexcoord2f(1,0); glvertex3f(0,1,0); gltexcoord2f(0,1); glvertex3f(-1,-1,0); gltexcoord2f(0,0); glvertex3f(1,-1,0); glend(); Primitive Assembly Rasterization & Interpolation Fragment Processing Raster Operations Framebuffer(s) : Advanced Graphics - Chapter X 21
48 Example Program/ API Driver Bus GPU Front End GPU Vertex Processing Primitive Assembly Rasterization & Interpolation Fragment Processing Raster Operations Framebuffer(s) : Advanced Graphics - Chapter X 22
49 Example Program/ API Driver Bus GPU Front End Vertex Processing viewing frustum Primitive Assembly Rasterization & Interpolation Fragment Processing Raster Operations Framebuffer(s) : Advanced Graphics - Chapter X 23
50 Example Program/ API Driver Bus GPU Front End Vertex Processing Primitive Assembly Rasterization & Interpolation Fragment Processing Raster Operations screen space Framebuffer(s) : Advanced Graphics - Chapter X 24
51 Example Program/ API Driver Bus GPU Front End Vertex Processing Primitive Assembly Rasterization & Interpolation Fragment Processing Raster Operations framebuffer Framebuffer(s) : Advanced Graphics - Chapter X 25
52 Example Program/ API Driver Bus GPU Front End Vertex Processing Primitive Assembly Rasterization & Interpolation Fragment Processing Raster Operations framebuffer Framebuffer(s) : Advanced Graphics - Chapter X 26
53 Summary of GPU part : Advanced Graphics - Chapter X 27
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