2.9 Mesh-free Physics · Animation •Morphing gn–Mih mphrsoe gnih mmpeur–Volo •...

320491: Advanced Graphics - Chapter 2 163

Visualization and Computer Graphics LabJacobs University

2.9 Mesh-free Physics



Mesh-free physics

• The continuum mechanics that were introduced in thecontext of finite elements methods can also beapplied to particle positions.



Mesh-free physics



Mesh-free physics

• The only challenge is to accurately determine thederivative of the displacement vector.

• As no connectivity is given between particles, derivative computation is not straight forward, evenif the displacement vectors of all nearby particles areknown.



Gradient approximation



Moving Least Squares

In order to have the resulting function be an interpolation, choose weights

,..2,1,)( 2 == − kttw k



Rendering

• To render the results of an animation, isosurfaces areshown.

• The isosurfaces are rendered using, again, a movingleast squares approximation.



Results

• Elastic solid melts to fluid:



Results

• Highly plastic deformation, where fracture isincorporated when strain gets too high:



2.10 Summary



Animation• Morphing

– Mesh morphing– Volume morphing

• Physically-based animation– Spring models Hair, Cloth– Continuum mechanics Deformable objects

• Finite elements• Mesh-less

– Particle systems Smoke, fire, …– Euler methods Fluids

• Motion capturing Humans, animals, …

320491: Advanced Graphics - Chapter X 1


X. GPU Programming



X.1 GPU Architecture



GPU

• Graphics Processing Unit• Parallelized SIMD Architecture

– 112 processing cores on nVidia GeForce 9800GT (2 years ago)– 512 processing cores on nVidia GeForce GTX 580 (newest)



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



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



Memory constructs

• Buffered Objects• Uniform Registers/State Table• Interpolated Registers• Temporary Registers• Textures



Memory constructs

• Buffered Objects– CPU Generated Streams of Data– Limited Modifiability– Example

• Vertex Data of a Mesh



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



Memory constructs

• Interpolated Registers– Per Vertex Data of a Polygon– Stores Information Interpolated Across Polygon– 10 General Purpose Interpolated Registers



Memory constructs

• Temporary Registers– Standard Notion of Registers– Temporary Registers for In Shader Calculations



Memory constructs

• Textures– Closest to Random Access Memory– Expensive to Access

• Multiple Dependent AccessesExtremely Expensive



GPU pipelineProgram/

API

GPU Front End

VertexProcessing

PrimitiveAssembly

Rasterization &Interpolation

FragmentProcessing

RasterOperations

Framebuffer

DriverCPU

GPUBus



GPU pipeline

• Program– Your Program

• API– Either OpenGL or DirectX Interface

Program/API



GPU pipeline

• Driver– Black-box

• Implementations are Company Secrets– Largest Bottleneck in many GPU programs

Driver



GPU pipeline

• GPU Front End– Receives commands & data from driver– PCI Express helps at this stage

GPU Front End



GPU pipeline

• Vertex Processing– Normally performs transformations– Programmable

VertexProcessing

VertexProcessor

vertex

data for interpolation

data for rasterizationPOSITION

PSIZE

FOG

TEXCOORD[0-7]COLOR[0-1]

shader

POSITION, NORMAL, BINORMAL*, TANGENT*, TEXCOORD[0-7], COLOR[0-1], PSIZE

textures



GPU pipeline

• Primitive Assembly– Compiles Vertices into Points, Lines and/or Polygons– Link elements and set rasterizer

PrimitiveAssembly



GPU pipeline

• Rasterization– For each fragment determine respective area of triangle

(Barycentric Coordinates) or other primitive• Interpolation


data for interpolation

data for rasterizationPOSITION

PSIZE

FOG


Rasterizer

Interpolator interpolated data


rasterized data

DEPTHBarycentricCoordinates

PrimitiveAssemblerPrimitive Type



GPU pipeline

• Fragment Processing– Programmable

FragmentProcessing

FragmentProcessor

shader

textures

interpolated data


rasterized data

DEPTHCOLOR[0-3]

DEPTH

data for raster ops



GPU pipeline

• 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

RasterOperations



ExampleProgram/

API

GPU Front End

VertexProcessing

PrimitiveAssembly


FragmentProcessing

RasterOperations Framebuffer(s)

Driver

Bus

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();

…



ExampleProgram/

API

GPU Front End

VertexProcessing

PrimitiveAssembly


FragmentProcessing


Driver

Bus

01001001100….

GP

U



ExampleProgram/

API

GPU Front End

VertexProcessing

PrimitiveAssembly


FragmentProcessing


Driver

Bus

viewing frustum



ExampleProgram/

API

GPU Front End

VertexProcessing

PrimitiveAssembly


FragmentProcessing


Driver

Bus

screen space



ExampleProgram/

API

GPU Front End

VertexProcessing

PrimitiveAssembly


FragmentProcessing


Driver

Bus

framebuffer



Summary of GPU part



Quick architecture notes

• Limits in Shader Size• MIMD

– Branches are supported with a large overhead• Unified Shading Architecture

– Xbox 360 – ATI– Pool of processors with load balancing



Higher-level shading languages

• Vectorized languages for designing shader programs• Easy way out of tedious assembly coding• Not Perfect

– Results Are Sometimes Clearly Not Optimized• Examples

– Cg– GLSL– HLSL



GPGPU

• General Purpose GPU Processing• Key Notes

– Goal to exploit fragment processor– Each pixel represents a compacted 4-component element of

data– Most optimal in gathering algorithms

• Vertex shader needed to re-order output• Possibly Optimal in Unified Shading Architecture

2.9 Mesh-free Physics · Animation •Morphing gn–Mih mphrsoe gnih mmpeur–Volo •...

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