Aktuálna revízia z 09:47, 13. november 2015

Physical based Animations and Mathematical Modelling (Course Materials)

This lecture ...

• Will focus on simulating natural phenomena
• Will show you what are current topics
• Will improve your skills in
  • Newtonian physics
  • Computational geometry
  • Algorithms and data structures
• Hopefully will not be boring

Student Projects

• Stránka Ráno do práce
• Stránka The_good_the_bad
• Stránka Kiwi Animácia KiWi
• Stránka Knihy Animácia Knihy
• Stránka Motorka

D-E-A-D-L-I-N-E-S

• Animators team (Axx): deadline 14.12.2015 the last lecture
  • Show your animation, how far have you made it. It should be 30% of the work done, otherwise your team gets Fx.
• Coders team (Cxx): deadline 17.12.2015 the last exercise
  • Show the short DEMO of your project, how far have you made it. It should be 30% of the work done, otherwise your team gets Fx.

• Coders team (Cxx): deadline 26.1.2016
  • Create a web page where you write your progress, upload source code, executable, images description of your project and short manual.
  • Send link to finished application (zipped source + executable.)
  • Your code should be well formatted and commented. Titles of functions, classes, variables should be representative for their purpose.
  • If you send it earlier you can get feedback how to improve your application
• Animators team (Axx): deadline 26.1.2016
  • Create a web page where you write your progress, upload animation, source of animation, images description of your project and describe all physical effects to be evaluated.
  • Upload your animation video on youtube (or some alternative online service)
  • Send link to your webpage
  • If you send it earlier you can get feedback how to improve your animation
• Oral/written exam (optional): deadline 18.1.2016, 8:00, classroom A
  • Instead of (optional) oral exam, you can get (0..+20) points due to a written exam.
  • It will be similar to final term, but less complicated.

What you Need to Pass

• Attend lessons. All lessons attended is +0 points. Four and more missed is Fx.
• Show your project (mandatory, 60 points). See later.
• Solve all homework problems (mandatory each one >=30%, 40 points)
• Pass oral/written exam: (optional, +0 .. +20 points) If you feel you are better, convince me ! You can get +20 points max.
• Summary
  • Attendance = +0 or -100 (Fx)
  • Homework = +40..+12 or 12..0 (Fx)
  • Project = +60..0
  • Oral/written exam optional = +20..0

• Grades
  • A = 92-100
  • B = 84-91
  • C = 76-83
  • D = 68-75
  • E = 60-67
  • Fx = 0-59

• VIEW RESULTS

Oral Examination

To the oral examination all the above requirements must be SATISFACTORILY completed.

How to Arrange your Project

• Take 1 friend and Team up
• Role1: The Coder
  • Choose a given animation algorithm
  • Code up hot demo app and show it
  • Present a selected research paper
• Role2: The Artist
  • Choose some authoring tool and create hot physically based demo reel
  • Present a selected research paper
  • Prepare a written report, at least 2 A4 pages, on the topic of state exam question.
• Projects with minimal requirements: Projects.pdf

• Teams fill the form (names and project): deadline 5.10.2015 Submit a link to created web page with project description or animation story board where you write your progress, continually.

Lesson01 "Introduction to Computer Animation"

• Introduction to Computer Animation
• Common animation techniques
• Cutting edge tools and packages
• Gurus and the State of the Art
• Lecture schedule
• "Terms and conditions" of this lecture
• Lecture notes: lesson01.pdf

Lesson02 "Basic methods in Computer Animation"

• Problem definition and motivations
• Key-framing and parameter interpolation
• Quternions, orientation
• Skeleton and skinning animation
• Forward and inverse kinematics
• Procedural techniques
• (Motion capture)
• Lecture notes: lesson02.pdf
• Štátnicová téma: S1 Animácie pohybu a orientácie, interpolačný spline na animáciu pohybu, splinu podľa dĺžky krivky, quaternion a orientácia, interpolácie dvoch a viacerých quaternionov.

Lesson03 "Particle Systems"

• Newton dynamics of particles
• Ordinary differential equation (ODE) solver
• Particle - obstacle collision detection
• Practical design of particle system
• Demos / tools / libs
• Lecture notes: lesson03.pdf
• Štátnicová téma: S2 Numerické riešenie diferenciálnych rovníc, Eulerova metóda, MidPoint metóda, Runge-Kuta metóda, podmienka stability na voľbu časového kroku, sily odozvy (response forces).

Lesson04 "Soft bodies, Cloths and hair”

• Problem definition and motivations
• Modeling solids with stress and strain
• Extending Mass-spring model for cloth and ropes
• Massive (self) collision and resolution for cloths
• Mesh-less deformations
• Modeling solids with infinitely stiff springs
• Demos / tools / libs
• Lecture notes: lesson04.pdf
• Štátnicová téma (Lesson 3,4): S3 Časticové systémy, rovnice pohybu prvého rádu, integračné metódy na výpočet rýchlosti a pozície, stavový vektor systému, vonkajšie sily, obmedzujúce podmienky – constraints, sily odozvy, kolízie častica - rovina.

Lesson05 "Broad Phase Collision Detection"

• Problem definition and motivations
• Hierarchical grids and spatial hashing
• Sweep and prune and radix sort
• Pair management – a practical guide
• Demos / tools / libs
• Lecture notes: lesson05.pdf

Lesson "All Saints' Day (no lesson)"

• No lesson

Lesson06 "Mid Phase Collision Detection"

• Problem definition and motivations
• Generic Bounding Volume Hierarchy (BVH)
• Tandem BVH traversal
• Proximity evaluation of primitive geometries
  • External Voronoi regions
  • Sphere x Capsule x Box x triangle collisions
• Approximate convex decomposition
• Lecture notes: lesson06.pdf

Lesson07 "Narrow Phase Collision Detection"

• Problem definition and motivations
• Proximity queries for convex objects (Minkowski space)
• GJK based algorithms (GJK, EPA, ISA-GJK)
• Voronoi-Clip (V-Clip) Algorithm
• Signed Distance Maps for collision detection
• Demos / tools / libs
• Lecture notes: lesson07.pdf
• Štátnicová téma (Lesson 5,6,7): S4 Detekcie kolízie, nutná a postačujúca podmienka kedy nie sú dve telesá v rovina, broad phase (hierachycká mriežka), mid phase (hierarchie obálok, Voronoiove oblasti v kolízii, vysvetlujte na príklade kolízie gula x kapsula, dekompozícia telesa na konvexné časti), narrow phase (Minkowskeho priestor a blízkosť konvexných telies).

Lesson08 "Rigid body Dynamics”

• Problem definition and motivations
• Dynamics of rigid bodies
• The equation of unconstrained motion (ODE)
• User and time control
• Mass properties of polyhedral objects
• Demos / tools / libs
• Lecture notes: lesson08.pdf
• Štátnicová téma (Lesson 9): S5 Dynamika tuhých telies, definícia problému, rovnice pohybu (4 ODE), rýchlosť, zrýchlenie, uhľová rýchlosť a uhľové zrýchlenie, matica hybnosti (matica inercie).

Lesson09 "Rigid body Collisions and Joints”

• Problem definition and motivations
• Simplified collision model
• Impulse based collision equation
• Friction-less collision resolution
• Algebraic collision resolution for Coulomb friction
• Linear and angular joint formulations
• Demos / tools / libs
• Lecture notes:lesson09.pdf

Lesson10 "Fluid, Fire and Smoke”

• Problem definition and motivations
• Navier-Stokes equations for fluid dynamics
• Grid based MAC method
• Particle based SPH method
• Neighbor search for coupled particles
• Modeling smoke and fire with fluid
• Demos / tools / libs
• Lecture notes: lesson10.pdf

Lesson11 "Final term"

• Don't panic - just few simple questions

Lesson12 "Animation Show"

• Show your animation to your colleagues

EXCERCISES

• Your presence at the seminar is optional.
• On every seminar we will focus on the selected problems from lessons. We will use the numerical methods to solve specific problems.

Excercise01 "Key Framing”

• Blender demo
• Blender https://www.blender.org/

Excercise02 "Quaternion Interpolation”

• Assigment
  • uloha1.pdf (deadline 8.10.)
  • resources:
    • catmull-rom.pdf
    • http://run.usc.edu/cs520-s15/quaternions/quaternions-cs520.pdf
    • http://www.academia.edu/4095904/Quaternion_calculus_as_a_basic_tool_in_computer_graphics
• Blender tutorial for skeleton modelling
  • rigging https://www.youtube.com/watch?v=mJwWTKt12ak

Excercise03 "Differential Equations”

• Analitical solution of ODE
• Runge-Kuta method
• Assigment
  • uloha2.pdf (deadline 22.10.)
  • resources:
    • diferencialne_rovnice.pdf
    • http://terpconnect.umd.edu/~petersd/246/matlabode.html
• Wolfram Mathematica http://mathworld.wolfram.com/
• FreeMat http://freemat.sourceforge.net/index.html
• Matlab tutorial http://www.tutorialspoint.com/matlab/index.htm

Excercise04 "Position based Dynamics”

• proving the distance constraint formulae
  • resources
    • Position based Dynamics.pdf
• Assigment
  • prepare presentation (deadline 29.10.)

Excercise05 "Particles”

• modeling particles
  • resources
    • https://www.youtube.com/watch?v=azXFwQWXjyQ

Excercise06 "STAR reports”

• STAR reports and paper presentations
  • animation resources
    • production.pdf
    • https://www.youtube.com/playlist?list=PL-bOh8btec4CXd2ya1NmSKpi92U_l6ZJd

Excercise07 "Separating Axis Theorem”

• Principal Components Analysis
• Assigment
  • uloha3.pdf (deadline 26.11.)
  • resources:
    • http://www.cs.otago.ac.nz/cosc453/student_tutorials/principal_components.pdf
    • http://www.sosmath.com/matrix/eigen2/eigen2.html
    • https://www.scss.tcd.ie/Rozenn.Dahyot/CS1BA1/SolutionEigen.pdf

RESOURCES

• Roman Ďurikovič, Vladimír Ďurikovič. Numerical Mathematics for Computer Science (in Slovak Numerická matematika pre informatika, Riešené príklady v programe MATHEMATICA). ISBN 978-80-8105-271-2, University of Saint Cyril and Metod Press, Trnava, Slovakia, pages 162, 2011. https://www.researchgate.net/publication/256681458_Numerick_matematika_pre_informatika_Rieen_prklady_v_programe_MATHEMATICA