Physical based Animations and Mathematical Modelling (Course Materials)

Obsah

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

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.)
- 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.

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

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

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
Projects with minimal requirements: Projects.pdf

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: Animácie pohybu a orientácie, interpolačný spline na animáciu pohybu, reparametrizácia splinu podľa dĺžky krivky, quaternion a orientácia, interpolácie dvoch a viacerých quaternionov.

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: Numerické riešenie diferenciálnych rovníc, Eulerova metóda, Runge-Kuta metóda, podmienka stability na voľbu časového kroku.

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): 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.

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
Assigment 4: assigment4.pdf

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): Detekcie kolízie, Z buffer algoritmus, nutná a postačujúca podmienka kedy nie sú dve telesá v kolízii, deliaca rovina, hierarchie obálok, sily odozvy (response forces).

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): Dynamika tuhých telies, rovnice pohybu, rýchlosť, zrýchlenie, uhľová rýchlosť a uhľové zrýchlenie, matica inercie.

SEMINARS

On every seminar we will implement selected problems from lessons. We will use software Mathematica to solve specific numerical problems.

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.
Wolfram Mathematica http://www.wolfram.com/