Department of Applied Informatics

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
• List of Open Source Physics Engines

Student Animation Projects

• Animácia Hunger
• Stránka Catching Spider Animácia Catching Spider
• Stránka Ráno do práce Animácia Ráno do práce
• Animácia Knihy
• Stránka Tvrdý Oriešok pre Vranu Animácia Vrana

What you Need to Pass

• Attend lessons. All lessons attended is +0 points. Four and more lectures missed you missed the course Fx.
• Solve all homework problems (mandatory each one >=30%, 50 points)
• Pass written Final term exam (mandatory each one >=30%, 30 points), no retakes. Realtime problem solution in Wolfram Mathematica or Wolfram Alpha.
• 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 (or Fx)
  • Homework = +50..+12 or 12..0 (or Fx)
  • Excercises = +20..0
  • Final term = +30..0
  • Optional oral exam = +20..0

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

• RESULTS

Oral / Written Examination

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

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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 rovine, 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.

Excercise00 "Key Framing”

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

• • resources:
  • Blender tutorial for skeleton modelling http://blender.freemovies.co.uk/stickman/
  • rigging https://www.youtube.com/watch?v=mJwWTKt12ak
  • motion capture database https://sites.google.com/a/cgspeed.com/cgspeed/motion-capture/daz-friendly-release

Excercise01 "Introductions”

• Vectors
  • https://reference.wolfram.com/language/tutorial/Lists.html#2534
• Matrices
• Linear interpolation
• https://www.wolfram.com/language/fast-introduction-for-programmers/en/interactive-usage/

• resources:
  • • uvod.pdf
    • catmull-rom.pdf

Excercise02 "Quaternion Interpolation”

• Assigment
  • uloha1.pdf (deadline see Attendance table)
    • HINT: If SLERP does not work, use linear interpolation.

• Euler angles
• Complex numbers and rotations
  • resources:
    • quaternion1.pdf
    • kvaternion2.pdf
    • http://run.usc.edu/cs520-s15/quaternions/quaternions-cs520.pdf
    • example.pdf
    • http://www.academia.edu/4095904/Quaternion_calculus_as_a_basic_tool_in_computer_graphics
    • https://www.youtube.com/watch?v=d4EgbgTm0Bg

Excercise03 "Differential Equations”

• Analitical solution of ODE
• Runge-Kuta method
• Assigment
  • uloha_diferencialne.pdf (deadline see Attendance table)
  • resources:
    • https://www.youtube.com/watch?v=p_di4Zn4wz4
    • https://emboliform.wordpress.com/test-page/solving-differential-equations-numerically-with-octave/
    • diferencialne_rovnice.pdf
    • explicit_midpoint.pdf
    • system_ode.pdf
    • http://terpconnect.umd.edu/~petersd/246/matlabode.html
    • https://computing.llnl.gov/casc/nsde/pubs/u113855.pdf
• Wolfram Mathematica http://mathworld.wolfram.com/
• FreeMat http://freemat.sourceforge.net/index.html
• Matlab tutorial http://www.tutorialspoint.com/matlab/index.htm
• Online Octave https://octave-online.net/

Excercise04 "Position based Dynamics”

• proving the distance constraint formulae
  • resources
    • Position based Dynamics.pdf

Excercise05 "Particles”

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

Excercise06 "STAR reports”

• • animation resources
    • production.pdf
    • https://www.youtube.com/playlist?list=PL-bOh8btec4CXd2ya1NmSKpi92U_l6ZJd

Excercise07 "Separating Axis Theorem”

• Principal Components Analysis
• Assigment
  • uloha_SAT.pdf (deadline see Attendance table)
  • resources:
    • principal_components.pdf
    • sat.pdf
    • 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

Excercise08 "Rigid body Dynamics”

• Rigid body Dynamics
• Assigment
  • domaca-uloha.pdf (deadline see Attendance table)

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