(Excercise03 "Differential Equations”)
Riadok 252: Riadok 252:
 
* Runge-Kuta method
 
* Runge-Kuta method
 
* Assigment
 
* Assigment
**[[media:uloha2Chaotic.pdf|uloha_diferencialne.pdf]] (deadline see Attendance table)
+
**[[media:uloha_dif_rov.pdf|uloha_dif_rov.pdf.pdf]] (deadline see Attendance table)
 
**resources:
 
**resources:
 
***https://www.youtube.com/watch?v=p_di4Zn4wz4
 
***https://www.youtube.com/watch?v=p_di4Zn4wz4

Verzia zo dňa a času 13:07, 18. október 2022

Ca10 lesson01.png

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

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%, 60 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 = +60..+18 or 12..0 (or Fx)
    • Excercises = +10..0
    • Final term = (better than Fx) +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
  • In case of online lecture connect to MS Teams Teams Teams code: 1himkdt

Oral / Written Examination

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



Lesson01 "Introduction to Computer Animation"

Ca10 lesson01.png

  • 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"

Ca10 lesson02.png

  • 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, nearest neighbor, lineárna interpolácia, interpolačný spline na animáciu pohybu, Kubická Bézierova interpolačná krivka, C1 spojitosť kompozície kriviek.
  • Štátnicová téma: S2 Quaternion a orientácia, os rotácie a uhol, reprezentácia quaterniónom, rotácia v priestore pomocou quaterniónov, inverzný quaternión, kompozícia rotácie dvoch quaterniónov, interpolácia SLERP (Sférická lineárna interpolácia), interpolácie dvoch a viacerých quaternionov, Catmull-Rom interpolácia.


Lesson03 "Particle Systems"

Ca10 lesson03.png

  • 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: S4 Numerické riešenie diferenciálnych rovníc, ODE prvého rádu separovateľné, Rovnice pohybu prvého rádu rýchlosť, zrýchlenie, Eulerova metóda, MidPoint metóda, Runge-Kuta metóda, podmienka stability na voľbu časového kroku.


Lesson04 "Soft bodies, Cloths and hair”

Ca10 lesson11.png

  • 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


Lesson05 "Broad Phase Collision Detection"

Ca10 lesson04.png

  • 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)"

Ca10 lesson07.png

  • No lesson


Lesson06 "Mid Phase Collision Detection"

Ca10 lesson05.png

  • 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"

Ca10 lesson06.png

  • 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): S3 Detekcie kolízie, nutná a postačujúca podmienka kedy nie sú dve telesá v kolízii, deliaca 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”

Ca10 lesson08.png

  • 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, Pozícia, ťažisko a orientácia telesa, rovnice pohybu (4 ODE), rýchlosť, zrýchlenie, uhľová rýchlosť a uhľové zrýchlenie, matica hybnosti (matica inercie) matica hybnosti pre guľu, pevný kváder, posunutý kváder.


Lesson09 "Rigid body Collisions and Joints”

Ca10 lesson09.png

  • 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”

Ca10 lesson10.png

  • 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"

Ca10 lesson12.png

  • 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 "Introductions”

Excercise02 "Quaternion Interpolation”

  • Assigment

Excercise03 "Differential Equations”

Excercise04 "Position based Dynamics”

Excercise05 "Particles”

Excercise06 "STAR reports”

Excercise07 "Separating Axis Theorem”

Excercise08 "Rigid body Dynamics”

RESOURCES