• • EN

# 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

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

### Oral / Written Examination

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

### 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

• 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

# 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.

• resources:

### Excercise02 "Quaternion Interpolation”

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

### Excercise06 "STAR reports”

• animation resources

### Excercise07 "Separating Axis Theorem”

• Principal Components Analysis
• Assigment