Probability Theory Review
Random variable: discrete versus continuous.
Expected value of a discrete RV:
E[V] i P[V i]
(assumes V is nonnegative)
i 0
Density and distribution functions.
For a discr
PPGCC Linha de Pesquisa SIV
Disciplina: Animao Computadorizada
Prof. Dr. Soraia Raupp Musse
Psdoc Dr Leandro Dihl
12/05/2015
Cloth Simulation
Cloth simulation has been an important topic in computer
ComputerGraphicsProgramming:
MatricesandTransformations
Outline
Computergraphicsoverview
Obj /G
Object/Geometrymodeling
d li
2Dmodelingtransformationsandmatrices
3Dmodelingtransformationsandmatrices
R
Interpola*on
and
Curves
and
Mo*on on a Path
Problem statement
How can we construct smooth paths?
Dene smoothness in terms of geometry
What is the input?
Where
Rota%on representa%on and
Interpola%on
Rota%on
Matrices
Rota%on Matrix must be orthonormal
Rota%on matrix is also the local coordinate system!
v
u
w
ux
M = uy
uz
vx
vy
vz
w
Chapter 24: SingleSource Shortest Paths
Given: A single source vertex in a weighted, directed
graph.
Want to compute a shortest path for each possible
destination.
Similar to BFS.
We will assume
Splay Trees
Our text for this
topic is the handout
SplayTrees.
Optional reading: SplayTreesJournalPaper.
In balanced tree schemes,
explicit rules are followed to ensure balance.
In splay trees, t
Chapter 25: AllPairs Shortest Paths
Application: Computing distance table for a road atlas.
Atlanta
Atlanta Chicago 650
Detroit 520
Chicago
650
210
Detroit
520
210

One Approach: Run singlesource
Chapter 18: BTrees
Example:
M
Note: Each leaf
has the same depth
BC
QTX
DH
FG
JKL
NP
RS
VW
YZ
Node x has the following fields:
n[x]  number of keys stored in x.
key1[x] key2[x] keyn[x][x]  the n[x
Chapter 21: Disjoint Sets
Want to maintain a collection S = cfw_S 1, , Sk of disjoint dynamic sets.
Each set has a representative member.
Operations:
MakeSet(x): Make new singleton set containing
Chapter 19: Binomial Heaps
A way to implement mergeable heaps.
Useful in scheduling algorithms and graph algorithms.
Operations:
Jim Anderson
This is Chapter 19 from
an old edition of the book.
See
Comp 455
Models of Languages and Computation.
Usually taught each Fall and Spring.
Common Textbooks:
Introduction to Automata Theory, Languages, and
Computation, Hopcroft, Motwani, and Ullman,
Add
Skip Lists
Our text for this
topic is the handout
SkipLists.
Supports same operations as redblack tree.
Key Idea: Store keys in sorted linked list, with
the following twist:
Provide extra pointer
Rigid Body Dynamics
Huamin Wang
The motion of a rigid body contains two parts: linear motion and angular motion. In this document, we will study both motions. We will also discuss how to detect collis