Announcements Class mailing list: send to Hyoungjune Yi: Homework at the end of class. Text is on reserve in the.

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Presentation transcript:

Announcements Class mailing list: send to Hyoungjune Yi: Homework at the end of class. Text is on reserve in the CS library. Powerpoint should be available by 10am class day.

Matlab tutorial and Linear Algebra Review Today’s goals: Learn enough matlab to get started. Review some basics of Linear Algebra Essential for geometry of points and lines. But also, all math is linear algebra. (ok slight exaggeration). Many slides today adapted from Octavia Camps, Penn State.

Starting Matlab For PCs, Matlab should be a program. For Sun’s: Numerical Analysis and Visualization Matlab 6.1

Help help help command Eg., help plus Help on toolbar demo Tutorial: /matlab/

Matlab interpreter Many common functions: see help ops

Vectors Ordered set of numbers: (1,2,3,4) Example: (x,y,z) coordinates of pt in space.

Indexing into vectors

Vector Addition v w V+w

Scalar Product v av

Operations on vectors sum max, min, mean, sort, … Pointwise:.^

Inner (dot) Product v w  The inner product is a SCALAR!

Matrices Sum: A and B must have the same dimensions

Matrices Product: A and B must have compatible dimensions Identity Matrix:

Matrices Transpose: If A is symmetric

Matrices Determinant: A must be square

Matrices Inverse: A must be square

Indexing into matrices

Euclidean transformations

2D Translation t P P’

2D Translation Equation P x y txtxtxtx tytytyty P’ t

2D Translation using Matrices P x y txtxtxtx tytytyty P’ t tP

Scaling P P’

Scaling Equation P x y s.x P’ s.y

Rotation P P’

Rotation Equations Counter-clockwise rotation by an angle  P x Y’ P’  X’ y

Degrees of Freedom R is 2x2 4 elements BUT! There is only 1 degree of freedom:  The 4 elements must satisfy the following constraints:

Stretching Equation P x y S x.x P’ S y.y

Stretching = tilting and projecting (with weak perspective)

Linear Transformation SVD

Affine Transformation

Files

Functions Format: function o = test(x,y) Name function and file the same. Only first function in file is visible outside the file.

Images

Debugging Add print statements to function by leaving off ; keyboard debug and breakpoint

Conclusions Quick tour of matlab, you should teach yourself the rest. We’ll give hints in problem sets. Linear algebra allows geometric manipulation of points. Learn to love SVD.