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Announcements

Announcements. Class mailing list: send email to Hyoungjune Yi: aster@cs.umd.edu 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:

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Announcements

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  1. Announcements • Class mailing list: send email to Hyoungjune Yi: aster@cs.umd.edu • Homework at the end of class. • Text is on reserve in the CS library. • Powerpoint should be available by 10am class day.

  2. 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.

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

  4. Help • help • help command Eg., help plus • Help on toolbar • demo • Tutorial: http://amath.colorado.edu/scico/tutorials/matlab/

  5. Matlab interpreter • Many common functions: see help ops

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

  7. Indexing into vectors

  8. Vector Addition V+w v w

  9. Scalar Product av v

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

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

  12. Matrices Sum: A and B must have the same dimensions

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

  14. Matrices Transpose: A is symmetric If

  15. Matrices Determinant: A must be square

  16. Matrices Inverse: A must be square

  17. Indexing into matrices

  18. Euclidean transformations

  19. 2D Translation P’ t P

  20. P’ t ty P y x tx 2D Translation Equation

  21. P’ t ty P t y x tx 2D Translation using Matrices P

  22. Scaling P’ P

  23. Scaling Equation P’ s.y P y x s.x

  24. Rotation P P’

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

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

  27. Stretching Equation P’ Sy.y P y x Sx.x

  28. Stretching = tilting and projecting(with weak perspective)

  29. Linear Transformation SVD

  30. Affine Transformation

  31. Files

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

  33. Images

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

  35. 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.

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