1. Admin; Starter Code Website Ready: Plans evolving...Website Ready: Plans evolving... Starter Code Ready: also evolves...Starter Code Ready: also evolves... About Your Projects:About Your Projects: –Simple directory-based version control: –Save & Number everything that works: NEVER edit an unsaved working program –Always, Always: One Little Step at a Time! –Explain it as you write it (comments) “Writing IS thinking”

2. Admin; Starter Code Website Ready: Plans evolving...Website Ready: Plans evolving... Starter Code Ready: also evolves...Starter Code Ready: also evolves... About Your Projects:About Your Projects: –Simple directory-based version control: –What works well for me: One master directory for the projectOne master directory for the project All files of latest version in one directoryAll files of latest version in one directory Numbered previous versions: ‘snapshot’ copiesNumbered previous versions: ‘snapshot’ copies Copy master directory EVERY time something works.Copy master directory EVERY time something works. Program is ALWAYS working; one step at a time...Program is ALWAYS working; one step at a time... > 1 hour without compile/run? too big a step!> 1 hour without compile/run? too big a step!

3. END --Please download the starter code, compile and run. --Then you can get started on Project 1 right away.

4. Conic Methods Review conics first (pg.8)Review conics first (pg.8) –‘Conics’ == intersection of cone & plane: –Many possible shapes: circles, ellipses, parabola, hyperbola, degenerates (lines & points

5. Conic Methods –Equation of any/all conics solve a 2D quadratic: ax 2 + bxy + cy 2 +dx +ey +f = 0 –Write in homogeneous coordinates: x T Cx = 0 x T Cx = 0 –C is symmetric, 5DOF ( not 6, because x 3 scaling) –Find any C from 5 homogeneous points (solve for null space—see book pg 9) a b/2 d/2 a b/2 d/2 b/2 c e/2 d/2 e/2 f x1x1x2x2x3x3x1x1x2x2x3x3 = 0 x 1 x 2 x 3 a ‘Point Conic’

6. Conic Methods –Matrix C makes conics from points: x T Cx = 0 C is a ‘point conic’ –Given a point x on a conic curve, the homog. tangent line l is given by l = C x –Matrix C* makes conics from lines: l T C*l = 0C* is a ‘Dual Conic’ defined by tangent lines l instead of points.

7. Conic Methods –If C is non-singular (rank 3), then C* = C -1 –If C (or C* ) has… Rank 3: it is an ellipse, circle, parab., hyperb. Rank 2: it is a pair of lines (forms an ‘x’) THE BIG IDEA---MOST USEFUL PROPERTY Projective transform of a conic C is conic C’: C’ = H -T C H -1 C’ = H -T C H -1