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### Mini-Presentation

**Computing Upper Envelope using Incremental Algorithm**

** The Problem: **

The Goal is to compute the upper envelope of a set of lines, using an already
defined algorithm used for computing CH for a set of points.

The problem is to find out which entries of the "dictionary" will be used to
this at each step of the algorithm.

**The "Known" Incremental Algorithm for Computing Convex Hull**

*Start w/ a set of pts.

*Sort points by x-coord

*Take the first 3 to form a triangle

*Add new pts in order

--- At each step compute tangents to find the new CH

--- Repeat for all points.

**Slight modification for computing lower CH**

*Start with a set of pts.

*Sort pts by x-coord

*Add points one by one

-- if the next pt in order is above p0, ignore and move to the next.

-- For the first two available points draw the connecting line

-- For each point:

if (line pi, pi-1 has pts below it)

{discard pt pi-1;

try forming lines w/ prev points

take the line that doesn't have any points below

else

draw line (pi, pi-1);

After transforming the steps of the algorithm using the duality dictionary,
this is what we get for the algorithm of uper envelope

*Start with a set of lines

*Take the intersection point oof the first line and the next avaialble one.

*For each line:

if (there are other prev intersection pts above that of li, li-1)

{discard line li-1;

try intersection pts with different lines;

take the one taht doesn't have any other pts above it;}

else

add that pt to the upper envelope

For more detailed presentation slides, check here