Chapter 1
Convex Set
A $T\subset\mathbb{R}^n$ is convex if $\forall x,y\inT, the segment $[x,y]in T$.
Exmaples:
- Filled in circle
- Regular filled - polygon.
- Strait line.
Not Examples:
- Seperated points or shapes
- Stars
- Polygons with concave edges.
- commonly intersection of shapes.
- any non straigth line.
Convex Hull of set T
A convex hull of T, conv(T), is the smallest convex set that contains T.
Example:
- T is 5-point regular star, conv(T) is the pentagon connecting the stars tips.
- T = {a,b}, conv(T)=[a,b]
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