Introduction
Smallest enclosing circle algorithm
Randomized incremental construction
Smallest enclosing circles and more
Computational Geometry
Lecture 6: Smallest enclosing circles and more
Computational Geometry
Lecture 6: Smallest enclosing circles and

Motivation
Line segment intersection
Plane sweep
Line segment intersection for map overlay
Computational Geometry
Lecture 2: Line segment intersection
for map overlay
Computational Geometry
Lecture 2: Line segment intersection for map overlay
Motivation
L

Orthogonal range searching part II
Orthogonal range searching
1
Range trees (recap)
Input: A set of n points S=cfw_s1, s2, , sn in the plane.
Aim: Preprocess S such that orthogonal range queries can be
handled efficiently.
2
Range trees
Observation: A 2D-

Brute-Force Triangulation
1. Find a diagonal.
2. Triangulate the two resulting subpolygons recursively.
How to find a diagonal?
w
leftmost
vertex
w
v
v
u
u
case 1
closest
to v
O(n) time to find a diagonal at every step.
(n 2) time in the worst case.
case

Motivation
Line segment intersection
Plane sweep
Line segment intersection for map overlay
Computational Geometry
Lecture 2: Line segment intersection
for map overlay
Computational Geometry
Lecture 2: Line segment intersection for map overlay
Motivation
L

Planar Subdivision
Induced by planar embedding of a graph.
Connected if the underlying graph is.
edge
Complexity = #vertices + #edges + #faces
vertex
face f
Typical operations:
Walk around a face.
hole in f
disconnected subdivision
Access one face from an