module8 - Computational Geometry TOPICS Preliminaries Point...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
CSE5311 1 Computational Geometry TOPICS ± Preliminaries ± Point in a Polygon ± Polygon Construction ± Convex Hulls Further Reading Chapter 35 from Text book CSE5311 2 Geometric Algorithms Geometric Algorithms find applications in such areas as Computer Graphics Computer Aided Design VLSI Design GIS Robotics During this week we will study algorithms dealing with points, lines, line segments, and polygons In particular, the algorithms will Determine whether a point is inside a Polygon Construct a Polygon Determine Convex Hulls
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
CSE5311 3 Preliminaries: A point p is represented as a pair of coordinates (x,y) A line is represented by a pair of points A path is a sequence of points p 1 ,p 2 , . . . p n and the line segments connecting them, p 1 -p 2 , p 2 -p 3 , . . . , p k-1 -p k . A closed path whose last point is the same as the first is a polygon. A simple polygon is one whose corresponding path does not intersect itself. It encloses a region in the plane. A Convex Polygon is a polygon such that any line segment connecting two points inside the polygon is itself entirely in the polygon. The convex hull of a set of points is defined as the smallest convex polygon enclosing all the given points. CSE5311 4 A line segment connecting two points: The points are inside the polygon The line segment is not entirely in the polygon This is not a convex polygon p(x 1 ,y 1 ) q(x 2 ,y 2 ) r(x 3 ,y 3 ) s(x 4 ,y 4 )
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 10

module8 - Computational Geometry TOPICS Preliminaries Point...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online