# Union Copy Data Structure

## Union Copy Data Structure

• Submitted By: malakas12
• Date Submitted: 08/12/2013 5:01 AM
• Category: Technology
• Words: 1874
• Page: 8
• Views: 90

Introduction
Many TopCoders seem to be mortally afraid of geometry problems. I think it's safe to say that the majority of them would be in favor of a ban on TopCoder geometry problems. However, geometry is a very important part of most graphics programs, especially computer games, and geometry problems are here to stay. In this article, I'll try to take a bit of the edge off of them, and introduce some concepts that should make geometry problems a little less frightening.

Vectors
Vectors are the basis of a lot of methods for solving geometry problems. Formally, a vector is defined by a direction and a magnitude. In the case of two-dimension geometry, a vector can be represented as pair of numbers, x and y, which gives both a direction and a magnitude. For example, the line segment from (1,3) to (5,1) can be represented by the vector (4,-2). It's important to understand, however, that the vector defines only the direction and magnitude of the segment in this case, and does not define the starting or ending locations of the vector.