Basic

Distance

Euclidean Distance

The distance between points p(x1, y1) and q(x2, y2) is given by

Manhattan Distance

The distance between points p(x1, y1) and q(x2, y2) is given by

Triangle

Signed Area

The area consist of three points p(x1, y1), q(x2, y2) and r(x3, y3) is given by

The advantage of this method is to check the alignment sequence of the three points using the sign as the following

Line

Intersection

Using the signed triangle area, two lines intersect if the following conditions are right.

References

1. Graphics Gems
2. 計算幾何―理論の基礎から実装まで (アルゴリズム・サイエンスシリーズ―数理技法編)
3. Computational Geometry: Algorithms and Applications