Geometry -> Vector And Orientation

Dot, cross, orientation, signed area, and exact integer geometry as the basis of most planar algorithms.

• Topic slug: geometry/vector-orientation
• Tutorial page: Open tutorial
• Ladder page: Open ladder
• Repo problems currently tagged here: 7
• Repo companion pages: 2
• Curated external problems: 5

Microtopics

• dot-product
• cross-product
• ccw
• signed-area
• collinearity
• integer-geometry

Learning Sources

Source	Type
cp-algorithms basic geometry	Reference
cp-algorithms oriented area	Reference
Princeton geometric primitives	Course

Practice Sources

Source	Type
CSES Point Location Test	Practice
CSES Polygon Area	Practice
CSES Line Segment Intersection	Practice

Repo Companion Material

Material	Type
Geometry cheatsheet	quick reference
Templates overview	template guide

Curated External Problems

Core

Problem	Source	Difficulty	Context	Style	Prerequisites	Tags	Why it fits
Point Location Test	CSES	Easy	-	Implementation	Cross Product Sign	Cross Product; Half-Plane; Left-Right; Point-In-Sector	Simple orientation logic with a direct geometric interpretation.
Polygon Area	CSES	Easy	Shoelace	Formula Derivation	Cross Product	Shoelace Formula; Area; Signed-Area; Cross-Product; Polygon	Shoelace is just accumulated oriented area.
Triangle	Codeforces	Easy	Triangle-Classification	-	-	Right-Angle; Integer-Coordinates; Bruteforce	A compact geometry check built entirely around distances and angle tests.
Line Segment Intersection	CSES	Medium	Segment-Geometry	Case Analysis	Orientation Test; Bounding Boxes	Segment Intersection; Cross Product; Ccw; Intersection	The standard cross-product intersection test in its cleanest form.
Triangle	Codeforces	Medium	Construction	-	-	Integer-Points; Right-Triangle; Existence	A direct construction problem for a right triangle on the integer grid.

Repo Problems

Code	Title	Fit	Difficulty	Pattern	Note	Solution
CONVEXHULL	Convex Hull	secondary	medium	andrew monotone chain; strict turn pop; boundary collinear points	Note	Code
LINESEGMENTINTERSECTION	Line Segment Intersection	secondary	easy	orientation test; on segment inclusion; collinear overlap handling	Note	Code
POINTINPOLYGON	Point in Polygon	secondary	medium	ray casting parity; boundary classification; on segment test	Note	Code
POINTLOCATIONTEST	Point Location Test	primary	easy	cross product orientation; signed area test; turn classification	Note	Code
POLYGONAREA	Polygon Area	secondary	easy	shoelace formula; signed area accumulation; integer polygon area	Note	Code
PRAVO	Tam giác vuông	secondary	medium	count right triangles; normalized directions; perpendicular pairing	Note	Code
VMCOINS	Trò chơi với những đồng xu	secondary	hard	promise-driven constructive; translation matching; small residual search	Note	Code

Regeneration

python3 scripts/generate_problem_catalog.py