AlgoScope

Orientation

AlgorithmintermediateGeometry Primitives

Clockwise, counter-clockwise or collinear from the sign of the cross product of (b - a) and (c - a).

Decision · step 2 of 3Plane Geometry: A left turn
ABC

cross(AB, AC) = 5 x 5 - 1 x 3 = 22. Positive: C is to the left of the line through A and B, so the path turns left (counter-clockwise). The magnitude, 22, is twice the area of triangle ABC.

Open in the player →or start at step 2

What you will see

Three points; the turn at b is labelled left or right.

How plane geometry works →

Cost

BestO(1)
AverageO(1)
WorstO(1)
SpaceO(1)

How you work with it here

play it through, step one change at a time, scrub to any step, run it on your own input, try operations in any order.

Screen readers: Points announce coordinates and role; each step announces the geometric test and its result in words (left turn, intersects).

Reduced motion: Shapes appear in place; the sweep line jumps between events.

Before this

Leads to

Topics that need this one first.