Orientation
GeometryEasyVerify Clockwise, Counter Clockwise, or Collinear relationships of three coordinates.
Alt+Shift+O
Orientation Interactive Grid (Drag A, B, or C)
Determinant Cross Value:16
Resulting Orientation:Clockwise (CW)
Time Complexity
O(1) direct equations
Space Complexity
O(1) auxiliary
Conceptual Overview
Orientation of three ordered points in a 2D plane determines if they form a collinear line segment, a clockwise turn, or a counter-clockwise turn.
Mathematical Formula
val = (y_B - y_A)(x_C - x_B) - (x_B - x_A)(y_C - y_B) \\ \text{CW if } val > 0, \text{ CCW if } val < 0, \text{ Collinear if } val = 0
Source: CP-Algorithms geometry reference