A Test for the Convexity of a Quadrilateral
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This Demonstration draws the quadrilateral green if convex, orange if concave, and red if reflex.
Contributed by: Jon Perry (October 2009)
Open content licensed under CC BY-NC-SA
The idea is to check if the diagonals of the quadrilateral intersect as line segments. See P. Bourke, "Intersection Point of Two Lines (2 Dimensions)" and take note of the last paragraph. The formulas involve determinants; see the Wikipedia entry, "Line-Line Intersection".
"A Test for the Convexity of a Quadrilateral"
Wolfram Demonstrations Project
Published: October 2 2009