# I need to program a test for polygonal convexity

I’ve just started programming in OpenGL. For my first program I need to create a polygon by clicking the mouse in the window. Each left-click adds a vertex, when I’m done clicking, I hit enter and the program displays the program. This portion I have working already. I just store the values of the vertices in a 3 dimensional array, the figure is 2d. How do I go about coding a test to determine if the polygon is convex or not?

If the polygon is defined by edges E1, E2,…En;

E1 X E2, E2 X E3,… En-1 X En all should point in the same direction (either up from the polygon or down … assuming the polygon is planer… contained in a single plane.)

• Chetan

Could you elaborate please? I’m unsure as to what you mean.

asuming your vertexs are (x1,y1,z1),(x2,y2,z2),(x3,y3,z3),(x…,y…,z…) and all the z coords are the same, then
n=(x2-x1)(y3-y2)-(x3-x2)(y2-y1)
n should be + or - depending if the points are convex or concave or will be 0 if in a streight line
email me if it dosnt work, I wrote this from memory email address is fuz_king@yahoo.co.nz

Check that the dot products of each line pair in the sequence have the same sign, make sure you check the boundary condition.

What is the dot product?

the dot product is just a multiplication of the coordinates of each point, for example u=(u1,u2,u3…un) v=v1,v2,v3…vn) thus the dot product would be
u . v = (u1v1+u2v2+u3v3…unvn)