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From “Geometric Tools for Computer Graphics”, the definition of convex given on pg 265 sec 7.7 is:

A set S is convex if given any two points P and Q in S,the line segment ( 1 − t ) P + t Q for t ∈ [0, 1] is also in S.

Said more plainly, if every line you can draw that connects two vertices a shape is completely contained inside the shape (tracing edges is allowed), then that shape is convex.

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