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Different approach to convex decomposition for games

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For a physics engine that i've built i've constructed a set of algorithms that will convert a drawn graphic into a set of convex polygons to be used in the engine, however i'm looking around different methods that will give better performance, one idea i've come up with gives me something like this: as you can see the set of convex polygons is bound to a grid and i'm using a variant of marching squares to construct the original set of polygons. Now, my idea behind this is that if i'm using a regular grid for broadphase collision detection, every polygon for the terrain is bound to a single cell of the grid without any very long thin triangles that are not very good for the broadphase, and can sometimes give dodgy results when colliding with them. I don't really have a means of testing properly the difference in performance between this method, and simply performing a convex decomposition on the full sized terrain polygons unbounded to a grid. Anyone have any ideas on whether this is good idea or not?

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