One problem in the field of computational geometry is the triangulation of convex layers. The rotating caliper algorithm is an alternative to the constrained Delaunay triangulation method. We present an improved triangulation algorithm, which gives a mesh quality close to that of the Constrained Delaunay but substantially faster. Each layer will be connected to the neighboring layer by edges and from the two vertices constituting an edge the proposed algorithm will select the shortest diagonal to its next neighbors in the polygonal chain on the other side, i.e. from the outer layer to the inner layer or vice versa. We discuss quality issues regarding the rotating caliper method and some improvements to it, as well as how a Constrained Delaunay can be efficiently implemented for convex layers.