A combinatorial algorithm to construct the triangular convex skull of a hole-free \(\varvec{2}\) -D digital object is presented in this paper. The object that is a finite subset of \(\mathbb {Z}^{\varvec{2}}\) is assumed to lie on a triangular grid and the proposed algorithm finds a maximal-area connected set of triangles of the triangular grid that is convex. To obtain the required skull, the inner triangle cover that tightly inscribes the given \(\varvec{2}\) -D digital object is constructed first. A traversal is then made along the inner triangular cover from the top-left vertex to construct the triangular convex skull. To maximize the total area of the triangular convex skull, a few combinatorial rules are formulated to exclude some portion of the inner triangular cover. The proposed algorithm is efficient as makes use of addition and comparison in the integer domain. The correctness of the algorithm is verified on various hole-free \(\varvec{2}\) -D digital objects and results are very promising. The proposed algorithm has the time complexity of \(\varvec{O}\varvec{(n)}\) , where \(\varvec{n}\) is the number of vertices of the inner triangular cover.
