PurposeTo focus on grid generation which is an essential part of any analytical tool for effective discretization.Design/methodology/approachThis paper explores the application of the possibility of unstructured triangular grid generation that deals with derivationally continuous, smooth, and fair triangular elements using piecewise polynomial parametric surfaces which interpolate prescribed R3 scattered data using spaces of parametric splines defined on R2 triangulations in the case of surfaces in engineering sciences. The method is based upon minimizing a physics‐based certain natural energy expression over the parametric surface. The geometry is defined as a set of stitched triangles prior to the grid generation. As for derivational continuities between the two triangular patches C0 and C1 continuity or both, as per the requirements, has been imposed. With the addition of a penalty term, C2 (approximate) continuity can also be achieved. Since, in this work physics‐based approach has been used, the grid is analyzed using intersection curves with three‐dimensional planes, and intrinsic geometric properties (i.e. directional derivatives), for derivational continuity and smoothness.FindingsThe triangular grid generation that deals with derivationally continuous, smooth, and fair triangular elements has been implemented in this paper for surfaces in engineering sciences.Practical implicationsThis paper deals with the important problem of grid generation which is an essential part of any analytical tool for effective discretization. And, the examples to demonstrate the theoretical model of this paper have been chosen from different branches of engineering sciences. Hence, the results of this paper are of practical importance for grid generation in engineering sciences.Originality/valueThe paper is theoretical with worked examples chosen from engineering sciences.