Solving flames in scalar or composition space usually requires the modeling of scalar dissipation rates, or scalar gradients, which appear in the Jacobian of the transformation from the physical-space coordinates to the scalar space coordinates attached to the flame surface. Recently, Scholtissek et al. (2019) have discussed a self-contained solution for freely propagating premixed flames, in which the gradient distribution of the coordinate is also solved in scalar space. This approach is here extended to include curvature, strain and effects of unsteadiness. The resulting method is applied to a constant pressure and homogeneous ignition case, a stagnation flame, a tubular flame and a spherical expanding flame, capturing accurately effects of unsteadiness, strain and curvature. The results are systematically validated against physical-space solutions and experiments. In addition to the possibility of exploring these various canonical problems with a single set of equations, it is shown that another major outcome of this new formulation lies in the possibility of studying steady flames subjected to negative strain.