We present two simple and efficient algorithmic frameworks using signed distance functions. The first one is a numerical scheme for computing certain area reserving geometric motion of curves in the plane, such as area preserving motion by curvature. The second is a general technique for integrating over curves and surfaces that are not defined by any explicit parameterization. This method is based on rewriting the curve or surface integral as a volumetric integral formulation over the ambient space. We show applications of both methods.