We propose an efficient real-space algorithm for the design of biplanar transverse gradient coils for use in open magnetic resonance imaging (MRI) systems. In our method, each wire arc is represented by a closed contour (Limacon). Using parametric equations, we deform/reshape an ensemble of closed contours in a simple manner, controllable by just a few parameters. These parameters are used to define system rearrangements in the design procedure. We use an iterative optimization procedure to adjust the control parameters in order to minimize cost functions such as gradient homogeneity and inductance. Here, we compare the coil pattern designed by our deformation-space method with a pattern designed by the conventional stream function approach, and we discuss the merit of the new method.