To design conformally invisible cloaks for arbitrarily shaped objects, we use the nonuniform rational B -spline (NURBS) to represent the geometrical modeling of the arbitrary object. Based on the method of optical transformation, analytical formulas of the permittivity and permeability tensors are proposed for arbitrarily shaped invisible cloaks. Such formulas can be easily implemented in the design of arbitrary cloaks. Full-wave simulations are given for heart-shaped invisible cloaks and perfectly electrical conducting (PEC) objects, in which we observe that the power-flow lines of incoming electromagnetic waves will be bent smoothly in the cloaks and will return to their original propagation directions after propagating around the object. We also show that the scattered field from the PEC object coated with the invisible cloak is much smaller than that from the PEC core. The application of NURBS in the design of arbitrary cloaks shows transformation optics to be a very general tool to interface with commercial softwares like 3D STUDIOMAX and MAYA.