We propose a method for interactive cloning of 3D surface geometry using a paintbrush interface, similar to the continuous cloning brush popular in image editing. Existing interactive mesh composition tools focus on atomic copy-and-paste of pre-selected feature areas, and are either limited to copying surface displacements, or require the solution of variational optimization problems, which is too expensive for an interactive brush interface. In contrast, our GeoBrush method supports real-time continuous copying of arbitrary high-resolution surface features between irregular meshes, including topological handles. We achieve this by first establishing a correspondence between the source and target geometries using a novel generalized discrete exponential map parameterization. Next we roughly align the source geometry with the target shape using Green Coordinates with automaticallyconstructed cages. Finally, we compute an offset membrane to smoothly blend the pasted patch with C1 conti...