A system for creating a hybrid representation of a three-dimensional object having one or more sharp edges, the system comprising: a user-controlled haptic interface device adapted to provide a user input to a computer and to transmit force to a user according to a user interface location in a virtual environment; and coded instructions that, when executed by the computer, cause the computer to operate with said user input to: (a) generate a haptic representation of the three-dimensional object in said virtual environment, wherein said haptic representation is a hybrid representation comprising a combination of a volumetric representation portion and a geometric representation portion, wherein said geometric representation portion defines at least one sharp edge of said hybrid representation; and (b) determine force transmitted to said user via said haptic interface device according to an interaction by said user with said three-dimensional object in said virtual environment on the basis of the haptic representation such that the volumetric representation portion and geometric representation portion of the hybrid representation can be interacted with seamlessly, wherein the user can feel both the volumetric representation portion and the geometric representation portion, wherein the volumetric representation portion comprises a voxel-based representation and wherein the geometric representation portion comprises a resolution-independent geometric representation portion comprising a NURBS representation that defines the at least one sharp edge, (c) create an additional resolution-dependent portion of the geometric representation portion comprising a plurality of polygons which connect by tessellation the surface of a volumetrically-defined solid to the NURBS representation of a sharp edge attached to said solid so as to obtain a closed surface and a sharpness of said attached sharp edge that is higher in resolution than the quantized resolution of the voxel-based representation of the connected volumetric solid. a user-controlled haptic interface device adapted to provide a user input to a computer and to transmit force to a user according to a user interface location in a virtual environment; and coded instructions that, when executed by the computer, cause the computer to operate with said user input to: (a) generate a haptic representation of the three-dimensional object in said virtual environment, wherein said haptic representation is a hybrid representation comprising a combination of a volumetric representation portion and a geometric representation portion, wherein said geometric representation portion defines at least one sharp edge of said hybrid representation; and (b) determine force transmitted to said user via said haptic interface device according to an interaction by said user with said three-dimensional object in said virtual environment on the basis of the haptic representation such that the volumetric representation portion and geometric representation portion of the hybrid representation can be interacted with seamlessly, wherein the user can feel both the volumetric representation portion and the geometric representation portion, wherein the volumetric representation portion comprises a voxel-based representation and wherein the geometric representation portion comprises a resolution-independent geometric representation portion comprising a NURBS representation that defines the at least one sharp edge, (c) create an additional resolution-dependent portion of the geometric representation portion comprising a plurality of polygons which connect by tessellation the surface of a volumetrically-defined solid to the NURBS representation of a sharp edge attached to said solid so as to obtain a closed surface and a sharpness of said attached sharp edge that is higher in resolution than the quantized resolution of the voxel-based representation of the connected volumetric solid. (a) generate a haptic representation of the three-dimensional object in said virtual environment, wherein said haptic representation is a hybrid representation comprising a combination of a volumetric representation portion and a geometric representation portion, wherein said geometric representation portion defines at least one sharp edge of said hybrid representation; and (b) determine force transmitted to said user via said haptic interface device according to an interaction by said user with said three-dimensional object in said virtual environment on the basis of the haptic representation such that the volumetric representation portion and geometric representation portion of the hybrid representation can be interacted with seamlessly, wherein the user can feel both the volumetric representation portion and the geometric representation portion, wherein the volumetric representation portion comprises a voxel-based representation and wherein the geometric representation portion comprises a resolution-independent geometric representation portion comprising a NURBS representation that defines the at least one sharp edge, (c) create an additional resolution-dependent portion of the geometric representation portion comprising a plurality of polygons which connect by tessellation the surface of a volumetrically-defined solid to the NURBS representation of a sharp edge attached to said solid so as to obtain a closed surface and a sharpness of said attached sharp edge that is higher in resolution than the quantized resolution of the voxel-based representation of the connected volumetric solid.