An apparatus for surgery preparation, the apparatus comprising: a tracking device for representing a surgical instrument; a display device for displaying a subject for surgery; one or more processors arranged to receive signals corresponding to the tracking device to determine the position of a virtual surgical instrument following the movement of the tracking device; and one or more memories comprising computer program code, the one or more memories and the computer program code configured to cause the one or more processors to: generate a model for three-dimensional representation of a tissue corresponding to the subject for surgery, the model comprising plurality of tissue elements arranged to together represent the tissue; based on the position of the virtual surgical instrument with respect to the tissue elements, alter the one or more constraints to indicate that a cut has been made to the tissue with the virtual surgical instrument; and characterized in that the one or more processors is further configured to determine a spatial location for each of the tissue elements with a local/global solver for a state equation of motion for the tissue elements, which local/global solver alternatingly obtains a set of local solutions under one or more constraints for the tissue elements indicating optimization of an elastic potential for the tissue elements and determines the spatial locations which optimize the state equation when the elastic potential corresponds to the local solutions. a tracking device for representing a surgical instrument; a display device for displaying a subject for surgery; one or more processors arranged to receive signals corresponding to the tracking device to determine the position of a virtual surgical instrument following the movement of the tracking device; and one or more memories comprising computer program code, the one or more memories and the computer program code configured to cause the one or more processors to: generate a model for three-dimensional representation of a tissue corresponding to the subject for surgery, the model comprising plurality of tissue elements arranged to together represent the tissue; based on the position of the virtual surgical instrument with respect to the tissue elements, alter the one or more constraints to indicate that a cut has been made to the tissue with the virtual surgical instrument; and characterized in that the one or more processors is further configured to determine a spatial location for each of the tissue elements with a local/global solver for a state equation of motion for the tissue elements, which local/global solver alternatingly obtains a set of local solutions under one or more constraints for the tissue elements indicating optimization of an elastic potential for the tissue elements and determines the spatial locations which optimize the state equation when the elastic potential corresponds to the local solutions. generate a model for three-dimensional representation of a tissue corresponding to the subject for surgery, the model comprising plurality of tissue elements arranged to together represent the tissue; based on the position of the virtual surgical instrument with respect to the tissue elements, alter the one or more constraints to indicate that a cut has been made to the tissue with the virtual surgical instrument; and characterized in that the one or more processors is further configured to determine a spatial location for each of the tissue elements with a local/global solver for a state equation of motion for the tissue elements, which local/global solver alternatingly obtains a set of local solutions under one or more constraints for the tissue elements indicating optimization of an elastic potential for the tissue elements and determines the spatial locations which optimize the state equation when the elastic potential corresponds to the local solutions.