A method comprising: transforming a three-dimensional image representing at least bony tissue cranio-facial features of a patient into an interactive two-dimensional image representing the same bony tissue cranio-facial features of a patient by defining a base ellipse which further defines an x-y coordinate plane for the three-dimensional image and by defining a base circle having its center at the origin of the x-y coordinate plane, then transforming the two-dimensional image to an intermediate image by mapping the base ellipse to the base circle, then transforming the intermediate image into a linear profile that forms the interactive two-dimensional image having one or more portions each associated with a corresponding portion of a bony tissue cranio-facial feature and containing at least one polygon or control point overlaid on the image at least one location; displaying one or more interactive two-dimensional images such that a user may, via a user input device, cause movement of at least one of the one or more portions of such two-dimensional image to simulate movement of the corresponding portion of the patient's bony tissue in an osteotomy procedure; displaying a three-dimensional image representing exterior soft-tissue cranio-facial features of the patient; receiving input from a user regarding movement of a particular portion of the one or more portions of the two- dimensional image, wherein input causes movement of at least one polygon or control point to at least one new location; and redrawing the three-dimensional image based at least on the movement of the particular portion of the two- dimensional image to simulate response of the exterior soft- tissue cranio-facial features of the patient to movement of a portion of the patient's bony tissue corresponding to the particular portion of the two-dimensional image, wherein redrawing uses at least one location of least one polygon or control point. transforming a three-dimensional image representing at least bony tissue cranio-facial features of a patient into an interactive two-dimensional image representing the same bony tissue cranio-facial features of a patient by defining a base ellipse which further defines an x-y coordinate plane for the three-dimensional image and by defining a base circle having its center at the origin of the x-y coordinate plane, then transforming the two-dimensional image to an intermediate image by mapping the base ellipse to the base circle, then transforming the intermediate image into a linear profile that forms the interactive two-dimensional image having one or more portions each associated with a corresponding portion of a bony tissue cranio-facial feature and containing at least one polygon or control point overlaid on the image at least one location; displaying one or more interactive two-dimensional images such that a user may, via a user input device, cause movement of at least one of the one or more portions of such two-dimensional image to simulate movement of the corresponding portion of the patient's bony tissue in an osteotomy procedure; displaying a three-dimensional image representing exterior soft-tissue cranio-facial features of the patient; receiving input from a user regarding movement of a particular portion of the one or more portions of the two- dimensional image, wherein input causes movement of at least one polygon or control point to at least one new location; and redrawing the three-dimensional image based at least on the movement of the particular portion of the two- dimensional image to simulate response of the exterior soft- tissue cranio-facial features of the patient to movement of a portion of the patient's bony tissue corresponding to the particular portion of the two-dimensional image, wherein redrawing uses at least one location of least one polygon or control point.