The power and flexibility of polynomial surfaces are unleashed when their degrees are no longer restricted to four or lower, as they are used in early CT phantoms. They have proved useful and appropriate for geometric simulation of human and animal anatomy. In this paper a general algorithm is presented for the x-ray transform of any polynomial surface, as long as its ray-surface intersection equation is implemented on the computer. A versatile and powerful polynomial utility C++ class is created to simplify the implementation. Three groups of surfaces are implemented and applied to build a heart phantom closely simulating the Visible Man's heart. The x-ray transform algorithm is tested and verified by the successful reconstruction of the heart phantom.