1. A method for rendering an image on computer system including a processor and a display, the method comprising: determining a first two-dimensional displacement map associated with a first surface material and a first value for an input parameter in the processor, wherein a value of a pixel of a two-dimensional displacement map is associated with a displacement; determining a second two-dimensional displacement map associated with the first surface material and a second value for the input parameter in the processor; determining a three-dimensional displacement data structure in the processor in response to the first two-dimensional displacement map, the first value for the input parameter, the second two-dimensional displacement map, and the second value for the input parameter in the computer system; receiving a third value for the input parameter; determining a third two-dimensional displacement map associated with the first surface material in the processor in response to the three-dimensional displacement data structure and the third value for the input parameter in the computer system, wherein determining the three-dimensional displacement data structure comprises interpolating the first two-dimensional displacement map and the second two-dimensional displacement map to form the third two-dimensional displacement map in the processor; rendering an image of an object in the processor, wherein an appearance of a surface of the object is determined in response to the third two-dimensional displacement map; and displaying the image on the display to a user.