difference matrix c 2 can be defined as q c 2 t c 2 where a trc can be calculated as f p t p u03b1q u2212 1 p t b where u03b1 is the smoothing parameter an initial smoothing parameter can be chosen by a person or it can be calculated as u03b1 tr p t p tr q where tr is the trace function in the example tr p t p 4 tr q tr c 1 t c 1 18 and therefore u03b1 0 22 using the matrices given the trc is if the trc is not smooth enough then a can be increased and another trc calculated conversely the trc can be too smooth which usually means that the trc does not agree well with the control points decreasing u03b1 reduces smoothness but increases agreement with the control points for example u03b1 0 01 gives fig6 illustrates a high level flow diagram for producing and refining a trc after the start 601 control points are obtained next a control vector and sampling matrix are constructed 603 as discussed above a smoothing matrix is obtained 604 and a smoothing parameter is then determined 605 before a trc is calculated 606 the process can stop at this point if there is no desire to refine the trc otherwise at least one image is printed using the trc 607 and the trc smoothness is checked 608 if the trc produces image contouring then the trc smoothness is not acceptable and the smoothing parameter is refined 609 in the direction of producing a smoother trc if the trc produces no image contouring then the trc smoothness is probably acceptable and the process flow is done 610 a.