There has been a disparity between the conventional method of describing topographic surfaces (i.e. contour line definition) and a format of surface description often used in continuous-line computer graphics (i.e. panel definition). The two differ enough that conversion from contours to panels is not a trivial problem. A computer program that performs such a conversion would greatly facilitate continuous tone display of topographical surfaces, or any other surface which is defined by contour lines. This problem has been addressed by Keppel and alluded to by Fuchs. Keppel's is a highly systematic approach in which he uses graph theory to find the panel arrangement which maximizes the volume enclosed by concave surfaces. Fuchs mentions an approach to the problem as part of an algorithm to reconstruct a surface from data retrieved from a laser scan sensor. This thesis elaborates on a general conversion system. Following a brief overview of computer graphics, a simple algorithm is described which extracts a panel definition from a pair of adjacent contour loops subject to the restriction that the two loops are similarly sized and shaped, and are mutually centered. Next, a mapping procedure is described which greatly relaxes the above restrictions. It is also shown that the conversion from contours to panels is inherently ambiguous (to various degrees) and that occasionally the ambiguity is great enough to require user interaction to guide the conversion algorithm. An important complication addressed in this thesis is the problem of handling cases where one contour loop branches into two or more (or vice versa). Attention turns next to a contour line definition of the human brain, and special problems encountered in preparing those data for continuous tone display, The final chapters explain the fortran implementation, present an example-problem, and show sample pictures of the brain parts.