In an interactive design process, tools that provide visual feedback on the design model are highly valuable. This research explores a specific topic of graphical visualization and geometric modeling. An approach dealing with projecting and mapping plane curves onto a B-spline surface is presented. The curve is mapped onto the surface using normal projection. All points on the curve are projected onto the surface in the direction of the plane normal. Intersections of projected lines and the surface patches are then found. For an open surface, the curve need not be contained in the interior of the design surface, for if it is mapped out of the surface boundaries, a novel approach has been devised to determine the appropriate edge boundaries of the surface to close the out-of-bounds mapped curve. The issue of mapping curves onto a surface provides a means of attaining a higher level of detailed visualization in a design process, such as the visual feedback on the placement of control surfaces on aircraft wings in an aircraft conceptual design process. The mapped curves can also be treated as trim curves on the surface. This research also proposes an idea for approximating the trim curve with the iso-parametric line segments of the surface to address a probable solution to the many problems facing geometrical surface trimming. The complete curve mapping process has been implemented in the conceptual aircraft design software ACSYNT (AirCraft SYNThesis).