For over 60 years researchers have worked on Numerical Control (NC) machines and CAx Software to implement toolpath strategies for sculpture surface manufacturing. Despite the significant progress since the beginning, automatic finishing processing for lapping or polishing is in general not possible. The quality of finishing processing relies mainly on manual skill, therefore requiring very experienced employees. To correct these deficiencies, the VDI/VDE Inno-Net 5570 Project was started, on which this thesis focuses with the algorithms for the CAD/CAM-Module to implement the toolpath strategies for finishing processing.In a first step, we investigated necessary toolpath conditions for finishing processing, which are the basis for our algorithms. It is desired that the trajectory is smooth, covers the whole surface without intersecting itself, and starts and ends at the border of the workpiece.General implementations of toolpath strategies calculate the toolpath on the surface and apply a gouge check afterwards and correct the path when necessary. However, the gouge check is computationally very expensive and difficult to implement. To avoid this step we use a precomputed configuration space (c-space), which makes the gouge check obsolete. The c-space is given in form of a regular quadrilateral height field mesh, which may be adaptively subdivided where the slope is large. Operating in a piecewise linear space suffices when using the G60-Mode. In the G60-Mode the toolpath is transferred to the machine controller as a piecewise linear curve and the controller converts it into a sufficiently smooth curve for the current processing application. This simple data structure is memory efficient and is widely used in CAD/CAM frameworks. Furthermore, it avoids the issues of patch-boundary oscillations or long stretched triangles, when operating on NURBS surfaces or triangular meshes.Our approach to fulfill the necessary conditions is based on offset curves, which ensure equal distances between neighboring curves and cover the whole surface. Since start- and stop-movements of the tool produce artifacts on the surface, we avoid multiple ones and guarantee having them at the border by generating a double spiral curve out of the offset curves. To flexibly fill the space between neighboring parts of the curve, we generate cycloid curves that are superimposed with the double spiral. We developed a fast technique to check for collisions between the processing robot and the workpiece when operating on the generated path during simulation.One can create the offset curves by iteratively intersecting the c-space with a surrounding tube of the current curve to generate each subsequent curve. The tube results from a C°-continous concatenation of cylinders surrounding the single piecewise linear curve segments. In each iteration step the intersecting points of the tube with the not-yet traversed part of the mesh are detected and checked for validity. The validity check efficiently removes global and local self-intersections of the new curve by just deleting the respective points. In a final step the detected points are connected to the next offset curve. Dealing with piecewise linear curves, we achieve low computation times for real world data sets.By blending adjacent offset curves and filling the center with a curve in b-spline form, one can create a double spiral curve. In the case that the input offset curve is split into multiple components, our algorithm creates several double spiral curves and connects them to one large intersection-free curve with starting and end-point on the border of the workpiece. The start and end-point position on the border can be chosen by the user. In the end, we create the overlaying cycloids for the spiral curve by successively intersecting the c-space with spheroids. Each intersection results in an elliptic arc; connecting these arcs forms the cycloid curve. The size of the spheroid can be flexibly adjusted to fill variations between adjacent parts of the toolpath.We developed a collision check algorithm for fast collision avoidance of the arms of the robot with the work piece and for accelerating sphere dropping. The latter is used for initializing the c-space. The algorithm is based on an extended linked voxel structure by adding distance values to the corner of the voxels and linking empty voxels to non-empty voxels. With the help of the link fewer voxels have to be considered to find the desired one and hence, fewer triangles of the mesh have to be considered for the collision check. The triangles within each non-empty voxel are stored in a bsp-tree.