Abstract: With the advent of architectural CAD applications, architects and designers could model almost any curved surface geometry imaginable, whereas it is not an obvious task for engineers to efficiently create a grid structure on a complex surface that meets the architectural requirements. To generate regular and fluent grids over free-form surfaces, a grid generation method is presented based offsetting the guide curve on the surface directly, called spatial guide curve method. Firstly, one or two curves were defined as guide curves on the surface. Secondly, reference points were decorated on the guide curve with reasonable spacings, and then were offset and fitted into an offset curve on the surface extended properly. Thirdly, taking the newly generated offset curve as the guide curve, new offset curves were generated iteratively, and thus a set of offset curves were arranged. Finally, taking the offset curves as grid lines, the final grid was generated by doing operations on offset curves, like segmenting, connecting, trimming, etc. The grid trend was controlled by the guide curve. The grid size was controlled by offset distances of reference points and the grid shape was optimized by merging offset points which were too close. Cases studies were provided to illustrate the successful execution of these procedures. The results show that the grids generated by this method have advantages of regular shapes, fluent lines and desired trend, thereby satisfying aesthetic requirements.

Key words: free-form surface; grid structure; guide curve; grid generation