p-Patches

H. Prautzsch, G. Umlauf

Beside the subdivision surfaces there are other methods for modelling of freeform surfaces. A very common but yet simple method are p-patches.

Here one too starts with an initial control net (left picture). With help of common CAGD methods (see Java Applets) one can construct from that net a surface with holes (middle pictue). Each hole corresponds to a node in the net that has not exactly six edges associated. An efficient method of how to fill these holes with "smooth" surface pieces are p-patches (right picture).


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Within a DFG-Project the freeform splines of [Prautzsch, CAGD 1997] are developed further. The free parameters of this construction are used to generate fair surfaces. Therefor a software-package has been implemented which computes free-form-splines of arbitrary topology and bidegree 4 and 6 respectively of geometric continuity 1 and 2 respectively.

Furthermore the freeform splines have been used for reconstruction of a surface form points. Thereby especially hierarchical approaches were stressed. In order to transfer the freeform splines to triangular nets, products of box splines have to be calculated. These products are no longer box splines. Thus the structure of the spaces containing those products was analysed.