This paper is concerned with the approximate solution of partial differential equations using meshfree Galerkin methods on arbitrary domains in two space dimensions which we assume to be given as CAD/IGES data. In particular we focus on the particle-partition of unity method (PPUM) yet the presented technique is applicable to most meshfree Galerkin methods. The basic geometric operation employed in our cut-cell type approach is the intersection of a planar NURBS patch and an axis-aligned rectangle. Note that our emphasis is on the speed of the clipping operations since these are invoked frequently while trying to attain a small number of patches for the representation of the intersection. We present some first numerical results of the presented approach.
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