Geometry representation, modification and iterative design using RKEM

We present a new method for representing smooth geometry using the reproducing kernel element method. Further, the formulation provides a simple method to modify geometry that does not require modification of the underlying RKEM mesh. We develop a method for determining the representation from a discrete point set that is applicable to both traditional engineering domains, as well as applications where only discrete point sets are available, such as biology and medicine. Geometry representation and modification are demonstrated using examples of analytic functions and on a digitized shark tooth. Finally, we develop an isogeometric analysis capability for modified and un-modified geometry. The isogeometric capability on modified geometry may be useful in an iterative design-analyze cycle or shape optimization.