Hermite variational implicit surface reconstruction

We propose a new technique for reconstructing surfaces from a large set of unorganized 3D data points and their associated normal vectors. The surface is represented as the zero level set of an implicit volume model which fits the data points and normal constraints. Compared with variational implicit surfaces, we make use of surface normal vectors at data points directly in the implicit model and avoid of introducing manufactured off-surface points. Given n surface point/normal pairs, the proposed method only needs to solve an nxn positive definite linear system. It allows fitting large datasets effectively and robustly. We demonstrate the performance of the proposed method with both globally supported and compactly supported radial basis functions on several datasets.