Fitting point clouds with normal vectors by geometric algorithm

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Interpolation is one of the most typical problems that arise in the application of B-spline curves and surfaces. In this research we are interested in not only interpolating a set of points, but also normal vectors given at these points by the B-spline curves and surfaces. Applications of point-normal fitting include enhancement in the free-form curve design by adding the normal control, and accurate approximation of offset curves/surfaces. Our method relies on a surprisingly simple geometric algorithm which iteratively updates the input control points in a global manner based on local point-curve/surface distance computations, imposition of orthogonality conditions of the normal vector, and offsetting procedures. Examples are provided to demonstrate the effectiveness of the proposed algorithms.