FITTING B-SPLINES CURVES TO COARSE DATA CLOUD USING MODIFIED SQUARED DISTANCE MINIMIZATION METHOD

Abstract

Additive manufacturing has made us realize that we can fabricate complex shapes that were difficult to manufacture with subtractive processes. Topology optimizations results have complex shapes and have rough surfaces which are difficult to manufacture even by additive manufacturing. To automate the process of converting rough surfaces into smooth surfaces for the benefit of manufacturability would be very desirable.

Computing curve segments to approximate point cloud data that represents rough surfaces and then lofting it to have a smooth surface seems to be a promising methodology to achieve automation. We implement B-spline formulation along with Pottmann’s iterative method based on Squared Distance Minimization to automate the process of smoothening of rough surfaces. Calculation of foot points is a repetitive step within Squared Distance Minimization (SDM) method and accounts for considerable amount of computation time. In this research work, we proposed and implemented an algorithm on simple and complex shapes to help gain reduction in time required for foot point calculation. We will discuss ways to use this method effectively, dealing with instability, steps to reduce computation time and future work.