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In order to generate free-form curves passing through given point sequence without solving the simultaneous equations which represent the relationships between the coefficients of curve segments, a method of inserting an extra control point between each two subsequent control points has been developed. Two methods for determining such an extra control point, which is called additional control point, are discussed. First the method for using the approximated solutions of the simultaneous equations is considered. Next a new method simpler than the former ones, which needs not solve the simultaneous equations, is presented. Curves generated by these methods are compared with each other and compared with the curves generated by solving the simultaneous equations.

Determining Control Points of Free-form Curves for Interpolations.