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1161. o. Juhasz I. [7] used similar idea of shape controlling except that he assumed end points to be unknown but known tangent vectors and signed curvatures. He constructed a solution to this problem by using Bezier representation of cubic arcs. The Bezier representation of cubic arc is derived mathematically using tangent vectors and curvatures and further two possible cases of tangent conditions were distinguished. A case when tangents vectors at end points are not parallel, one parameter family of cubic’s is obtained and another when the tangent vectors are assumed parallel, various cases for end curvatures are explored for which special cases were studied by keeping either or both of the end curvatures zero. The free parameters in both the tangent conditions were used to fulfil additional conditions like arc length, area and tangent directions for first case which can be used for curvature based curve blending with C1 ,G1 continuity and length, area and curvature conditions for the later which can also be used for constraint-based curve blending but with G2 continuity. Here the free parameters mean degrees of freedom. In the above case, loci of the end points are a straight line.
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