Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: An algorithm is presented to approximate planar offset curves within an arbitrary tolerance �> 0. Given a planar parametric curve C(t) and an offset radius r, the circle of radius r is first approximated by piecewise quadratic Bezier curve segments within the tolerance � . The exact offset curve Cr(t) is then approximated by the convolution of C(t) with the quadratic Bezier curve segments. For a polynomial curve C(t )o f degree d, the offset curve Cr(t) is approximated by planar rational curves, C a r (t)'s, of degree 3d − 2. For a rational curve C(t) of degree d, the offset curve is approximated by rational curves of degree 5d − 4. When they have no self-intersections, the approx- imated offset curves, C a (t)'s, are guaranteed to be within � -distance from the exact offset curve Cr(t). The effectiveness of this approximation technique is demonstrated in the offset computation of planar curved objects bounded by polynomial/rational parametric curves.
['In-Kwon Lee', 'Myung-Soo Kim', 'Gershon Elber']
I am writing a research paper on a idea Planar curve offset based on circle approximation
[{"from": "human", "value": "I am writing a research paper on a idea Planar curve offset based on circle approximation"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: An algorithm is presented to approximate planar offset curves within an arbitrary tolerance \ufffd> 0. Given a planar parametric curve C(t) and an offset radius r, the circle of radius r is first approximated by piecewise quadratic Bezier curve segments within the tolerance \ufffd . The exact offset curve Cr(t) is then approximated by the convolution of C(t) with the quadratic Bezier curve segments. For a polynomial curve C(t )o f degree d, the offset curve Cr(t) is approximated by planar rational curves, C a r (t)'s, of degree 3d \u2212 2. For a rational curve C(t) of degree d, the offset curve is approximated by rational curves of degree 5d \u2212 4. When they have no self-intersections, the approx- imated offset curves, C a (t)'s, are guaranteed to be within \ufffd -distance from the exact offset curve Cr(t). The effectiveness of this approximation technique is demonstrated in the offset computation of planar curved objects bounded by polynomial/rational parametric curves."}]