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Approximation of circular arcs by quartic splines

Approximation of circular arcs by quartic splines. Ahn, Young Joon Dept. Math. Edu., Chosun Univ. History approximation of order 2n. C. Circular arc. Quartic basis of spline. Control coefficients. Quartic spline. Bernstein polynomial. coefficients. Quartic Bezier curves. Error function.

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Approximation of circular arcs by quartic splines

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  1. Approximation of circular arcs by quartic splines Ahn, Young Joon Dept. Math. Edu., Chosun Univ.

  2. Historyapproximation of order 2n

  3. C Circular arc

  4. Quartic basis of spline Control coefficients Quartic spline

  5. Bernstein polynomial coefficients Quartic Bezier curves

  6. Error function Alternative error function Hausdorff distance They have the maximum at the same positions

  7. & C0 end-point interpolation C1 end-point interpolation & symmetric Approximation Method

  8. b and C have GC0 at t=1/2 b and C have GC2 at t=1/2 Theorem[AhnKim] b and C have geometric contact of order k (GCk) at t0

  9. Polynomial of degree eight with zeros at t=0,0,1/2,1/2,1/2,1/2,1,1. Error Analysis

  10. Comparison of Hausdorff distance

  11. future works • Extension this method to all even degree (2) Extension to conic approximation (3) Extension to surface case (quadric surface)

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