Abstract:
Subdivision is a method of generating smooth curves or surfaces. In recent years,
subdivision curves and surfaces have come to the forefront of geometric modeling.
There is a variety of existing subdivision schemes whose classification can be based
on different criteria. In this dissertation non-stationary subdivision schemes are de
veloped using the hyperbolic form of Lagrange-like interpolant, trigonometric and hy
perbolic forms of uniform B-spline. These schemes are presented mainly to overcome
the limitation of generation of conics by subdivision schemes especially parabolas and
hyperbolas. Asymptotic equivalence method has been used for convergence analysis
of the proposed schemes. Curvature plot technique has been employed to check the
accuracy and efficiency of the proposed schemes to construct conic-sections. The ge
ometrical behavior of the proposed schemes has been depicted through explanatory
examples.
