Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
Nonlinear pyramid transforms based on median-interpolation
SIAM Journal on Mathematical Analysis
Subdivision Methods for Geometric Design: A Constructive Approach
Subdivision Methods for Geometric Design: A Constructive Approach
Gliding spline motions and applications
Computer Aided Geometric Design
Continuous M-Estimators and Their Interpolation by Polynomials
SIAM Journal on Numerical Analysis
A variational approach to spline curves on surfaces
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
Intrinsic subdivision with smooth limits for graphics and animation
ACM Transactions on Graphics (TOG)
Computer Aided Geometric Design
On parametric smoothness of generalised B-spline curves
Computer Aided Geometric Design
Bézier curves and C2 interpolation in Riemannian manifolds
Journal of Approximation Theory
Nonlinear subdivision through nonlinear averaging
Computer Aided Geometric Design
ACM SIGGRAPH Asia 2008 papers
Four-point curve subdivision based on iterated chordal and centripetal parameterizations
Computer Aided Geometric Design
ACM SIGGRAPH 2009 papers
Splitting methods for SU(N) loop approximation
Journal of Approximation Theory
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Curve subdivision schemes on manifolds and in Lie groups are constructed from linear subdivision schemes by first representing the rules of affinely invariant linear schemes in terms of repeated affine averages, and then replacing the operation of affine average either by a geodesic average (in the Riemannian sense or in a certain Lie group sense), or by projection of the affine averages onto a surface. The analysis of these schemes is based on their proximity to the linear schemes which they are derived from. We verify that a linear scheme S and its analogous nonlinear scheme T satisfy a proximity condition. We further show that the proximity condition implies the convergence of T and continuity of its limit curves, if S has the same property, and if the distances of consecutive points of the initial control polygon are small enough. Moreover, if S satisfies a smoothness condition which is sufficient for its limit curves to be C1, and if T is convergent, then the curves generated by T are also C1. Similar analysis of C2 smoothness is postponed to a forthcoming paper.