ACM Transactions on Graphics (TOG)
Key developments in computer-aided geometric design
Computer-Aided Design
Trends in curve and surface design
Computer-Aided Design
Offsets of polynomial Be´zier curves: Hermite approximation with error bounds
Mathematical methods in computer aided geometric design II
Algorithms for computer algebra
Algorithms for computer algebra
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Functional composition algorithms via blossoming
ACM Transactions on Graphics (TOG)
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
The conformal map z→z2 of the hodograph plane
Computer Aided Geometric Design
NURB curves and surfaces: from projective geometry to practical use
NURB curves and surfaces: from projective geometry to practical use
Rational curves and surfaces with rational offsets
Computer Aided Geometric Design
Offset-rational parametric plane curves
Computer Aided Geometric Design
The symmetric analogue of the polynomial power basis
ACM Transactions on Graphics (TOG)
Bounds on the moving control points of hybrid curves
Graphical Models and Image Processing
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Comparing Offset Curve Approximation Methods
IEEE Computer Graphics and Applications
s-power series: an alternative to Poisson expansions for representing analytic functions
Computer Aided Geometric Design
s-power series: an alternative to Poisson expansions for representing analytic functions
Computer Aided Geometric Design
Hermite approximation for free-form deformation of curves and surfaces
Computer-Aided Design
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We propose a unified methodology to tackle geometry processing operations admitting explicit algebraic expressions. This new approach is based on representing and manipulating polynomials algebraically in a recently basis, the symmetric analogue of the power form (s-power basis for brevity), so called because it is associated with a “Hermite two-point expansion” instead of a Taylor expansion. Given the expression of a polynomial in this basis over the unit interval u &egr;[0, 1], degree reduction is trivally obtained by truncation, which yields the He many terms as desired of the corresponding Hermite interpolant and build “s-power series,” akin to Taylor series. Applications include computing integral approximations of rational polynomials, or approximations of offset curves.