Numerical analysis: 4th ed
Computational geometry: curve and surface modeling
Computational geometry: curve and surface modeling
IBM Journal of Research and Development
Locally controllable conic splines with curvature continuity
ACM Transactions on Graphics (TOG)
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
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
Geometric Hermite interpolation with maximal order and smoothness
Computer Aided Geometric Design
Hermite interpolation with Tschirnhausen cubic spirals
Computer Aided Geometric Design
Designing Fair Curves and Surfaces: Shape Quality in Geometric Modeling and Computer-Aided Design
Designing Fair Curves and Surfaces: Shape Quality in Geometric Modeling and Computer-Aided Design
Planar G2 Hermite interpolation with some fair, C-shaped curves
Journal of Computational and Applied Mathematics
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A long-standing problem in computer graphics is to find a planar curve that is shaped the way you want it to be shaped. A selection of various methods for achieving this goal is presented. The focus is on mathematical conditions that we can use to control curves while still allowing the curves some freedom. We start with methods invented by Newton (1643-1727) and Lagrange (1736-1813) and proceed to recent methods that are the subject of current research. We illustrate almost all the methods discussed with diagrams. Three methods of control that are of special interest are interpolation methods, global minimization methods (such as least squares), and (Bézier) control points. We concentrate on the first of these, interpolation methods.