Browsing by Author "Ramanantoanina, Andriamahenina"

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    Trigonometric Tangent Interpolating Curves
    (The Eurographics Association, 2024) Ramanantoanina, Andriamahenina; Hormann, Kai; Chen, Renjie; Ritschel, Tobias; Whiting, Emily
    Due to their favourable properties, cubic B-spline curves are the de facto standard for modelling closed curves in computer graphics and computer-aided design. Their shapes can be modified intuitively by moving the vertices of a control polygon, but they are only twice differentiable at the knots. Even though this is sufficient for most applications, curves with higher smoothness are still of valuable interest. For example, periodic Bézier curves provide an alternative for designing closed curves as C∞ smooth trigonometric polynomials, but their shapes are not as intuitive to control, because of the global influence of each control point. The same space of curves can also be described in vertex interpolating form, but this may result in other shape artefacts. In this paper we introduce two new representations of trigonometric polynomial curves that are inspired by the idea behind polynomial Gauss-Legendre curves and likewise use the control polygon for controlling the tangents of the curves. The first variant gives curves that closely follow the control polygon, and the curves generated with the second variant are less tied to the control polygon and instead very similar to uniform cubic B-spline curves.