In this paper a linear algorithm is derived for constructing B-spline control nets for spline developable surfaces of arbitrary degree and number of pieces. Control vertices are written in terms of five free parameters related to the type of developable surface. Aumann's algorithm for constructing Bézier developable surfaces is recovered as a particular… (More)
It has been recently proved that rational quadratic circles in standard Bézier form are parameterized by chord-length. If we consider that standard circles coincide with the isoparametric curves in a system of bipolar coordinates, this property comes as a straightforward consequence. General curves with chord-length parametrization are simply the analogue… (More)
Keywords: Conic sections Bézier curves Eccentricity Asymptotes Axes Foci In this paper, we address the calculation of geometric characteristics of conic sections (axes, asymptotes, centres, eccentricity, foci) given in Bézier form in terms of their control polygons and weights, making use of real and complex projective and affine geometry and avoiding the… (More)
In this paper we review the derivation of implicit equations for non-degenerate quadric patches in rational Bézier triangular form. These are the case of Steiner surfaces of degree two. We derive the bilinear forms for such quadrics in a coordinate-free fashion in terms of their control net and their list of weights in a suitable form. Our construction… (More)
When defining a ship hull surface, the main objective is to obtain a faired surface or surfaces that contain some specific points of the hull, that have been selected in the design process and give the ship its hydrodynamic, stability and other properties. So, the hull surface should be a compromise between fairness and precision, and this is not and easy… (More)
In this talk we show a construction for characterising developable surfaces in the form of Bézier triangular patches. It is shown that constructions used for rectangular patches are not useful, since they provide degenerate triangular patches. Explicit constructions of non-degenerate developable triangular patches are provided.
In this paper we classify and derive closed formulas for geometric elements of quadrics in rational Bézier triangular form (such as the center, the conic at infinity, the vertex and the axis of paraboloids and the principal planes), using just the control vertices and the weights for the quadric patch. The results are extended also to quadric tensor product… (More)
In this paper we address the problem of interpolating a spline developable patch bounded by a given spline curve and the first and the last rulings of the developable surface. To complete the boundary of the patch, a second spline curve is to be given. Up to now this interpolation problem could be solved, but without the possibility of choosing both… (More)