WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 25, 2026
Steiner Conics and Quadratic Bézier Curves with Control Mass Points
Authors: , ,
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Abstract: The authors propose a new approach of the Steiner problem. The Steiner problem consists in
constructing a conic tangent to three sides of a triangle—possibly extended sides-. The method in use
is based on Bézier curves with control mass points. Bézier curves with control mass points generalize
classical rational Bézier curves by introducing control vectors in addition to control points. Here, any
quadratic rational Bézier curves with three control mass points model conic arcs, semi-ellipses, and hyperbola
branches while preserving rational parameterizations with any homographic parameter change.
This method simplifies the construction and avoids implicit conic equations, solving systems of five linear
equations in five unknowns, or reducing the implicit form of a conic. All conic features can be obtained
by reparametrizations.
Pages: 446-464
DOI: 10.37394/23206.2026.25.43