We review the theory of homogeneous splines and their relationship to special rational spliens considered by J. Sanchez-Reyes and independently by P. de Casteljau who called them focal splines. Applying an appropriate duality, we transform focal splines into a remarkable class of ratinal curves with rational offsets. We investigate geometric properties of these dual focal splnes and discuss applications to curve design problems.
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机译：我们回顾了齐次样条的理论及其与J. Sanchez-Reyes以及P. de Casteljau独立称其为焦点样条的特殊有理斯普林的关系。应用适当的对偶性，我们将焦点样条曲线转换为具有合理偏移量的出色的梯形曲线。我们调查这些双焦点splnes的几何特性，并讨论在曲线设计问题中的应用。
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