A circular biarc can be defined by using two points K and L with their (oriented) tangents $g_K$ and $g_L$ as input. It is well-known that one can determine a one parametric set of circular arc pairs $k,\ell$ such that k starts at K with tangent $g_K$, ℓ ends at L with tangent $g_L$ and k and ℓ meet with a common tangent in an intermediate point P. In this paper we investigate a similar construction where we replace the circle biarcs by pairs of conic arcs. It turns out that in this case we can prescribe a conic $k_0$ with a point K on it, another conic ${\ell }_0$ with a point L on it, and moreover an intermediate point P to obtain a unique pair $k,\ell$ of conics such that k osculates $k_0$ in K, ℓ osculates ${\ell }_0$ in L and k and ℓ osculate each other in P. This also confirms a result of H. Pottmann from 1991. We use our method to solve an interpolation task of Hermite type whose input consists of a series of points with their curvature circles and another series of intermediate points. The output is a $G{C}^2$ spline curve with conic arc segments.

可以通过使用两个点K和L及其切线（定向）来定义圆形偏移$G_{ķ}$ 和 $G_{\mathrm{大号}}$作为输入。众所周知，可以确定一组参数的圆弧对$ķ，\ell$使得ķ在开始ķ与切线$G_{ķ}$，ℓ以切线结尾于L$G_{\mathrm{大号}}$和ķ和ℓ满足在中间点处的公切线P。在本文中，我们研究了一种类似的构造，其中我们用成对的圆锥形弧替换圆偏置。事实证明，在这种情况下，我们可以开一个圆锥${ķ}_0$上面有一个点K，另一个圆锥${\ell }_0$上面有一个点L，还有一个中间点P，以获得唯一对$ķ，\ell$圆锥形，使k触动${ķ}_0$在ķ，ℓ osculates${\ell }_0$在大号和ķ和ℓ osculate彼此P。这也证实了1991年H. Pottmann的结果。我们使用我们的方法来解决Hermite类型的插值任务，该输入的输入由具有其曲率圆的一系列点和一系列中间点组成。输出是$G{C}^2$ 圆锥曲线段的样条曲线。