Conchoid surfaces of spheres

The conchoid of a surface F with respect to given fixed point O is roughly speaking the surface obtained by increasing the radius function with respect to O by a constant. This paper studies conchoid surfaces of spheres and shows that these surfaces admit rational parameterizations. Explicit parameterizations of these surfaces are constructed using the relations to pencils of quadrics in R 3 and R 4 . Moreover we point to remarkable geometric properties of these surfaces and their construction.

大致来说，曲面\(F\)关于给定定点\(O\)的蚌线是通过将关于\(O\)的半径函数增加一个常数而得到的曲面。本文研究了球面的蚌线曲面，并表明这些曲面具有有理参数化。利用与\(\mathbb{R}^3\)和\(\mathbb{R}^4\)中二次曲面束的关系，构建了这些曲面的显式参数化。此外，我们指出了这些曲面及其构造的显著几何性质。