Digital architecture refers to buildings that use digital information technology for design, construction, operation and maintenance. The parametric design of complex buildings must establish a complete geometric control system. Geometry is an important basic theory in parametric design. The language and methods of manifold geometry can be used to express and analyze curved three-dimensional geometric shapes conveniently. The concepts of"parallel"and"equidistant"of the curves on the curved surface provide us with a geometric intuitive and logical basis for the parametric design of geometric shapes. It focuses on the external equidistance between surfaces and the geodesic equidistance between curves on the surface, Levi-Civita parallel(intrinsic geometry)concepts, and expounds the geometric theory and methods in parametric design. The geometric methods used in the parametric design of the 2022 Hangzhou Asian Games table tennis competition venues and venue non-linear enclosure systems and roof systems are introduced.