A C 1 Globally Interpolatory Spline of Arbitrary Topology [chapter]

Ying He, Miao Jin, Xianfeng Gu, Hong Qin
2005 Lecture Notes in Computer Science  
Converting point samples and/or triangular meshes to a more compact spline representation for arbitrarily topology is both desirable and necessary for computer vision and computer graphics. This paper presents a C 1 manifold interpolatory spline that can exactly pass through all the vertices and interpolate their normals for data input of complicated topological type. Starting from the Powell-Sabin spline as a building block, we integrate the concepts of global parametrization, affine atlas,
more » ... splines defined over local, open domains to arrive at an elegant, easy-to-use spline solution for complicated datasets. The proposed global spline scheme enables the rapid surface reconstruction and facilitates the shape editing and analysis functionality.
doi:10.1007/11567646_25 fatcat:vbzdt43br5c7zcyeglnidihaly