Developable \((1, n)\)-Bézier surfaces
The authors show that a rational Béziers patch of degree \((1,n)\) and control points \(p^{ij}\) (\(i=0,1\); \(j=0,\ldots,n\)) is a developable surface iff \[ \sum^{n-1}_{i,j,k,l=0}{n-1\choose i}{n-1\choose j}{n- 1\choose k}{n-1\choose l}\text{det}(p^{0i},p^{0j+1},p^{1k},p^{1l+1})=0 \] for all \(i+j+k+l=s\), \(0\leq s\leq 4n-4\). They give explicit formulas for \((1,2)\) and \((1,3)\) surfaces and a number of graphic examples.
scientific article; zbMATH DE number 97033