Narrowing-Cascade splines for control nets that shed mesh lines

Quad-dominant meshes are popular with animation designers and can efficiently be generated from point clouds. To join primary regions, quad-dominant meshes include non-4-valent vertices and non-quad regions. To transition between regions of rich detail and simple shape, quad-dominant meshes commonly use a cascade of (Formula presented) triangles that reduce the number of parallel quad strips from (Formula presented) to 2. For these cascades, the Narrowing-Cascade spline, short NCⁿ[jls-end-space/], provides a new shape-optimized G¹spline surface. NCⁿcan treat cascade meshes as B-spline-like control nets. For (Formula presented), as opposed to (Formula presented), cascades have interior points that both guide and complicate the construction of the output tensor-product NC. The NCⁿspline follows the input mesh, including interior points, and delivers a high-quality curved surface of low degree.