Interactive rendering of NURBS surfaces

• RPNS, a new pipeline for the efficient rendering of NURBS surfaces, is presented.
• It is based on a non-recursive evaluation of a NURBS surface’s basis function on GPU.
• Different GPU implementations of RPNS are proposed on DirectX11.
• A comparison with an approach based on NURBS–Bézier conversion on CPU is carried out.
• RPNS achieves real-time frame rates even when the models are interactively deformed.

NURBS (Non-uniform rational B-splines) surfaces are one of the most useful primitives employed for high quality modeling in CAD/CAM tools and graphics software. Since direct evaluation of NURBS surfaces on the GPU is a highly complex task, the usual approach for rendering NURBS is to perform the conversion into Bézier surfaces on the CPU, and then evaluate and tessellate them on the GPU. In this paper we present a new proposal for rendering NURBS surfaces directly on the GPU in order to achieve interactive and real-time rendering. Our proposal, Rendering Pipeline for NURBS Surfaces (RPNS), is based on a new primitive KSQuad that uses a regular and flexible processing of NURBS surfaces, while maintaining their main geometric properties to achieve real-time rendering. RPNS performs an efficient adaptive discretization to fine tune the density of primitives needed to avoid cracks and holes in the final image, applying an efficient non-recursive evaluation of the basis function on the GPU. An implementation of RPNS using current GPUs is presented, achieving real-time rendering rates of complex parametric models. Our experimental tests show a performance several orders of magnitude higher than traditional approximations based on NURBS to Bézier conversion.