Ray Casting of Trimmed NURBS Surfaces on the GPU

Abstract

We propose a conceptual extension of the standard triangle-based graphics pipeline by an additional intersection stage. The corresponding intersection program performs ray-object intersection tests for each fragment of an object's bounding volume. The resulting hit fragments are transfered to the fragment shading stage for computing the illumination and performing further fragment operations. Our approach combines the efficiency of the standard hardware graphics pipeline with the advantages of ray casting such as pixel accurate rendering and exact normals as well as early ray termination.This concept serves as a framework for the implementation of an interactive ray casting system for trimmed NURBS surfaces. We show how to realize an iterative ray-object intersection method for NURBS primitives as an intersection program. Convex hulls are used as tight bounding volumes for the NURBS patches to minimize the number of fragments to be processed. In addition, we developed a trimming algorithm for the GPU that works with an exact representation of the trimming curves. First experiments with our implementation show that real-time rendering of medium complex scenes is possible on current graphics hardware.

Hybrid ray tracing and path tracing of Bezier surfaces using a mixed hierarchy

“…GPU based Tessellation of parametric surfaces was proposed by [10]. Ray Casting of trimmed NURBS Surfaces using a combination of Newton iteration and bezier clipping on the GPU was done by [19].…”

“…To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. ICVGIP '12, December [16][17][18][19]2012 provides smooth appearances and silhouettes over a range of viewpoints. Second, it produces exact secondary rays as the coordinates and normals are available at the intersections.…”

“…The massive compute power of modern CPUs and GPUs has made ray tracing possible on ordinary workstations, but has not been applied to parametric surfaces. Ray tracing primary rays at 4-5 fps has been reported recently [7,1,19], but interactive multi-bounce ray tracing or advanced methods like path tracing have not been reported in the literature.…”

Performing Efficient NURBS Modeling Operations on the GPU

“…Ray tracing was performed on parametric and rational surfaces by solving for the ray-surface intersection point using numerical methods [8], [9], [10]. There has also been previous work on ray tracing using the GPU, which includes [4], [11], [12], [13]. Another application of inverse evaluation of NURBS is solving for geometric constraints.…”

“…However, since evaluation of a NURBS surface is inherently a computation-intensive process, commercial CAD packages deal with it by preprocessing NURBS surfaces, usually tessellating them and using the triangulated model for display as well as certain modeling operations like selection. With the advent of programmable graphics hardware, the need for tessellating the NURBS surface in the CPU for display was obviated, since the GPU can be used for the evaluation and direct display of the surfaces [1], [2], [3], [4]. However, CAD packages still perform modeling operations using the CPU with either the tessellated surfaces or analytically using NURBS definitions.…”