In Computer-Aided Design (CAD), Non-Uniform Rational B-Splines (NURBS) are a common model representation for export, simulation and visualization. In this paper, we present a direct rendering method for trimmed NURBS models based on their parametric description. Our approach builds on a novel trimming method and a three-pass pipeline which both allow for a sub-pixel precise visualization. The rendering pipeline bypasses tessellation limitations of current hardware using a feedback mechanism. In contrast to existing work, our trimming method scales well with a large number of trim curves and estimates the trimmed surface's footprint in screen-space which allows for an anti-aliasing with minimal performance overhead. Fragments with trimmed edges are routed into a designated off-screen buffer for subsequent blending with background faces. The evaluation of the presented algorithms shows that our rendering system can handle CAD models with ten thousands of trimmed NURBS surfaces. The suggested two-level data structure used for trimming outperforms state-of-the-art methods while being more precise and memory efficient. Our curve coverage estimation used for anti-aliasing provides an efficient trade-off between quality and performance compared to multisampling or screen-space anti-aliasing approaches.

Modern virtual reality simulations require a constant high-frame rate from the rendering engine. They may also require very low latency and stereo images. Previous rendering engines for virtual reality applications have exploited spatial and temporal coherence by using image-warping to re-use previous frames or to render a stereo pair at lower cost than running the full render pipeline twice. However these previous approaches have shown artifacts or have not scaled well with image size. We present a new image-warping algorithm that has several novel contributions: an adaptive grid generation algorithm for proxy geometry for image warping; a low-pass hole-filling algorithm to address un-occlusion; and support for transparent surfaces by efficiently ray casting transparent fragments stored in per-pixel linked lists of an A-Buffer. We evaluate our algorithm with a variety of challenging test cases. The results show that it achieves better quality image-warping than state-of-the-art techniques and that it can support transparent surfaces effectively. Finally, we show that our algorithm can achieve image warping at rates suitable for practical use in a variety of applications on modern virtual reality equipment.

In this paper, we present a flexible and efficient approach for the integration of order-independent transparency into a deferred shading pipeline. The intermediate buffers for storing fragments to be shaded are extended with a dynamic and memory-efficient storage for transparent fragments. The transparency of an object is not fixed and remains programmable until fragment processing, which allows for the implementation of advanced materials effects, interaction techniques or adaptive fade-outs. Traversing costs for shading the transparent fragments are greatly reduced by introducing a tile-based light-culling pass. During deferred shading, opaque and transparent fragments are shaded and composited in front-to-back order using the retrieved lighting information and a physically-based shading model. In addition, we discuss various configurations of the system and further enhancements. Our results show that the system performs at interactive frame rates even for complex scenarios.

In NURBS-based isogeometric analysis, the basis functions of a 3D model's geometric description also form the basis for the solution space of variational formulations of partial differential equations. In order to visualize the results of a NURBS-based isogeometric analysis, we developed a novel GPU-based multi-pass isosurface visualization technique which performs directly on an equivalent rational Bézier representation without the need for discretization or approximation. Our approach utilizes rasterization to generate a list of intervals along the ray that each potentially contain boundary or isosurface intersections. Depth-sorting this list for each ray allows us to proceed in front-to-back order and enables early ray termination. We detect multiple intersections of a ray with the higher-order surface of the model using a sampling-based root-isolation method. The model's surfaces and the isosurfaces always appear smooth, independent of the zoom level due to our pixel-precise processing scheme. Our adaptive sampling strategy minimizes costs for point evaluations and intersection computations. The implementation shows that the proposed approach interactively visualizes volume meshes containing hundreds of thousands of Bézier elements on current graphics hardware. A comparison to a GPU-based ray casting implementation using spatial data structures indicates that our approach generally performs significantly faster while being more accurate.

This paper presents a highly efficient direct trimming technique for NURBS surfaces, which is applicable to tessellation-based rendering as well as ray tracing systems. The central idea is to split the trim curves into monotonic segments with respect to the two parameter dimensions of the surface patches. We use an optimized bisection method to classify a point with respect to each monotonic trim curve segment without performing an actual intersection test. Our hierarchical acceleration structure allows the use of a large number of such curve segments and performs the bisection method only for points contained in the bounding boxes of the curve segments. We have integrated our novel point classification scheme into a GPU-based NURBS ray casting system and implemented the entire trimmed NURBS rendering algorithm in a single OpenGL GLSL shader. The shader can handle surfaces and trim curves of arbitrary degrees, which allows the use of original CAD data without incorporating any approximations. Performance data confirms that our trimming approach can deal with hundreds of thousands of trim curves at interactive rates. Our point classification scheme can be applied to other application domains dealing with complex curved regions including flood fills, font rendering and vector graphics mapped on arbitrary surfaces.