Interactively rendering solid CAD models currently relies on tessellation of the models and passing of the tessellation onto the graphics card (GPU). Direct rendering on the GPU, without a tessellation preprocess, has many advantages -- pixel-level quality, less memory requirements, and less preprocessing, to name a few. However, one of the main problems with existing solutions for rendering solid models directly is the appearance of crack/gap artifacts between faces due to the approximations of the trimming curves. This prevents the usage of direct GPU rendering in CAD systems. In this paper we present a novel solution to the gap problem. The new method combines a unique representation of the faces of the solid model, with fragment shader algorithms that utilize the representation for identifying the surface area to be rendered. This enables us to render the models with high quality in interactive speed without the crack/gap artifacts. We have implemented our method in a ray casting system for viewing CAD solid models and present our results.

We present practical algorithms for accelerating distance queries on models made of trimmed NURBS surfaces using programmable Graphics Processing Units (GPUs). We provide a generalized framework for using GPUs as coprocessors in accelerating CAD operations. By supplementing surface data with a surface bounding-box hierarchy on the GPU, we answer distance queries such as finding the closest point on a curved NURBS surface given any point in space and evaluating the clearance between two solid models constructed using multiple NURBS surfaces. We simultaneously output the parameter values corresponding to the solution of these queries along with the model space values. Though our algorithms make use of the programmable fragment processor, the accuracy is based on the model space precision, unlike earlier graphics algorithms that were based only on image space precision. In addition, we provide theoretical bounds for both the computed minimum distance values as well as the location of the closest point. Our algorithms are at least an order of magnitude faster and about two orders of magnitude more accurate than the commercial solid modeling kernel ACIS.

Constraint-based geometric modeling is the standard modeling paradigm in current modern CAD systems. Generally, the user defines constraints on the geometric objects and a solver is applied to find a configuration of the geometry, which satisfies these constraints. Proper application of these constraints allows rapid modification of the geometry without loss of design intent.

We present practical algorithms for accelerating geometric queries on models made of NURBS surfaces using programmable Graphics Processing Units (GPUs). We provide a generalized framework for using GPUs as co-processors in accelerating CAD operations. By attaching the data corresponding to surface-normals to a surface bounding-box structure, we can calculate view-dependent geometric features such as silhouette curves in real time. We make use of additional surface data linked to surface bounding-box hierarchies on the GPU to answer queries such as finding the closest point on a curved NURBS surface given any point in space and evaluating the clearance between two solid models constructed using multiple NURBS surfaces. We simultaneously output the parameter values corresponding to the solution of these queries along with the model space values. Though our algorithms make use of the programmable fragment processor, the accuracy is based on the model space precision, unlike earlier graphics algorithms that were based only on image space precision. In addition, we provide theoretical bounds for both the computed minimum distance values as well as the location of the closest point. Our algorithms are at least an order of magnitude faster than the commercial solid modeling kernel ACIS.

We present algorithms for evaluating and performing modeling operations on NURBS surfaces using the programmable fragment processor on the Graphics Processing Unit (GPU). We extend our GPU-based NURBS evaluator that evaluates NURBS surfaces to compute exact normals for either standard or rational B-spline surfaces for use in rendering and geometric modeling. We build on these calculations in our new GPU algorithms to perform standard modeling operations such as inverse evaluations, ray intersections, and surface-surface intersections on the GPU. Our modeling algorithms run in real time, enabling the user to sketch on the actual surface to create new features. In addition, the designer can edit the surface by interactively trimming it without the need for retessellation. Our GPU-accelerated algorithm to perform surface-surface intersection operations with NURBS surfaces can output intersection curves in the model space as well as in the parametric spaces of both the intersecting surfaces at interactive rates. We also extend our surface-surface intersection algorithm to evaluate self-intersections in NURBS surfaces.

We present algorithms for evaluating and performing modeling operatyons on NURBS surfaces using the programmable fragment processor on the Graphics Processing Unit (GPU). We extend our GPU-based NURBS evaluator that evaluates NURBS surfaces to compute exact normals for either standard or rational B-spline surfaces for use in rendering and geometric modeling. We build on these calculations in our new GPU algorithms to perform standard modeling operations such as inverse evaluations, ray intersections, and surface-surface intersections on the GPU. Our modeling algorithms run in real time, enabling the user to sketch on the actual surface to create new features. In addition, the designer can edit the surface by interactively trimming it without the need for re-tessellation. We also present a GPU-accelerated algorithm to perform surface-surface intersection operations with NURBS surfaces that can output intersection curves in the model space as well as in the parametric spaces of both the intersecting surfaces at interactive rates.