To repeatedly evaluate linear combinations of box-splines in a fast and stable way, in particular along knot planes, the box-spline is con- verted to and tabulated as piecewise polynomial in BB-form (Bernstein- Bézier-form). We show that the BB-coefficients can be derived and stored as integers plus a rational scale factor and derive a hash table for effi- ciently accessing the polynomial pieces. This preprocessing, the resulting evaluation algorithm and use in a widely-used ray-tracing package are il- lustrated for splines based on two trivariate box-splines: the 7-directional box-spline on the Cartesian lattice and the 6-directional box-spline on the Face-Centered Cubic lattice.

Good surgical training depends greatly on case experiences that have been difficult to model in software since current training technology does not provide the flexibility to teach and practice uncommon procedures, or to adjust a training scenario on the fly. The TIPS kit aims to overcome these limitations. To the expert, it presents visual and haptic tools that make illustrating procedures easy and can model unusual anatomic variations. For a non-specialist, it provides a locally customized learning environment and repeated practice in a safe environment. We used the toolkit to illustrate removal of the adrenal gland.

The rapid development and deployment of novel laparoscopic instruments present the surgical educator and trainee with a significant challenge. Several useful instruments have been particularly difficult to teach the novice. We have developed a platform that allows the combination of the actual instrument handle with a virtual re-creation of the instrument tip. We chose the Autosuture™ Endo Stitch™ device as the prototypical instrument because it satisfies our subjective experience of “useful, but hard to teach.” A software package was developed to support the re-creation of the needle and suture that accompany the device. The apparatus has haptic capabilities and collision detection so that the needle driver is “aware” of suture and instrument contact. The developed virtual environment allows re-creation of the necessary motion to simulate the instrument, the trainee can use the actual instrument handle, and the system can be altered to accommodate other instruments.

We have developed a computer based simulation process which allows a surgical expert to create a customized operative environment. This virtual environment, the Toolkit for Illustration of Procedures in Surgery (3D TIPS), is deployed on a low-cost computer system and requires minimal training for the programmer. The learner can be engaged in training immediately and the educator can modify the system and annotate the procedure to highlight specific points using video clips, operative images, and the like. A laparoscopic adrenalectomy is presented as a proof of concept in the accompanying article.

Real-time, plausible visual and haptic feedback of deformable objects without shape artifacts is important in surgical simulation environments to avoid distracting the user. We propose to leverage highly parallel stream processing, available on the newest generation graphics cards, to increase the level of both visual and haptic fidelity. We implemented this as part of the University of Florida's haptic surgical authoring kit.

In “A realtime GPU subdivision kernel” (SIGGRAPH 2005), Shiue et al. showed that, in principle, all major features of subdivision algorithms can be realized in the framework of highly parallel stream processing. Shiue et al. tested the approach by implementing Catmull-Clark subdivision, with semi-smooth creases and global boundaries, in programmable graphics hardware, at near realtime speed. Here, we report on the challenges when adapting the approach to Loop subdivision.

Finding the intersection of two surfaces, usually a collection of curves, is an important challenge in modeling geometry. This thesis presents a method to find parametric (B-spline) intersection curves which approximate the actual intersection curves of two Bézier surfaces. We first approximate the original surfaces using SLEFEs (Subdividable Linear Efficient Function Enclosures) and their mid-structures. The piecewise linear curves, which are the intersections of two mid-structures, are inverted to the B-spline curves which approximate the exact intersection curves. Our method is fast, has known error bounds, and generates B-spline curves, which are very useful for many applications. Moreover, our method can be refined with the guarantee of decreasing error bound.