Teapot Subdivision

This image celebrates my third-generation updating of Martin Newell's original tea-table scene. Dr. Newell taught my computer graphics class in 1975-76 at the University of Utah. He became the chair of my thesis research committee in 1976-77.

His ideas of combining object-oriented procedural modeling with curved-surface geometry strongly influenced my career for the next 20 years, developing the Alpha_1 research geometric modeling system at the University of Utah.

Dr. Newell's Bézier teapot model was one of the first curved-surface objects available to the computer graphics research community. The teapot became a "benchmark model" for image synthesis programs and an icon in the SIGGRAPH research community.

In creating this image, I improved on Hank Driskill's second-generation Alpha_1 procedural/NURBS teapot model and modeled and rendered a scene revealing the lovely new insides of the teapot by slicing it in half like an onion (slightly surreal, I admit).

The title, "Teapot Subdivision," is also an oblique reference to the recursive NURBS surface-subdivision algorithm, based on the Oslo algorithms, that is is used to adaptively create a bounding volume tree to speed up ray-traced rendering in Alpha_1.

Technical Overview
This is a third-generation teapot model, in a scene modeled using Alpha_1 and rendered by the Alpha_1 ray tracer.

Martin Newell's classic 1975 teapot model contains 28 bicubic Bézier patches, each with 16 3D control points in a 4 x 4 grid. In the circular directions of the teapot body and lid, each patch covers 1/4 of a circle and is round within about 1 percent.

There were originally no bottom or inside surfaces for the body, lid, and spout of the teapot. The spout and handle penetrated the body of the teapot, so their ends were visible inside.

Hank Driskill made a second-generation teapot as an Alpha_1 procedurally generated, NURBS-surface solid model. The srfOfRevolution operator made continuous, truly round swept surfaces from the Bézier profile curves. Hank added missing interior and bottom surfaces, and a hole drilled down the spout, subtracting it as a post-process while generating polygons for rendering.

This third-generation teapot model has nicer inside shapes and is a true trimmed-surface NURBS solid model. There is one trimmed NURBS surface each for the body, lid, handle, and spout.

The hole down the middle of the spout is procedurally tapered and contoured from the outer surface. The combineShells operator joins the body and spout solids together with trimming curves and adjacencies, and is also used to slice the teapot body and lid in half for this scene.

A cleaver and chopping block complete the scene. The cleaver was modeled after a real Sabatier knife, which was photocopied, cut out, and taped to a monitor. Outline curves were designed in the Alpha_1 graphical user interface, and the handle and tapered blade were procedurally modeled. The chopping-block surface textures were procedurally sliced and colored from stock wood-grain images, using the Utah Raster Toolkit.

Russell Fish
School of Computing, University of Utah
Fish (at) cs.utah.edu