Russell Manning > Research > Manifold Gallery

Screw-Transform Manifold Gallery

This page contains several visualizations of individual and intersecting screw-transform manifolds, both as movies and still images.

Movie: Individual Manifold

We start with a movie showing a single screw-transform manifold rotating in 3D. The following stills from the movie are separated by 60 degree intervals and are in reading order:

The manifold continues past the jagged ends but was truncated in order to focus on the most significant region of the manifold. The full movie is here:

Single manifold rotating: [0.9M mpeg-1] or [1.3M MS mpeg-4(V2) AVI] or [1.1M DivX AVI]

Movie: Intersecting Manifolds

Next is a movie showing 3 screw-transform manifolds intersecting at a single point (this point determines camera calibration). Here are some stills from the begining of the movie; the intersection point is at the center of each image:

The full movie is here:

Intersection of 3 manifolds: [1.9M mpeg-1] or [2.4M MS mpeg-4(V2) AVI] or [2.4M DivX AVI]

Intersecting Collections of Manifolds

Lastly is an alternative visualization of the mutual-intersection point of 3 screw-transform manifolds. The mutual intersection point is visible as a small yellow patch near the center of each image. (Note: It may be that more than one mutual intersection point exists. The one shown in yellow corresponds to the camera calibration used in generating the data set.) These images also give some sense of (1) the piecewise-linear surface patches (triangles) used to approximate each manifold, (2) the quality of the approximation given by the patches, and (3) the general shape of a screw-transform manifold, especially their non-trivial but relatively mild curvature. Although not evident in these images, a screw-transform manifold typically has two distinct lobes that touch at a single point; this point represents a discontinuity in the value of kappa. Note that, to simplify the visualization, only patches that where within a certain distance from the mutual intersection point are shown, leading to the ragged edges of the manifolds.

The images are in the following arrangement (you may need to scroll your browser window):

View 1

View 1 Close-Up

View 2

View 2 Close-Up