The ability of observers to perceive three-dimensional (3-D) distances or lengths along intrinsically curved surfaces was investigated in three experiments. Three physically curved surfaces were used: convex and/or concave hemispheres (Experiments 1 and 3) and a hyperbolic paraboloid (Experiment 2). The first two experiments employed a visual length-matching task, but in the final experiment th...

Infinitesimal bending of curves lying with a given precision on ruled surfaces in 3-dimensional Euclidean space is studied. In particular, the cylinder, hyperbolic paraboloid and helicoid are considered appropriate fields found. Some examples graphically presented.

Colonic polyps are growths on the inner wall of the colon. They appear like elliptical protrusions which can be detected by curvature-derived shape discriminators. For reasons of computation efficiency, much of the past work in computeraided diagnostic CT colonography adopted kernel-based convolution methods in curvature estimation. However, kernel methods can yield erroneous results at thin st...

Hyperbolic paraboloid surfaces or saddle-shaped materials can exist in two equilibrium shapes when the saddle shape reverses on itself and, therefore, be used as structural elements of new stimuli-responsive and shape-changing materials. Here we propose a fast easy approach to nanoarchitectonics graphene oxide nanosheets form curved interfaces. Our technology involves computer-aid design, three...