The mu-basis of a planar rational curve is a polynomial ideal basis comprised of two polynomials that greatly facilitates computing the implicit equation of the curve. This paper defines a mu-basis for a rational ruled surface, and presents a simple algorithm for computing the mu-basis. The mu-basis consists of two polynomials p(x, y, z, s) and q(x, y, z, s) that are linear in x, y, z and degre...

Conditions in which saccadic gaze shifts within planar surfaces facilitate stereo-slant discrimination for slant about the horizontal and vertical axis were investigated. When horizontal disparity noise was added, large gaze shifts in the direction of the slant lowered stereo-slant discrimination thresholds compared to thresholds measured with steady central fixation, whereas eye movements orth...

We classify ruled minimal surfaces in R3 with density ez. It is showed that there is no noncylindrical ruled minimal surface and there is a family of cylindrical ruled minimal surfaces in R3 with density ez. It is also proved that all translation minimal surfaces are ruled. AMS Subject Classification (2000): Primary 53C25; Secondary 53A10; 49Q05

A projective algebraic surface which is homeomorphic to a ruled surface over a curve of genus g ≥ 1 is itself a ruled surface over a curve of genus g. In this note, we prove the analogous result for projective algebraic manifolds of dimension 4 in case g ≥ 2.

We sought to determine if perceived depth can elicit vergence eye movements independent of binocular disparity. A flat surface in the frontal plane appears slanted about a vertical axis when the image in one eye is vertically compressed relative to the image in the other eye: the induced size effect (Ogle, 1938). We show that vergence eye movements accompany horizontal gaze shifts across such s...

To achieve high precision and high productivity in machining sculptured surfaces, a new architecture for a five-axis CNC interpolator for machining ruled surfaces was developed and demonstrated on a milling machine. The objective of the five-axis interpolator is to continuously maintain the milling cutter axis in parallel with the straight lines of the ruled surface. The cutter position and ori...

The aim of Shape From Shading (SFS) problem is to reconstruct the relief of an object from a single gray level image. In this paper we present a new method to solve the problem of SFS using Machine learning method. Our approach belongs to Local resolution category. The orientation of each part of the object is represented by the perpendicular vector to the surface (Normal Vector), this vector i...

Subjects adjusted a local gauge figure such as to perceptually " fit " the apparent surfaces of objects depicted in photographs. We obtained a few hundred data points per session, covering the picture according to a uniform lattice. Settings were repeated 3 times for each of 3 subjects. Almost all of the variability resided in the slant; the relative spread in the slant was about 25% (Weber fra...