Let X be a non-singular ruled surface over an algebraically closed field of characteristic zero. There is a non-trivial surjective endomorphism f : X → X if and only if X is (1) a toric surface, (2) a relatively minimal elliptic ruled surface, or (3) a relatively minimal ruled surface of irregularity greater than one which turns to be the product of P and the base curve after a finite étale bas...

Three experiments investigated whether 14- and 15-month-old infants use information for both friction and slant for prospective control of locomotion down slopes. In Experiment 1, high- and low-friction conditions were interleaved on a range of shallow and steep slopes. In Experiment 2, friction conditions were blocked. In Experiment 3, the low-friction surface was visually distinct from the su...

The conchoid surface G of a given surface F with respect to a point O is roughly speaking the surface obtained by increasing the radius function of F with respect to O by a constant d. This paper studies real rational ruled surfaces in this context and proves that their conchoid surfaces possess real rational parameterizations, independently on the position of O. Thus any rational ruled surface...

Chen, Sederberg, and Zheng introduced the notion of a μ-basis for a rational ruled surface in Chen et al. (2001) and showed that its resultant is the implicit equation of the surface, if the parametrization is generically injective. We generalize this result to the case of an arbitrary parametrization of a rational ruled surface. We also give a new proof for the corresponding theorem in the cur...

Texture information about surface shape can be decomposed into three constituents: compression, density and scaling. Blake, Bülthoff and Sheinberg's (1993, Vision Research, 33, 1723-1737) Ideal Observer theory of slant from texture predicts that the relative contribution of compression and density to the percept of planar surface slant should vary with field of view (FOV). The contribution of c...

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 fract...

Li and Zaidi (Li, A., and Zaidi, Q. (2000) Vision Research, 40, 217-242) showed that the veridical perception of the 3-dimensional (3D) shape of a corrugated surface from texture cues is entirely dependent on the visibility of critical patterns of oriented energy. These patterns are created by perspective projection of surface markings oriented along lines of maximum 3D curvature. In images mis...