In this work, we use the formal definition of $k$-slant helix cite{ali2} to obtain the intrinsic equations as well as the position vector for emph{slant-slant helices} which a generalization of emph{general helices} and emph{slant helices}. Also, we present some characterizations theorems for $k$-slant helices and derived, in general form, the intrinsic equations for such curves. Thereafter, fr...

Texture can be an effective source of information for perception of slant and curvature. A computational assumption required for some texture cues is that texture must be flat along a surface. There are many textures which violate this assumption, and have some sort of texture relief: variations perpendicular to the surface. Some examples include grass, which has vertical elements, or scattered...

Motion parallax provides cues to the three-dimensional layout of a viewed scene and, in particular, to surface tilt and slant. For example, as a textured surface, inclined around a horizontal axis, translates horizontally relative to an observer's view point, then, in the absence of head and eye movements, the observer's retinal flow will contain a one-dimensional (1D) vertical speed gradient. ...

A slant immersion is an isometric immersion from a Riemannian manifold into an almost Hermitian manifold with constant Wirtinger angle (1~ . In this article we study and characterize slant surfaces in the complex 2-plane ~2 via the Gauss map. We also prove that every surface without complex tangent points in a 4-dimensional almost Hermitian manifold M is slant with respect to a suitably chosen ...

By presenting oriented Gabor patches either monocularly or binocularly, we dissociated retinal orientation from perceived tilt and perceived slant. After adapting to binocular patches, with zero apparent tilt and non-zero slant, small tilt after-effects (TAEs) and large slant after-effects (SAE) were measured. Adapting to monocular patches with non-zero tilt and zero slant produced large TAEs a...

Perceived slant produced by size disparities in random-dot displays was measured by tactile matching. For a 60 deg surface, slant produced by vertical-size disparity (the induced effect) was opposite to that produced by horizontal-size disparity. Overall-size disparity produced a little slant. With small displays, effects of horizontal and vertical disparities were reduced but not those of over...

This paper presents a computationally and statistically efficient parametric solution to the problem of estimating the orientation in space of a planar textured surface from a single, noisy, observed image of it. The coordinate transformation from surface to image coordinates, due to the perspective projection, transforms each homogeneous sinusoidal component of the surface texture into a sinus...