5 citations · 14 across the 20 of their papers we have counts for
12 papers · 1 filter
Shapes of light: singularities of slant functions and the Gauss map of a surface
Shuhei Honda, Yutaro Kabata
The slant function on a regular surface in three-space, introduced by Koenderink, is the inner product of a fixed light direction with the unit normal; under the standard Lambertia…
Visualization of curvature on curve and surface by tangential angle parametrization
Yutaro Kabata, Shigeki Matsutani, Yuta Ogata
We propose a unified method to visualize curvature on planar curves and surfaces of revolution using the tangential angle parameter. For plane curves, placing markers at equal incr…
A view-parametric extension of the d'Ocagne formula for a surface in
Ken Anjyo, Yutaro Kabata
In this paper, we consider the orthogonal projection of a surface in for a given view direction. We then introduce and investigate several invariants of the families…
On discrete constant principal curvature surfaces
Y. Kabata, S. Matsutani, Y. Ogata
Recently, it is discovered that a certain class of nanocarbon materials has geometrical properties related to the discrete geometry, pre-constant discrete principal curvature [9] b…
Contact cylindrical surfaces and a projection of a surface around a parabolic point
Masaru Hasegawa, Yutaro Kabata, Kentaro Saji
We investigate differential geometric properties of a parabolic point of a surface in the Euclidean three space. We introduce the contact cylindrical surface which is a cylindrical…
Capturing information on curves and surfaces from their projected images
Masaru Hasegawa, Yutaro Kabata, Kentaro Saji
Obtaining complete information about the shape of an object by looking at it from a single direction is impossible in general. In this paper, we theoretically study obtaining diffe…
Projection of crosscap
Martín Barajas Sichacá, Yutaro Kabata
We determine the precise bifurcation diagrams of the apparent contours of generic crosscaps, which contain the information of bifurcations with respect to the images of the singula…
Binary differential equations at parabolic and umbilical points for -parameter families of surfaces
Jorge Luiz Deolindo Silva, Yutaro Kabata, Toru Ohmoto
We determine local topological types of binary differential equations of asymptotic curves at parabolic and flat umbilical points for generic -parameter families of surfaces in…
Projective classification of jets of surfaces in
Jorge Luiz Deolindo Silva, Yutaro Kabata
We are interested in the local extrinsic geometry of smooth surfaces in 4-space, and classify jets of Monge forms by projective transformations according to -types o…
Bifurcation of plane-to-plane map-germs with corank two of parabolic type
Toshiki Yoshida, Yutaro Kabata, Toru Ohmoto
We study a moduli stratum of A-orbits of plane-to-plane germs of corank 2 with codimension 3. We describe explicitly the bifurcation diagram of its topologically A-versal unfolding…
Projective classification of jets of surfaces in 3-space
Hiroaki Sano, Yutaro Kabata, Jorge Luiz Deolindo Silva +1
We present a local classification of smooth projective surfaces in 3-space via projective transformations in accordance with singularity types of central projections up to codimens…
Recognition of plane-to-plane map-germs
Yutaro Kabata
We present a complete set of criteria for determining A-types of plane-to-plane map-germs of corank one with A-codimension <7, which provides a new insight into the A-classificatio…