Grasping the apparent contour

1994 ◽  
pp. 25-34 ◽  
Author(s):  
Michael J. Taylor ◽  
Andrew Blake
Keyword(s):  
Apparent Contour

Versal topological stratification and the bifurcation geometry of map-germs of the plane

1990 ◽  
Vol 107 (1) ◽  
pp. 127-147 ◽  
Author(s):  
J. H. Rieger
Keyword(s):  
Differential Geometry ◽  
Classical Result ◽  
Smooth Surface ◽  
Critical Values ◽  
Central Projections ◽  
Apparent Contour ◽  
Smooth Map

The set of critical values of a map of the plane (of corank 1) can be regarded as the apparent contour of a smooth surface. It is a classical result of Whitney[13] that generically the apparent contour is a smooth fold curve with isolated cusps and transverse fold crossings. More recent classifications of smooth map-germs of the plane of low codimension (occurring in generic 2- or 3-parameter families), e.g. in [1, 5, 7], were motivated by a question in differential geometry: given any smooth surface which is generically embedded in ℝ3, produce a list of all possible (orthogonal or central) projections of such a surface.

Stable Maps and Morse Descriptions of an Apparent Contour

2015 ◽  
pp. 25-52
Author(s):  
Giovanni Bellettini ◽  
Valentina Beorchia ◽  
Maurizio Paolini ◽  
Franco Pasquarelli
Keyword(s):  
Stable Maps ◽  
Apparent Contour

scholarly journals LEGENDRIAN GRAPHS GENERATED BY TANGENTIAL FAMILY GERMS

2006 ◽  
Vol 49 (1) ◽  
pp. 29-37 ◽  
Author(s):  
Gianmarco Capitanio
Keyword(s):  
Cotangent Bundle ◽  
Normal Forms ◽  
Plane Curve ◽  
Parameter Family ◽  
Apparent Contour ◽  
The Family ◽  
Whitney Umbrella ◽  
Envelope Theory

AbstractWe construct a Legendrian version of envelope theory. A tangential family is a one-parameter family of rays emanating tangentially from a regular plane curve. The Legendrian graph of the family is the union of the Legendrian lifts of the family curves in the projectivized cotangent bundle $PT^*\mathbb{R}^2$. We study the singularities of Legendrian graphs and their stability under small tangential deformations. We also find normal forms of their projections into the plane. This allows us to interpret the beak-to-beak perestroika as the apparent contour of a deformation of the double Whitney umbrella singularity $A_1^\pm$.

Geometric Modeling and Visualization of Manipulator Workplace

1991 ◽  
Author(s):  
X. Chen ◽  
K. C. Gupta
Keyword(s):  
Geometric Modeling ◽  
Geometric Model ◽  
Three Dimensional ◽  
Extraction Methods ◽  
Boundary Representation ◽  
Three Dimensions ◽  
Contour Method ◽  
Boundary Extraction ◽  
Volumetric Features ◽  
Apparent Contour

Abstract This paper introduces a new and powerful technique to determine the workspace shape of a general n-joint manipulator by utilizing geometric modeling. A complete three-dimensional geometric model of the workspace shape can be generated which is compatible with the computer graphics. The resulting workspace image can be visualized in three-dimensions realistically, manipulated interactively and analyzed for topological and volumetric features. The first part of the paper presents a general discussion of the workspace geometry and boundary representation concept. The remainder of the paper focuses on two workspace boundary extraction methods in a CAD environment: Radial-Slice-Layering method (RSL) and Apparent-Contour method (AC). Several specific examples are presented to illustrate the basic technique.

Invariants of an Apparent Contour

2015 ◽  
pp. 157-194
Author(s):  
Giovanni Bellettini ◽  
Valentina Beorchia ◽  
Maurizio Paolini ◽  
Franco Pasquarelli
Keyword(s):  
Apparent Contour

scholarly journals Projection of crosscap

2019 ◽  
Vol 16 (09) ◽  
pp. 1950130
Author(s):  
Martín Barajas Sichacá ◽  
Yutaro Kabata
Keyword(s):  
Singularity Theory ◽  
Bifurcation Diagrams ◽  
Orthogonal Projections ◽  
Apparent Contour ◽  
Singular Sets

The apparent contour of a surface in [Formula: see text]-space can be investigated in terms of singularity theory. We show the precise bifurcation diagrams of the apparent contours of generic crosscap surfaces with respect to orthogonal projections. Especially, our bifurcation diagrams contain also the information of the projected images of the singular sets of crosscap surfaces.

scholarly journals Interactions between shape-persistent macromolecules as probed by AFM

2017 ◽  
Vol 13 ◽  
pp. 938-951 ◽  
Author(s):  
Johanna Blass ◽  
Jessica Brunke ◽  
Franziska Emmerich ◽  
Cédric Przybylski ◽  
Vasil M Garamus ◽  
...  
Keyword(s):  
Polymer System ◽  
Water Soluble ◽  
Polymer Chains ◽  
Contour Length ◽  
Polymer Backbone ◽  
Guest Molecules ◽  
Apparent Contour ◽  
Multiple Inclusion ◽  
Regular Configuration ◽  
Shearing Mechanism

Water-soluble shape-persistent cyclodextrin (CD) polymers with amino-functionalized end groups were prepared starting from diacetylene-modified cyclodextrin monomers by a combined Glaser coupling/click chemistry approach. Structural perfection of the neutral CD polymers and inclusion complex formation with ditopic and monotopic guest molecules were proven by MALDI–TOF and UV–vis measurements. Small-angle neutron and X-ray (SANS/SAXS) scattering experiments confirm the stiffness of the polymer chains with an apparent contour length of about 130 Å. Surface modification of planar silicon wafers as well as AFM tips was realized by covalent bound formation between the terminal amino groups of the CD polymer and a reactive isothiocyanate–silane monolayer. Atomic force measurements of CD polymer decorated surfaces show enhanced supramolecular interaction energies which can be attributed to multiple inclusion complexes based on the rigidity of the polymer backbone and the regular configuration of the CD moieties. Depending on the geometrical configuration of attachment anisotropic adhesion characteristics of the polymer system can be distinguished between a peeling and a shearing mechanism.

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