ON THE "CROSSROAD AREA–SADDLE AREA" AND "CROSSROAD AREA–SPRING AREA" TRANSITIONS

1991 ◽  
Vol 01 (03) ◽  
pp. 641-655 ◽  
Author(s):  
C. MIRA ◽  
J. P. CARCASSÈS
Keyword(s):  
Three Dimensional ◽  
Parameter Plane ◽  
Flip Bifurcation ◽  
Two Dimensional ◽  
Cusp Point ◽  
Dimensional Representation ◽  
One Dimensional ◽  
Transition Mechanism ◽  
Three Dimensional Representation ◽  
Spring Area

Let T be a one-dimensional or two-dimensional map. The three considered areas are related to three different configurations of fold and flip bifurcation curves, centred at a cusp point of a fold curve in the T parameter plane (b, c). The two transitions studied here occur via a codimension-three bifurcation defined in each case, when varying a third parameter a. The transition "mechanism," from an area type to another one, is given with a three-dimensional representation describing the sheet configuration of the parameter plane.

"CROSSROAD AREA–SPRING AREA" TRANSITION (I) PARAMETER PLANE REPRESENTATION

1991 ◽  
Vol 01 (01) ◽  
pp. 183-196 ◽  
Author(s):  
J. P. CARCASSES ◽  
C. MIRA ◽  
M. BOSCH ◽  
C. SIMÓ ◽  
J. C. TATJER
Keyword(s):  
Parameter Plane ◽  
Flip Bifurcation ◽  
Two Dimensional ◽  
Bifurcation Structure ◽  
One Dimensional ◽  
Codimension Two ◽  
Transition Mechanism ◽  
Spring Area ◽  
Cusp Points ◽  
Codimension Two Bifurcation

This paper is devoted to the bifurcation structure of a parameter plane related to one- and two-dimensional maps. Crossroad area and spring area correspond to a characteristic organization of fold and flip bifurcation curves of the parameter plane, involving the existence of cusp points (fold codimension-two bifurcation) and flip codimension-two bifurcation points. A transition "mechanism" (among others) from one area type to another one is given from a typical one-dimensional map.

"CROSSROAD AREA–SPRING AREA" TRANSITION (II) FOLIATED PARAMETRIC REPRESENTATION

1991 ◽  
Vol 01 (02) ◽  
pp. 339-348 ◽  
Author(s):  
C. MIRA ◽  
J. P. CARCASSÈS ◽  
M. BOSCH ◽  
C. SIMÓ ◽  
J. C. TATJER
Keyword(s):  
Complete Information ◽  
Parametric Representation ◽  
Periodic Points ◽  
Parameter Plane ◽  
Flip Bifurcation ◽  
Cusp Point ◽  
Dimensional Representation ◽  
Bifurcation Structure ◽  
Spring Area

The areas considered are related to two different configurations of fold and flip bifurcation curves of maps, centred at a cusp point of a fold curve. This paper is a continuation of an earlier one devoted to parameter plane representation. Now the transition is studied in a thee-dimensional representation by introducing a norm associated with fixed or periodic points. This gives rise to complete information on the map bifurcation structure.

“CROSSROAD AREA- DISSYMMETRICAL SPRING AREA — SYMMETRICAL SPRING AREA,” AND “DOUBLE CROSSROAD AREA — DOUBLE SPRING AREA” TRANSITIONS

1993 ◽  
Vol 03 (02) ◽  
pp. 429-435 ◽  
Author(s):  
REZK ALLAM ◽  
CHRISTIAN MIRA
Keyword(s):  
Parameter Plane ◽  
Flip Bifurcation ◽  
Two Dimensional ◽  
Cusp Point ◽  
Symmetrical Configuration ◽  
Spring Area

In a parameter plane, crossroad areas and spring areas are two typical organizations of fold and flip bifurcation curves centred at a fold cusp point. Till now only spring areas in a “symmetrical” configuration have been described. This letter introduces another type of spring area for which such a “symmetry” does not exist. It is called a dissymmetrical spring area. When a third parameter is varied, qualitative modifications of the parameter plane are considered, and an example of a two-dimensional diffeomorphism is given.

A CAD/CAM Representation Model Applied to Tolerance Transfer Methods

1998 ◽  
Author(s):  
Alain Desrochers
Keyword(s):  
Three Dimensional ◽  
Dimensional Representation ◽  
One Dimensional ◽  
Dimensional Tolerance ◽  
Representation Model ◽  
Three Dimensional Representation ◽  
Tolerance Chart ◽  
Cad Cam ◽  
Tolerance Charts

Abstract This paper presents the adaptation of tolerance transfer techniques to a model called TTRS for Technologically and Topologically Related Surfaces. According to this model, any three-dimensional part can be represented as a succession of surface associations forming a tree. Additional tolerancing information can be associated to each TTRS represented as a node on the tree. This information includes dimensional tolerances as well as tolerance chart values. Rules are then established to simulate tolerance chains or stack up along with tolerance charts directly from the graph. This way it becomes possible to combine traditional one dimensional tolerance transfer techniques with a powerful three-dimensional representation model providing high technological contents.

scholarly journals A system for generating virtual seeds

1998 ◽  
Vol 55 (spe) ◽  
pp. 39-45 ◽  
Author(s):  
Y. Sako ◽  
K. Fujimura ◽  
M.B. McDonald ◽  
D. James
Keyword(s):  
Three Dimensional ◽  
Promising Method ◽  
Two Dimensional ◽  
Dimensional Representation ◽  
Accurate Identification ◽  
Computer Screen ◽  
Three Dimensional Objects ◽  
Three Dimensional Representation ◽  
Quicktime Vr

Seed analysts need to identify seeds, and seed catalogs are used as a reference to accomplish this task. Conventional seed catalogs supply two-dimensional photographs and hand-drawn diagrams. In this study, a new, three-dimensional representation of seeds is developed to supplement these traditional photographs and drawings. QuickTime VR is a promising method for viewing three-dimensional objects on a computer screen. It permits manipulation of an object by rotating and viewing it from any pre-specified angle at an interactive speed, allowing the viewer the sense of examining a hand-held object. In this study, QuickTime VR object movies of seeds were created as interactive "movies" of seeds that can be rotated and scaled to give the viewer the sensation of examining actual seeds. This approach allows the examination of virtual seeds from any angle, permitting more accurate identification of seeds by seed analysts.

The Sahara

2017 ◽  
Author(s):  
Barbara E. Barich
Keyword(s):  
Human Body ◽  
Manufacturing Process ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Dimensional Representation ◽  
Three Dimensional Representation ◽  
The Difference ◽  
Symbolic Content ◽  
The Relationship

This chapter discusses the collection of objects, in clay and stone, from various pastoral Saharan sites whose original core area lay between Libya (Tadrart Acacus) and Algeria (Tassili- n-Ajjer). The chapter starts from the general theme of the relationship between the figurines and the subjects they represent, and the difference between two-dimensional and three-dimensional representation. It goes on to discuss the manufacturing process of the clay specimens (dating from between 7000 and 4000 years ago) and the significance of the changes introduced by the Neolithic. Most of the items studied fall into the category of zoomorphic figurines, with only two anthropomorphic examples, and find in the depiction of cattle their most striking subject. These representations possess an evident symbolic content which must be framed within the pastoral ideology of the Saharan Neolithic. In the anthropomorphic figurines the representation of the human body also plays the role of recapturing the sense of wholeness.

scholarly journals 2.5D Visualisation of Overlapping Biological Networks

2008 ◽  
Vol 5 (1) ◽  
pp. 77-93 ◽  
Author(s):  
David C.Y. Fung ◽  
Seok-Hee Hong ◽  
Dirk Koschützki ◽  
Falk Schreiber ◽  
Kai Xu
Keyword(s):  
Biological Networks ◽  
Metabolic Networks ◽  
Visual Analysis ◽  
Three Dimensional ◽  
Biological Data ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Dimensional Representation ◽  
Three Dimensional Representation ◽  
Interconnected Networks

Abstract Biological data is often structured in the form of complex interconnected networks such as protein interaction and metabolic networks. In this paper, we investigate a new problem of visualising such overlapping biological networks. Two networks overlap if they share some nodes and edges. We present an approach for constructing visualisations of two overlapping networks, based on a restricted three dimensional representation. More specifically, we use three parallel two dimensional planes placed in three dimensions to represent overlapping networks: one for each network (the top and the bottom planes) and one for the overlapping part (in the middle plane).Our method aims to achieve both drawing aesthetics (or conventions) for each individual network, and highlighting the intersection part by them. Using three biological datasets, we evaluate our visualisation design with the aim to test whether overlapping networks can support the visual analysis of heterogeneous and yet interconnected networks.

DETERMINATION OF DIFFERENT CONFIGURATIONS OF FOLD AND FLIP BIFURCATION CURVES OF A ONE OR TWO-DIMENSIONAL MAP

1993 ◽  
Vol 03 (04) ◽  
pp. 869-902 ◽  
Author(s):  
JEAN-PIERRE CARCASSES
Keyword(s):  
Flip Bifurcation ◽  
Two Dimensional ◽  
Bifurcation Curve ◽  
Cusp Point ◽  
Contour Lines ◽  
Spring Area ◽  
The Matrix ◽  
Point Of Intersection ◽  
Qualitative Changes

Three different configurations of fold and flip bifurcation curves of maps, centered round a cusp point of a fold curve, are considered. They are called saddle area, spring area and crossroad area. For one and two-dimensional maps, this paper uses the notion of contour lines in a parameter plane. A given contour line is related to a constant value of a "reduced multiplier" constructed from the trace and the Jacobian of the matrix associated with a given periodic point. The singularities of such lines define the configuration type of the areas indicated above. When a third parameter varies, the qualitative changes of such areas are directly identified. These singularities also enable the determination of a point of intersection of two bifurcation curves of the same nature (flip or fold), and, when a third parameter varies, the appearance (or disappearance) of a closed fold or flip bifurcation curve.

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