scholarly journals The method of generating a developable surface between two space curves and unfolding it in unifying way.

2020 ◽  
Vol 54 (2) ◽  
pp. 3
Author(s):  
Osamu ARIMA
Keyword(s):  
Developable Surface ◽  
Space Curves

Newer Theory and More Robust Algorithms for Computer-Aided Design of Developable Surfaces

2005 ◽  
Vol 42 (03) ◽  
pp. 71-79
Author(s):  
B. Konesky
Keyword(s):  
Computer Aided Design ◽  
Developable Surface ◽  
Robust Algorithms ◽  
Developable Surfaces ◽  
Space Curves ◽  
Surface Areas ◽  
C Programming ◽  
Computer Aided ◽  
Reliable Solution ◽  
Aided Design

The use of developable surfaces in design is of engineering importance because of the relative ease with which they can be manufactured. The problem of how to make surfaces developable is not new. The usual technique is by using two space curves, defining the edges of the surface. These are first created, and then a set of rulings are constructed between the space curves under the constraint of being developable. A problem with existing algorithms for designing developable surfaces is the tendency to include nondevelopable portions of the surface: areas of regression. A more reliable solution to the problem of creating a developable surface is presented. The key to the method is to define the developable surface in terms of a normal directrix. The shape of the normal directrix defines the resulting developable surface. Algorithms are defined to compute the shape of a normal directrix from a pair of space curves. Intersecting adjacent developable surfaces and generating the flat plate layouts were also accomplished. This paper presents research and development that started around 1987. The algorithms were implemented using ANSI C++ programming language and commercial computer-aided design and manufacturing (CAD and CAM) software programs.

Particle and Astro-physics Challenge Kant’s Phenomenolism

1998 ◽  
pp. 323-333
Author(s):  
Lawrence H. Starkey
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
Physical Basis ◽  
Primary Sources ◽  
One Dimension ◽  
Space Curves ◽  
Slowing Down ◽  
Parity Conservation ◽  
Charge Parity ◽  
Einstein’S General Relativity

For two centuries Kant's first Critique has nourished various turns against transcendent metaphysics and realism. Kant was scandalized by reason's impotence in confronting infinity (or finitude) as seen in the divisibility of particles and in spatial extension and time. Therefore, he had to regard the latter as subjective and reality as imponderable. In what follows, I review various efforts to rationalize Kant's antinomies-efforts that could only flounder before the rise of Einstein's general relativity and Hawking's blackhole cosmology. Both have undercut the entire Kantian tradition by spawning highly probable theories for suppressing infinities and actually resolving these perplexities on a purely physical basis by positing curvatures of space and even of time that make them reëntrant to themselves. Heavily documented from primary sources in physics, this paper displays time’s curvature as its slowing down near very massive bodies and even freezing in a black hole from which it can reëmerge on the far side, where a new universe can open up. I argue that space curves into a double Möbius strip until it loses one dimension in exchange for another in the twin universe. It shows how 10-dimensional GUTs and the triple Universe, time/charge/parity conservation, and strange and bottom particle families and antiparticle universes, all fit together.

Research on trajectory planning of non-developable surface for automated tape placement processing of composite

2017 ◽  
Vol 24 (6) ◽  
pp. 929-936
Author(s):  
Lin Liu ◽  
Jun Xiao ◽  
Yong Li
Keyword(s):  
Trajectory Planning ◽  
Local Stress ◽  
Developable Surface ◽  
Software Environment ◽  
Quantitative Characterization ◽  
Large Size ◽  
Variable Step ◽  
The Cost ◽  
Wing Panel

AbstractTape placement manufacturing process, as one of the automated forming technologies for composite material, not only substantially improves the productivity of composite component and reduces the cost of production significantly but also raises the reliability and stability of composite structure. Automated tape placement technology is mainly applied for manufacturing the fuselage and wing panel of airplane characterized by small curvature and large size. For these kinds of structural components with a non-developable surface, trajectory planning by “natural path” method could reduce the internal stress and improve the quality of composite products to a certain extent but not be optimized by quantitative characterization. On the basis of preliminary work, the theoretical model of “unnatural degree” (UD) is introduced in the first step, which could characterize the tensile and shear strain of the laying tape quantitatively. Secondly, by adjusting the iterative step and laying direction to diminish the UD, local stress could be softened in order to optimize the laying track. Ultimately, the simulation model of the non-developable surface is established under the Matlab software environment, and the “variable step-angle” algorithm is adopted to verify the adjustment effect of the tape-laying track.

scholarly journals Interpolation for Brill–Noether space curves

2017 ◽  
Vol 156 (1-2) ◽  
pp. 137-147 ◽  
Author(s):  
Isabel Vogt
Keyword(s):  
Space Curves

scholarly journals Parallel Software to Offset the Cost of Higher Precision

2021 ◽  
Vol 40 (2) ◽  
pp. 59-64
Author(s):  
Jan Verschelde
Keyword(s):  
Power Series ◽  
Parallel Algorithms ◽  
Series Expansions ◽  
Use Case ◽  
Double Precision ◽  
Algebraic Space ◽  
Space Curves ◽  
Computational Overhead ◽  
Power Series Expansions ◽  
The Cost

Hardware double precision is often insufficient to solve large scientific problems accurately. Computing in higher precision defined by software causes significant computational overhead. The application of parallel algorithms compensates for this overhead. Newton's method to develop power series expansions of algebraic space curves is the use case for this application.

Geometric Design and Fabrication of Developable Bezier Surfaces

1992 ◽  
Author(s):  
R. M. C. Bodduluri ◽  
B. Ravani
Keyword(s):  
Geometric Design ◽  
Developable Surface ◽  
Developable Surfaces ◽  
Surface Patches ◽  
Bézier Surfaces ◽  
Point Representation ◽  
Cad Cam ◽  
C2 Continuity ◽  
Type Construction ◽  
Bezier Surfaces

Abstract In this paper we study Computer Aided Geometric Design (CAGD) and Manufacturing (CAM) of developable surfaces. We develop direct representations of developable surfaces in terms of point as well as plane geometries. The point representation uses a Bezier curve, the tangents of which span the surface. The plane representation uses control planes instead of control points and determines a surface which is a Bezier interpolation of the control planes. In this case, a de Casteljau type construction method is presented for geometric design of developable Bezier surfaces. In design of piecewise surface patches, a computational geometric algorithm similar to Farin-Boehm construction used in design of piecewise parametric curves is developed for designing developable surfaces with C2 continuity. In the area of manufacturing or fabrication of developable surfaces, we present simple methods for both development of a surface into a plane and bending of a flat plane into a desired developable surface. The approach presented uses plane and line geometries and eliminates the need for solving differential equations of Riccatti type used in previous methods. The results are illustrated using an example generated by a CAD/CAM system implemented based on the theory presented.

Developed Plate Expansion Using Geodesics

1984 ◽  
Vol 21 (04) ◽  
pp. 384-388
Author(s):  
John C. Clements
Keyword(s):  
Differential Equation ◽  
Numerical Quadrature ◽  
Developable Surface ◽  
Accuracy Control ◽  
Isometric Mapping ◽  
Variable Stepsize ◽  
Mapping Algorithm ◽  
Equation Solving ◽  
Expansion Procedure ◽  
The Relationship

This work is concerned with the application of a new isometric mapping algorithm to hull plate expansion procedures for ships with all or portions of the hull consisting of developable surfaces. The expansion procedure is based on the relationship between the ruling lines r⇀(s) generating the developable surface S⇀(s,t) and one additional geodesic g⇀(s) constructed within the surface as the solution of the differential equation det(g⇀'g⇀"n⇀) = 0 where n⇀ is the unit normal to S⇀ at g⇀. Precise accuracy control is achieved through the use of adaptive numerical quadrature and a variable stepsize differential equation solving routine.

Sign in / Sign up

Export Citation Format

Share Document