Modelling and animation of generalized cylinders with variable radius offset space curves

1994 ◽  
Vol 5 (4) ◽  
pp. 189-207 ◽  
Author(s):  
Myung-Soo Kim ◽  
Eun-Joo Park ◽  
Hwan-Yong Lee
Keyword(s):  
Variable Radius ◽  
Space Curves ◽  
Generalized Cylinders

Blending Cylinders and Cones using Canal Surfaces

2000 ◽  
Vol 5 ◽  
pp. 77-89 ◽  
Author(s):  
M. Kazakevičiūtė ◽  
R. Krasauskas
Keyword(s):  
Canal Surface ◽  
Variable Radius ◽  
Rolling Ball ◽  
Canal Surfaces ◽  
Rational Parameterization

There is reviewed the construction of a rational blending surface between cylinders and cones in some interlocation cases. This surface is constructed as a patch of rolling ball envelope, i.e. as a patch of tangent canal surface of rational-variable radius. This construction defines rational parameterization of a blending surface. The constructed surface is Laguerre invariant.

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.

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.

scholarly journals Degen Generalized Cylinders and Their Properties

2006 ◽  
pp. 83-94
Author(s):  
Liangliang Cao ◽  
Jianzhuang Liu ◽  
Xiaoou Tang
Keyword(s):  
Generalized Cylinders
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