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BibTeX entry
@Article{Vranek:2002:FAC,
author = "David Vranek",
title = "Fast and Accurate Circle-Circle and Circle-Line {$3$D}
Distance Computation",
journal = j-J-GRAPHICS-TOOLS,
volume = "7",
number = "1",
pages = "23--32",
year = "2002",
CODEN = "JGTOFD",
ISSN = "1086-7651",
ISSN-L = "1086-7651",
bibdate = "Tue Dec 16 13:47:48 2003",
bibsource = "http://www.math.utah.edu/pub/tex/bib/jgraphtools.bib",
URL = "http://www.acm.org/jgt/papers/Vranek02/",
abstract = "This paper presents a novel high-precision algorithm
for the calculation of the minimal distance between two
circles in three dimensions. Contrary to the common
approach that mainly utilizes a solution of an
eighth-degree polynomial equation, the proposed
algorithm is based on directly using the distance
function and its derivatives. As the theory is not too
complicated, the algorithm is very easy to implement.
The paper also suggests a small modification of the
circle-circle distance algorithm for the circle-line
distance calculation. Results of computational
simulation compared with Eberly's Wild Magic library
are given and summarized in detail at the end of the
paper. They show that the proposed algorithm always
correctly finds the global minimum with much higher
accuracy at the same speed in the circle-circle
distance calculation case, whereas circle-line
calculation is approximately four times faster. The
source code is available online at the web site given
at the end of the paper.",
acknowledgement = ack-nhfb,
journal-URL = "http://www.tandfonline.com/loi/ujgt20",
}
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4(1)1,
4(1)25,
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6(1)7,
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15(3)183
- same,
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- show,
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2(2)1,
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7(1)45,
7(2)9,
8(1)33,
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9(1)23,
17(1)45
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2(1)29,
2(2)31,
3(4)33,
4(3)11,
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5(1)9,
6(3)17,
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8(3)23,
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6(1)7,
6(1)29,
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6(2)27,
6(4)1,
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- suggest,
1(4)41
- three,
1(2)5,
1(2)31,
1(3)29,
1(4)21,
2(3)37,
2(4)25,
3(2)21,
3(3)29,
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8(1)25,
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- time,
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4(3)1,
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6(1)29,
6(3)1,
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7(4)69,
8(3)23,
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- two,
1(1)3,
1(2)5,
1(3)1,
1(4)21,
2(2)9,
2(2)25,
2(3)45,
2(4)1,
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7(1)1,
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7(3)43,
8(1)25,
8(1)33,
8(2)31,
8(2)41,
8(4)21,
11(1)37,
14(1)63
- using,
1(3)1,
1(3)7,
2(2)1,
2(4)1,
3(3)1,
3(3)29,
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13(4)61,
14(4)1,
15(1)29,
15(4)225,
16(3)123,
17(1)17,
17(3)99,
17(4)151
- utilizes,
6(4)13,
8(3)1
- very,
1(1)3,
1(1)21,
1(3)29,
2(1)29,
2(2)1,
2(2)31,
4(1)1,
4(4)23,
4(4)37,
6(2)43,
7(4)69,
8(4)1,
9(1)23,
9(2)21
- web,
14(1)43