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BibTeX entry
@Article{Sunday:2002:FPA,
author = "Daniel Sunday",
title = "Fast Polygon Area and {Newell} Normal Computation",
journal = j-J-GRAPHICS-TOOLS,
volume = "7",
number = "2",
pages = "9--13 (??)",
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/Sunday02/",
abstract = "The textbook formula for the area of an $n$-vertex
two-dimensional polygon uses $2n+1$ multiplications and
$2n-1$ additions. We give an improved formula that uses
$n+1$ multiplications and $2n-1$ additions. A similar
formula is derived for a three-dimensional planar
polygon where, given the unit normal, the textbook
equation cost of $6n+4$ multiplications and $4n+1$
additions is reduced to $n+2$ multiplications and
$2n-1$ additions. Our formula also speed up Newell's
method to compute a robust approximate normal for a
nearly planar three-dimensional polygon, using $3n$
fewer additions than the textbook formula. Further,
when using this method, one can get the polygon's
planar area as equal to the length of Newell's normal
for a small additional fixed cost.",
acknowledgement = ack-nhfb,
journal-URL = "http://www.tandfonline.com/loi/ujgt20",
xxremark = "Web site has 4-page gap between this article and the
next.",
}
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- $n$,
6(3)29,
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4(1)11
- additional,
7(1)33,
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9(1)35
- approximate,
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7(4)3,
7(4)53,
9(2)1,
9(3)21,
10(4)33,
12(1)27,
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- area,
2(2)1,
2(3)45,
3(2)21,
4(2)37,
4(3)23,
5(3)1,
5(4)1,
6(4)29,
7(3)27,
8(1)3,
9(1)13
- computation,
1(1)33,
1(2)25,
1(2)31,
1(3)1,
2(3)45,
4(1)11,
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4(2)37,
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6(3)17,
6(4)29,
7(1)13,
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7(2)17,
7(4)43,
8(3)23,
9(1)13,
9(2)11,
9(3)1,
11(2)37,
12(4)47,
15(3)183
- compute,
1(1)3,
2(3)45,
3(3)29,
4(2)37,
4(3)1,
4(3)11,
5(1)1,
5(4)1,
5(4)25,
6(4)1,
6(4)29,
7(4)9,
8(1)3,
9(1)35
- cost,
1(3)1,
2(2)9,
6(1)1,
7(2)41,
7(4)19,
8(2)17,
9(3)1
- derived,
2(3)1,
3(1)1,
3(2)21,
6(1)29
- dimensional, three-,
1(1)21,
1(1)33,
2(3)15,
2(3)37,
3(3)1,
3(4)33,
4(2)27,
4(2)37,
4(4)23,
5(2)15,
6(3)1,
6(3)45,
6(4)41,
7(2)27,
8(2)41,
8(3)1,
8(4)25
- dimensional, two-,
2(4)45,
4(1)39,
4(2)37,
4(4)23,
5(4)13,
5(4)25,
7(3)43,
8(2)31,
9(1)35
- equal,
6(1)35
- equation,
3(3)29,
4(2)1,
6(2)43,
7(1)13,
7(1)23,
7(4)33
- fast,
1(2)25,
1(2)31,
1(3)1,
2(1)21,
2(2)25,
2(3)29,
2(4)15,
3(4)1,
3(4)33,
4(2)7,
4(2)37,
4(4)5,
5(2)33,
5(4)25,
6(1)29,
6(2)1,
6(2)27,
6(2)43,
6(4)1,
6(4)13,
6(4)29,
7(1)23,
7(2)17,
7(3)27,
7(3)43,
7(4)69,
7(4)91,
8(1)16,
8(1)25,
8(2)17,
8(4)1,
8(4)37,
9(1)23,
9(1)35,
9(2)1,
9(2)11,
9(3)21,
10(2)41,
10(3)13,
11(2)37,
11(4)39,
12(2)59,
12(4)35,
12(4)47,
13(3)53,
14(2)1,
15(3)161,
17(1)17
- fewer,
8(1)33
- formula,
2(2)9,
3(2)21
- further,
4(1)11,
4(3)1,
4(4)37,
5(3)1,
7(4)69,
8(3)23,
8(3)33
- give,
1(2)5,
1(2)31,
4(4)1,
5(2)33,
7(1)1,
8(1)33,
8(3)33
- given,
1(3)1,
2(3)1,
3(1)15,
3(2)21,
4(3)11,
4(4)33,
5(2)33,
5(3)1,
5(3)11,
6(1)35,
6(2)43,
7(1)23,
7(1)33,
7(4)43,
8(1)3,
9(3)1
- improved,
1(1)33,
4(2)7,
5(2)1,
8(2)31,
10(2)41,
11(1)51,
17(1)5,
17(4)127,
17(4)151
- length,
2(4)45,
3(2)21,
6(1)35,
6(2)17,
6(4)29
- nearly,
1(1)33,
6(1)1,
7(4)9,
9(1)23
- normal,
1(2)25,
2(3)29,
3(1)43,
4(2)1,
7(4)19,
7(4)69,
10(3)65,
12(1)27,
12(4)47,
16(2)71
- one,
1(2)1,
1(3)1,
2(2)31,
2(4)15,
3(3)1,
4(2)27,
4(3)11,
4(4)1,
6(1)35,
6(2)27,
6(2)43,
8(1)16,
8(1)25,
8(3)1,
9(3)21,
14(1)63
- planar,
1(2)1,
1(2)25,
6(1)7,
6(1)19,
7(4)33
- polygon,
1(2)1,
1(2)5,
1(2)25,
3(1)1,
4(1)1,
6(1)35,
6(2)27,
7(1)13,
8(4)25,
9(1)1,
9(3)41,
10(1)17,
10(2)27,
10(2)51,
13(2)55
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2(4)1,
6(3)37
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1(1)33,
2(3)45,
2(4)15,
4(2)7,
6(4)13,
7(3)27,
8(1)25,
8(2)17,
8(2)31,
8(4)37,
9(3)41,
10(1)49,
13(1)19
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5(4)1,
8(3)23
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1(3)13,
1(4)21,
2(2)1,
3(3)29,
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7(1)45,
8(1)33,
8(2)1,
8(4)1,
8(4)25,
9(1)23,
17(1)45
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3(1)15,
4(1)11,
4(2)37,
4(4)1,
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5(2)33,
5(4)1,
5(4)25,
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6(1)29,
6(2)27,
6(3)37,
6(4)1,
7(4)69,
8(1)16,
8(1)25,
8(2)31,
8(2)41,
8(3)1,
8(3)23,
9(1)35,
9(3)21
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2(3)37,
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4(4)23,
5(2)15,
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6(3)45,
6(4)41,
7(2)27,
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8(4)25
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4(2)37,
4(4)23,
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5(4)25,
7(3)43,
8(2)31,
9(1)35
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4(4)1,
4(4)33,
16(3)151,
17(1)45
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1(2)25,
1(3)29,
1(4)21,
2(3)1,
2(3)29,
2(3)37,
2(4)1,
3(1)15,
3(2)1,
3(3)1,
3(3)29,
3(4)33,
4(1)11,
4(2)7,
4(3)1,
4(3)11,
4(3)23,
5(1)1,
5(2)25,
5(3)35,
5(4)13,
5(4)33,
6(1)7,
6(1)19,
6(2)1,
6(2)17,
6(3)37,
7(1)1,
7(2)1,
7(4)3,
7(4)19,
7(4)91,
8(1)3,
8(2)1,
8(3)23,
8(4)37,
9(3)21
- using,
1(3)1,
1(3)7,
2(2)1,
2(4)1,
3(3)1,
3(3)29,
3(4)13,
4(1)1,
4(1)11,
4(2)7,
4(2)27,
4(3)23,
4(3)35,
4(4)11,
4(4)23,
5(1)1,
5(1)9,
5(2)1,
5(2)15,
5(2)33,
5(3)35,
5(4)13,
5(4)33,
6(1)19,
6(1)29,
6(2)27,
6(4)1,
6(4)29,
7(1)23,
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7(2)27,
7(4)9,
7(4)19,
7(4)27,
7(4)33,
7(4)43,
7(4)53,
7(4)69,
7(4)91,
8(1)16,
8(1)25,
8(1)33,
8(2)17,
8(3)1,
8(3)23,
8(3)33,
8(3)41,
8(4)1,
8(4)37,
9(1)13,
9(2)1,
9(3)21,
9(4)57,
10(3)1,
10(4)1,
10(4)61,
11(4)1,
11(4)17,
12(1)27,
12(1)47,
12(2)13,
12(3)17,
12(4)35,
13(3)53,
13(4)61,
14(4)1,
15(1)29,
15(4)225,
16(3)123,
17(1)17,
17(3)99,
17(4)151
- vertex,
1(2)1,
1(3)13,
3(1)43,
3(2)21,
4(2)1,
6(1)1,
8(1)3,
8(2)41,
8(3)1,
8(4)21,
12(4)47,
16(3)144
- when,
1(3)1,
3(4)13,
4(2)1,
4(4)37,
5(2)1,
5(3)11,
6(1)1,
6(4)1,
6(4)41,
7(3)27,
7(4)9,
7(4)91,
8(1)33,
9(2)11,
9(3)21
- where,
2(1)21,
2(3)45,
3(3)1,
5(2)33,
6(1)1,
7(3)19,
8(4)25