Last update: Sun Oct 15 02:29:44 MDT 2017
Top |
Symbols |
Math |
A |
B |
C |
D |
E |
F |
G |
H |
I |
J |
K |
L |
M |
N |
O |
P |
Q |
R |
S |
T |
U |
V |
W |
X |
Y |
Z
BibTeX entry
@Article{Nasri:2001:SAG,
author = "Ahmed Nasri and Gerald Farin",
title = "A subdivision algorithm for generating rational
curves",
journal = j-J-GRAPHICS-TOOLS,
volume = "6",
number = "1",
pages = "35--47",
year = "2001",
CODEN = "JGTOFD",
ISSN = "1086-7651",
ISSN-L = "1086-7651",
bibdate = "Wed Feb 06 11:23:34 2002",
bibsource = "http://www.acm.org/jgt/issues.html;
http://www.math.utah.edu/pub/tex/bib/jgraphtools.bib",
URL = "http://www.acm.org/jgt/papers/",
abstract = "The well-known Chaikin algorithm generates uniform
quadratic B-spline curves by repeating the process of
cutting off the corners of a polygon. One disadvantage
of this algorithm is the incapability of generating
circles. This paper proposes a modification of this
algorithm to produce piecewise rational curves; in
particular a circle is produced from a given square.
For a general control polygon, every two subsequent
polygon legs of equal length will correspond to a
circular arc. Such an arc will be parameterized by arc
length and will remain circular under affine
transformations. Both properties are not shared by the
standard rational quadratic form.",
acknowledgement = ack-nhfb,
journal-URL = "http://www.tandfonline.com/loi/ujgt20",
}
Related entries
- affine,
4(2)7,
6(1)1,
15(2)73
- arc,
6(4)29,
15(2)95,
17(1)45
- B-spline,
5(1)1,
17(1)53
- both,
1(1)3,
1(3)1,
3(3)1,
3(3)29,
4(1)1,
4(1)11,
4(4)5,
4(4)11,
5(1)1,
5(2)15,
5(2)33,
5(3)11,
8(4)25,
9(1)13
- circle,
2(3)45,
6(3)45,
6(4)29,
7(1)23,
17(1)5
- circular,
15(2)95,
17(1)45
- control,
1(4)41,
2(1)1,
2(2)31,
4(4)37,
5(1)1,
5(2)15,
5(4)13,
6(4)41,
7(3)43,
7(4)3,
9(3)21
- curve,
1(3)13,
3(4)33,
5(2)1,
6(3)17,
6(3)45,
6(4)29,
7(3)13,
7(3)43,
8(3)41,
11(1)37,
11(3)17,
13(2)37,
16(1)25,
16(2)105,
16(3)123
- disadvantage,
4(3)35
- equal,
7(2)9
- every,
4(4)37,
6(2)17
- form,
1(4)21,
2(3)37,
3(2)21,
4(2)27,
6(4)1,
7(1)13,
7(3)43,
10(4)61
- general,
1(2)31,
3(2)21,
3(4)1,
3(4)33,
5(1)27,
6(1)7,
7(4)69,
8(1)25,
8(4)25,
9(2)21,
12(1)61
- generate,
1(4)41,
2(2)9,
3(4)33,
4(1)39,
4(2)27,
5(2)1,
5(4)9,
6(1)19,
6(3)45,
6(4)41,
8(1)3,
8(3)41,
9(1)35
- generating,
3(1)1,
5(4)9,
6(3)45,
11(3)17
- 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(2)43,
7(1)23,
7(1)33,
7(2)9,
7(4)43,
8(1)3,
9(3)1
- known, well-,
4(3)35,
5(1)9
- length,
2(4)45,
3(2)21,
6(2)17,
6(4)29,
7(2)9
- modification,
1(2)25,
3(3)11,
7(1)23,
8(2)31
- not,
1(1)3,
1(3)29,
2(1)1,
2(2)9,
2(2)25,
2(2)31,
2(4)1,
3(2)21,
3(3)1,
3(4)13,
4(1)1,
4(1)39,
4(3)35,
5(3)11,
5(4)1,
7(1)23,
7(1)45,
7(4)69,
8(1)25,
8(1)33,
8(2)41,
8(4)21,
9(1)13,
9(1)35,
9(3)1,
15(3)183
- 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(2)27,
6(2)43,
7(2)9,
8(1)16,
8(1)25,
8(3)1,
9(3)21,
14(1)63
- particular,
1(4)1,
3(2)21,
5(1)9,
5(2)25,
5(3)1,
7(4)83
- piecewise,
1(2)5
- polygon,
1(2)1,
1(2)5,
1(2)25,
3(1)1,
4(1)1,
6(2)27,
7(1)13,
7(2)9,
8(4)25,
9(1)1,
9(3)41,
10(1)17,
10(2)27,
10(2)51,
13(2)55
- process,
1(2)1,
4(4)11,
4(4)23,
4(4)37,
7(1)45,
7(4)33
- produce,
1(1)21,
2(2)31,
3(3)1,
5(1)1,
5(3)11,
6(2)43,
6(3)17,
7(1)45,
8(4)25,
9(1)23
- property,
1(1)33,
1(2)31,
1(3)29,
3(2)21,
6(4)29,
6(4)41,
7(1)13
- propose,
1(4)41,
2(3)15,
2(4)15,
3(1)15,
3(4)13,
4(2)1,
5(4)9,
6(1)7,
7(4)83
- rational,
4(4)37,
6(4)41,
11(3)17
- spline, B-,
5(1)1,
17(1)53
- square,
2(3)45,
4(1)39,
4(4)1,
9(1)13,
10(3)37,
14(2)1
- standard,
1(2)25,
1(3)29,
2(4)25,
3(1)15,
3(3)1,
3(4)33,
4(3)23,
5(4)13,
7(1)1,
7(2)27,
7(4)19,
7(4)69,
7(4)83,
15(3)183
- subdivision,
2(2)1,
2(4)15,
5(3)1,
5(3)35,
6(3)29,
6(4)1,
6(4)13,
7(1)33,
9(3)1,
9(4)3,
12(3)7,
12(4)1,
14(2)61
- subsequent,
6(3)45
- such,
1(1)21,
1(2)1,
1(2)25,
1(3)29,
2(1)1,
2(2)1,
2(3)1,
2(4)1,
3(3)1,
3(3)29,
3(4)13,
3(4)33,
4(1)1,
4(1)39,
4(2)7,
4(3)1,
5(3)1,
5(4)13,
6(1)1,
6(3)29,
6(3)37,
6(4)41,
7(1)33,
7(2)27,
7(3)1,
7(3)19,
7(3)27,
7(4)9,
8(1)3,
8(3)1,
8(4)21,
9(1)1,
9(3)1
- transformation,
1(1)21,
4(2)7,
4(2)27,
6(1)1,
6(3)45,
7(4)83,
8(2)31
- 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,
4(1)39,
4(3)11,
4(3)35,
5(1)23,
5(2)33,
5(3)11,
6(2)1,
6(3)29,
6(3)45,
6(4)13,
7(1)1,
7(1)23,
7(2)17,
7(3)43,
8(1)25,
8(1)33,
8(2)31,
8(2)41,
8(4)21,
11(1)37,
14(1)63
- uniform,
1(2)5,
1(2)31,
3(2)21,
4(1)39,
5(3)1,
6(3)17,
6(4)13,
13(4)61,
17(1)17
- well-known,
4(3)35,
5(1)9
- will,
15(3)183