Entry Shene:1994:LDI from tog.bib
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BibTeX entry
@Article{Shene:1994:LDI,
author = "Ching-Kuang Shene and John K. Johnstone",
title = "On the Lower Degree Intersections of Two Natural
Quadrics",
journal = j-TOG,
volume = "13",
number = "4",
pages = "400--424",
month = oct,
year = "1994",
CODEN = "ATGRDF",
ISSN = "0730-0301",
bibdate = "Sat Jan 13 12:49:28 1996",
URL = "http://www.acm.org/pubs/toc/Abstracts/0730-0301/197316.html",
abstract = "In general, two quadric surface intersect in a space
quartic curve. However, the intersection frequently
degenerates to a collection of plane curves. Degenerate
cases are frequent in geometric/solid modeling because
degeneracies are often required by design. Their
detection is important because degenerate intersections
can be computed more easily and allow simpler treatment
of important problems. In this paper, we investigate
this problem for natural quadrics. Algorithms are
presented to detect and compute conic intersections and
linear intersections. These methods reveal the
relationship between the planes of the degenerate
intersections and the quadrics. Using the theory
developed in the paper, we present a new and simplified
proof of a necessary and sufficient condition for conic
intersection. Finally, we present a simple method for
determining the types of conic in a degenerate
intersection without actually computing the
intersection, and an enumeration of all possible conic
types. Since only elementary geometric routines such as
line intersection are used, all of the above algorithms
are intuitive and easily implementable.",
acknowledgement = ack-nhfb,
keywords = "algorithms; design",
subject = "{\bf I.3.5}: Computing Methodologies, COMPUTER
GRAPHICS, Computational Geometry and Object Modeling,
Curve, surface, solid, and object representations. {\bf
J.6}: Computer Applications, COMPUTER-AIDED
ENGINEERING, Computer-aided design (CAD).",
}
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28(4)99,
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26(3)108,
27(1)7,
27(3)31,
27(3)36,
27(3)45,
27(3)95,
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27(5)156,
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16(2)155,
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28(1)5,
28(3)57,
28(3)67,
28(3)80,
28(3)90,
28(3)96,
28(4)106
- conic,
2(1)1,
2(3)182,
3(3)223,
8(2)89,
10(4)366,
17(1)1
- degenerate,
8(3)174,
9(1)66,
17(1)32
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5(2)79,
6(2)159,
12(1)1,
13(1)3,
13(2)156,
13(4)313,
14(3)203,
14(4)363,
15(3)223,
16(3)319,
17(1)1,
18(2)96,
18(2)128,
19(1)27,
20(1)1,
25(4)1281,
26(3)40,
26(3)43,
26(3)46,
26(3)104,
27(3)28,
27(3)57,
27(3)85,
27(5)112,
28(2)13,
28(3)46,
28(3)47,
28(3)48,
28(3)53,
28(3)62,
28(3)72,
28(4)99
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16(1)74,
17(3)177,
26(3)43,
27(3)26,
27(3)39,
27(3)87,
27(5)111,
28(2)17,
28(3)35,
28(3)76,
28(3)98
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8(1)51,
13(3)277,
14(2)171,
15(3)179,
17(3)177,
18(3)257,
19(1)1,
23(3)393,
23(3)679,
24(3)991,
25(2)439,
25(3)560,
26(3)15,
26(3)30,
26(4)17,
27(3)39,
27(3)69,
27(3)87,
27(5)161
- determining,
11(4)336,
12(4)305,
17(4)259,
19(1)56,
26(3)5,
26(3)24,
26(3)77,
27(1)1,
27(3)33,
28(3)60
- developed,
10(1)1,
10(1)71,
11(4)305,
12(4)277,
13(4)313,
13(4)376,
16(1)34,
18(1)56,
19(2)122,
26(3)84,
26(3)90,
26(3)107,
26(4)15,
27(2)12,
27(3)94,
27(5)123,
28(1)3,
28(3)55,
28(3)56,
28(3)65,
28(3)72,
28(3)78,
28(4)102
- easily,
5(2)79,
10(1)92,
12(4)327,
14(3)266,
15(3)211,
17(3)158,
18(1)56,
26(2)8,
26(3)21,
26(3)41,
26(3)44,
26(3)45,
26(3)49,
26(3)52,
26(3)67,
26(3)99,
26(3)101,
26(3)106,
27(3)36,
27(3)53,
27(3)90,
27(3)95,
27(5)128,
27(5)160,
28(2)14,
28(2)17,
28(2)18,
28(3)41,
28(3)54,
28(3)65,
28(3)87
- elementary,
10(2)182,
16(2)179,
17(4)209,
27(5)108,
27(5)161
- ENGINEERING,
4(1)12,
4(4)291,
5(1)1,
5(2)110,
5(3)179,
5(3)244,
5(4)283,
5(4)318,
5(4)345,
6(3)238,
6(4)274,
7(1)1,
7(1)42,
7(2)83,
7(3)180,
7(3)198,
8(1)25,
8(1)51,
8(3)204,
8(4)263,
8(4)325,
8(4)335,
8(4)360,
9(1)28,
9(1)133,
9(2)147,
9(2)160,
9(2)212,
10(1)1,
10(1)71,
10(2)111,
10(2)201,
10(3)213,
10(3)297,
10(3)312,
10(4)366,
10(4)378,
11(1)12,
11(2)140,
11(2)152,
12(1)56,
12(2)113,
12(3)209,
12(4)277,
12(4)305,
12(4)327,
13(1)3,
13(1)43,
13(3)209,
13(3)277,
14(2)103,
14(3)266,
15(3)211,
15(4)265,
16(1)34,
16(1)74,
16(2)155,
16(2)179,
16(3)319,
17(4)259,
18(1)35
- enumeration,
9(3)245
- finally,
3(1)52,
10(2)182,
14(1)77,
14(4)311,
14(4)363,
16(1)3,
16(2)179,
16(3)296,
17(2)84,
17(4)259,
20(3)151,
20(4)232,
21(1)20,
26(2)11,
26(3)6,
26(3)13,
26(3)34,
26(3)37,
26(3)76,
26(3)88,
26(4)19,
27(1)1,
27(3)40,
27(3)46,
27(3)60,
27(3)67,
27(3)73,
27(5)109,
27(5)126,
27(5)128,
27(5)139,
27(5)149,
27(5)153,
27(5)156,
27(5)161,
28(1)1,
28(3)24,
28(3)26,
28(3)32,
28(3)42,
28(3)44,
28(3)52,
28(3)56,
28(3)57,
28(3)71,
28(3)80,
28(3)85,
28(4)99
- frequent,
27(3)47,
28(3)81
- frequently,
13(1)43,
14(3)203,
26(3)21,
27(3)59
- general,
1(1)1,
1(3)191,
4(1)1,
4(2)74,
9(1)1,
9(2)160,
9(4)424,
10(1)1,
10(2)182,
11(1)12,
11(2)183,
12(1)35,
12(2)136,
12(3)251,
13(1)3,
13(3)308,
15(1)1,
15(1)37,
15(1)72,
15(3)223,
15(4)301,
16(2)179,
16(3)296,
16(3)319,
17(1)32,
17(2)71,
17(2)84,
17(2)116,
17(3)158,
17(4)238,
17(4)259,
18(1)35,
18(1)56,
18(2)96,
18(2)128,
18(2)171,
18(2)195,
18(3)257,
18(4)329,
18(4)361,
19(1)27,
19(4)246,
19(4)279,
22(2)131,
26(3)24,
26(3)58,
26(3)76,
26(3)96,
27(2)13,
27(3)19,
27(3)22,
27(3)46,
27(3)62,
27(4)106,
27(5)126,
27(5)127,
27(5)135,
27(5)143,
27(5)145,
27(5)148,
28(1)10,
28(2)16,
28(3)65,
28(3)74,
28(3)80,
28(3)81
- however,
10(1)1,
11(2)140,
11(4)336,
11(4)348,
12(4)277,
13(1)73,
13(2)103,
13(2)177,
13(4)313,
14(1)58,
15(3)211,
16(4)397,
17(1)32,
17(1)50,
17(2)84,
18(2)171,
19(1)1,
19(2)79,
19(3)204,
21(1)52,
26(1)4,
26(3)1,
26(3)14,
26(3)32,
26(3)38,
26(3)39,
26(3)45,
26(3)52,
26(3)62,
26(3)76,
26(4)18,
26(4)20,
27(2)12,
27(3)20,
27(3)26,
27(3)31,
27(3)51,
27(3)52,
27(3)54,
27(3)66,
27(3)70,
27(3)80,
27(3)87,
27(3)102,
27(5)111,
27(5)115,
27(5)132,
27(5)155,
28(1)6,
28(2)13,
28(2)17,
28(3)23,
28(3)24,
28(3)27,
28(3)53,
28(3)65,
28(3)82,
28(4)105
- important,
5(2)79,
7(3)151,
11(3)228,
11(4)373,
15(4)265,
17(2)71,
17(4)209,
18(1)1,
18(2)96,
18(3)257,
20(1)10,
20(2)67,
26(1)2,
26(1)4,
26(2)7,
26(3)6,
26(3)53,
26(3)58,
26(3)97,
26(3)107,
27(1)1,
27(3)20,
27(3)52,
27(3)65,
27(3)67,
27(3)80,
27(3)91,
27(3)94,
27(3)100,
27(5)118,
27(5)143,
28(1)2,
28(1)11,
28(2)18,
28(3)61,
28(3)67,
28(3)85,
28(3)92,
28(3)97
- intersect,
3(3)223,
12(4)305,
26(3)30,
28(3)94
- intersection,
2(3)161,
3(3)223,
4(4)291,
6(4)274,
8(1)25,
8(3)174,
8(3)235,
9(2)147,
10(1)92,
10(4)378,
11(1)12,
11(2)140,
13(1)73,
13(3)277,
13(3)308,
13(4)337,
14(1)21,
15(3)223,
16(1)74,
16(3)296,
18(3)257,
25(3)1154,
27(1)3,
27(3)79,
27(3)87,
28(3)47,
28(3)84
- intuitive,
13(2)103,
15(3)211,
23(3)630,
26(3)3,
26(3)14,
26(3)17,
26(3)55,
26(3)64,
26(3)80,
26(3)81,
26(3)86,
27(3)40,
27(3)91,
27(3)92,
27(3)103,
27(5)162,
28(1)10,
28(2)20,
28(3)23,
28(3)24,
28(3)34,
28(3)42,
28(3)54,
28(4)103
- investigate,
18(1)1,
20(3)151,
26(3)54,
27(1)2,
27(5)138,
27(5)145,
28(3)28,
28(3)55,
28(3)73
- J.6,
4(1)12,
4(4)291,
5(1)1,
6(3)238,
6(4)274,
7(1)1,
7(1)42,
7(2)83,
7(3)198,
8(1)25,
8(1)51,
8(3)204,
8(4)263,
8(4)325,
8(4)335,
8(4)360,
9(2)147,
9(2)160,
9(2)212,
10(1)71,
10(3)297,
10(3)312,
10(4)366,
10(4)378,
11(1)12,
11(2)140,
11(2)152,
12(1)56,
12(2)113,
12(3)209,
12(4)305,
12(4)327,
13(1)3,
13(3)277,
14(2)103,
14(3)266,
16(1)34,
16(1)74,
16(2)155,
16(2)179,
16(3)319,
17(4)259,
18(1)35,
18(4)329,
19(1)27,
19(1)56
- line,
1(4)274,
3(1)1,
3(3)223,
4(3)182,
6(1)19,
6(4)308,
7(1)61,
8(1)25,
9(3)278,
9(4)376,
11(3)259,
11(3)276,
13(1)3,
13(3)308,
15(3)223,
16(2)109,
17(1)1,
17(1)50,
17(4)209,
18(4)293,
18(4)316,
22(1)33,
23(3)609,
24(3)512,
26(3)11,
26(3)18,
26(3)19,
26(3)29,
26(3)41,
26(3)42,
26(3)64,
26(3)104,
27(3)64,
27(3)76,
27(3)88,
27(5)147,
27(5)156,
27(5)159,
28(1)11,
28(2)17,
28(3)28,
28(3)43,
28(3)65,
28(3)77
- lower,
11(1)12,
27(3)32,
27(5)137,
28(3)42,
28(3)93
- more,
8(1)41,
10(1)92,
10(2)111,
11(1)40,
11(3)201,
12(4)277,
13(3)240,
13(3)256,
13(4)313,
13(4)337,
14(1)77,
15(1)72,
15(3)179,
15(3)211,
15(4)265,
15(4)332,
16(1)3,
17(2)116,
17(4)259,
18(2)96,
18(2)171,
19(2)122,
19(3)204,
20(3)169,
26(1)6,
26(3)15,
26(3)20,
26(3)30,
26(3)42,
26(3)45,
26(3)47,
26(3)52,
26(3)55,
26(3)57,
26(3)63,
26(3)64,
26(3)70,
26(3)71,
26(3)73,
26(3)86,
26(3)89,
26(3)90,
26(3)93,
26(3)97,
26(4)20,
27(1)2,
27(1)5,
27(3)22,
27(3)26,
27(3)31,
27(3)34,
27(3)52,
27(3)60,
27(3)64,
27(3)82,
27(5)111,
27(5)123,
27(5)128,
27(5)130,
27(5)151,
28(1)1,
28(2)20,
28(3)34,
28(3)40,
28(3)53,
28(3)61,
28(3)64,
28(3)66,
28(3)67,
28(3)69,
28(3)74,
28(3)75,
28(3)87,
28(3)94,
28(4)99,
28(4)101
- natural,
6(3)167,
6(3)215,
13(2)177,
13(4)337,
14(1)77,
15(3)211,
16(3)217,
18(2)96,
18(4)293,
20(4)203,
24(3)1090,
25(3)779,
25(3)1180,
26(1)3,
26(2)8,
26(3)8,
26(3)16,
26(3)35,
26(3)36,
26(3)80,
26(3)97,
26(3)105,
26(3)106,
27(3)46,
27(3)58,
27(3)63,
27(3)78,
27(3)82,
27(5)145,
27(5)163,
28(1)1,
28(2)20,
28(3)24,
28(3)34,
28(3)35,
28(3)80,
28(4)102
- necessary,
4(4)291,
11(4)406,
13(3)277,
17(4)259,
20(1)10,
26(1)3,
26(3)5,
26(3)14,
26(3)46,
26(3)55,
26(3)60,
27(1)6,
27(5)130,
27(5)149,
28(3)82,
28(4)99
- often,
11(3)201,
13(3)256,
13(4)313,
14(1)21,
14(3)203,
17(4)238,
18(3)257,
26(1)4,
26(3)17,
26(3)20,
26(3)38,
26(3)43,
26(3)46,
26(3)50,
26(3)62,
26(3)74,
26(3)89,
26(3)96,
26(3)98,
27(2)13,
27(3)15,
27(3)38,
27(3)42,
27(3)67,
27(3)71,
27(5)143,
27(5)145,
28(3)28,
28(3)35,
28(3)37,
28(3)38,
28(3)82,
28(3)83,
28(3)85,
28(3)93
- only,
10(1)71,
10(1)92,
11(4)373,
13(1)3,
13(2)103,
13(2)156,
13(2)177,
14(1)58,
15(4)332,
16(1)3,
16(3)296,
17(4)238,
18(1)56,
18(2)96,
18(3)278,
19(1)1,
21(1)1,
26(1)1,
26(1)5,
26(1)6,
26(3)3,
26(3)4,
26(3)10,
26(3)36,
26(3)39,
26(3)44,
26(3)55,
26(3)59,
26(3)74,
26(3)75,
26(3)83,
26(3)88,
26(3)91,
26(3)92,
26(3)106,
26(4)16,
26(4)19,
27(3)19,
27(3)20,
27(3)36,
27(3)37,
27(3)41,
27(3)50,
27(3)51,
27(3)57,
27(3)59,
27(3)64,
27(3)75,
27(3)93,
27(5)109,
27(5)112,
27(5)118,
27(5)134,
27(5)140,
27(5)141,
27(5)155,
27(5)163,
28(2)19,
28(3)30,
28(3)44,
28(3)47,
28(3)48,
28(3)52,
28(3)54,
28(3)55,
28(3)65,
28(3)90,
28(3)97
- plane,
7(2)83,
8(3)235,
9(4)424,
11(1)61,
13(1)3,
15(3)211,
15(3)223,
16(2)109,
16(3)296,
17(1)32,
17(1)50,
19(1)1,
19(2)79,
19(3)185,
26(3)19,
26(3)22,
26(3)69,
26(3)70,
26(3)78,
27(3)30,
27(3)38,
27(3)87,
27(5)133,
27(5)134,
27(5)161,
28(2)13,
28(3)72
- possible,
3(3)223,
4(4)291,
11(4)336,
11(4)348,
12(4)305,
13(1)3,
13(2)137,
13(3)240,
13(4)337,
13(4)376,
14(1)77,
14(3)233,
15(3)179,
16(3)296,
17(3)158,
19(2)122,
20(2)67,
21(1)1,
26(3)32,
26(3)33,
26(3)36,
26(3)88,
27(2)11,
27(2)12,
27(3)25,
27(3)28,
27(3)42,
27(3)43,
27(3)54,
27(3)58,
27(3)69,
27(3)71,
27(3)80,
27(3)81,
27(3)98,
27(5)114,
27(5)116,
27(5)118,
27(5)122,
27(5)125,
27(5)127,
27(5)130,
27(5)164,
28(3)52,
28(3)53,
28(3)55,
28(3)57,
28(3)59,
28(3)60,
28(3)61,
28(3)77,
28(3)78,
28(3)90,
28(3)94,
28(4)101
- presented,
3(1)52,
3(3)223,
4(4)291,
5(2)79,
5(3)244,
7(3)151,
9(1)1,
10(1)92,
11(1)61,
11(2)103,
11(2)140,
11(2)152,
11(3)201,
11(4)305,
13(1)43,
13(3)209,
13(3)240,
13(3)277,
14(1)77,
14(4)337,
15(1)1,
15(1)72,
15(3)249,
16(2)179,
17(2)116,
19(2)79,
19(3)185,
19(4)246,
20(3)151,
20(3)169,
20(4)203,
26(3)44,
27(3)38,
27(3)86,
27(5)138,
27(5)146,
27(5)155,
28(1)8,
28(3)55,
28(3)70,
28(3)75,
28(3)84,
28(4)100
- proof,
18(3)257,
26(3)57
- quadric,
6(4)274,
8(3)174,
10(4)378,
27(5)148
- quartic,
8(3)235,
9(3)301,
19(1)56
- relationship,
9(1)1,
11(1)12,
11(1)40,
14(1)58,
16(2)155,
18(1)35,
26(3)27,
27(3)27,
27(3)61,
27(5)121,
28(3)89
- required,
11(2)140,
11(4)406,
13(1)3,
13(1)43,
13(2)103,
13(2)137,
13(2)177,
13(3)240,
14(1)21,
15(4)332,
17(2)84,
19(3)164,
19(3)204,
21(1)1,
26(3)3,
26(3)6,
26(3)7,
26(3)69,
26(3)70,
26(3)78,
26(3)86,
26(3)90,
26(4)18,
26(4)20,
27(1)5,
27(3)18,
27(3)81,
27(3)83,
27(3)85,
27(5)115,
27(5)137,
27(5)151,
28(1)8,
28(2)13,
28(2)18,
28(3)32
- reveal,
14(3)203,
27(3)43
- routine,
12(2)113,
13(3)209,
17(2)71,
26(3)66,
27(3)84,
28(3)80
- simpler,
27(1)2,
27(3)56,
27(3)60,
28(3)50
- simplified,
19(3)204,
26(3)104,
26(4)20,
28(3)61,
28(3)76
- since,
3(1)52,
9(3)245,
13(4)313,
15(3)223,
17(2)84,
19(1)27,
26(1)2,
26(3)19,
26(3)38,
26(3)43,
26(3)52,
26(3)80,
26(3)82,
27(3)36,
27(3)70,
27(3)98,
27(4)107,
27(5)123,
27(5)151,
28(2)18,
28(3)26,
28(3)54,
28(3)56,
28(3)65,
28(4)106
- sufficient,
11(1)40,
13(1)3,
15(3)211,
17(4)259,
26(4)18,
27(3)21,
27(3)85,
27(5)115,
28(3)77,
28(3)84
- treatment,
6(4)308,
14(3)203,
21(3)594,
26(3)38,
26(3)73,
27(3)23,
27(3)46,
27(3)63,
28(3)75,
28(3)88
- type,
7(3)180,
8(1)41,
12(3)233,
13(3)256,
13(4)376,
14(3)203,
15(1)37,
15(4)354,
16(1)34,
19(2)79,
19(2)122,
20(4)232,
26(1)1,
26(2)7,
26(3)30,
26(3)37,
26(3)60,
26(3)65,
26(3)74,
26(3)79,
26(4)13,
26(4)15,
27(1)7,
27(3)26,
27(3)28,
27(3)42,
27(3)53,
27(3)70,
27(3)84,
27(3)89,
27(3)95,
27(3)98,
27(4)106,
27(5)112,
27(5)113,
27(5)122,
28(1)4,
28(1)11,
28(2)13,
28(2)16,
28(2)19,
28(3)28,
28(3)35,
28(3)70,
28(3)72,
28(3)73,
28(3)77,
28(3)79,
28(3)94,
28(4)101