3205:
3215:
1364:
3225:
497:. However, in some applications, the polygon in question is invariant, while the point represents a query. For example, the input polygon may represent a border of a country and a point is a position of an aircraft, and the problem is to determine whether the aircraft violated the border. Finally, in the previously mentioned example of computer graphics, in
52:. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems are also considered to be part of computational geometry. While modern computational geometry is a recent development, it is one of the oldest fields of computing with a history stretching back to antiquity.
504:
In some contexts of query problems there are reasonable expectations on the sequence of the queries, which may be exploited either for efficient data structures or for tighter computational complexity estimates. For example, in some cases it is important to know the worst case for the total time for
1052:
Below is the list of the major journals that have been publishing research in geometric algorithms. Please notice with the appearance of journals specifically dedicated to computational geometry, the share of geometric publications in general-purpose computer science and computer graphics journals
440:, in which the goal is to find an efficient algorithm for finding a solution repeatedly after each incremental modification of the input data (addition or deletion input geometric elements). Algorithms for problems of this type typically involve
2125:
175:
Although most algorithms of computational geometry have been developed (and are being developed) for electronic computers, some algorithms were developed for unconventional computers (e.g. optical computers )
58:
is central to computational geometry, with great practical significance if algorithms are used on very large datasets containing tens or hundreds of millions of points. For such sets, the difference between
1191:
2170:
1177:
1008:
2175:
1416:
241:) time; i.e. its execution time is proportional to the square of the number of points. A classic result in computational geometry was the formulation of an algorithm that takes O(
1794:
167:, which deals primarily with representing real-world objects in forms suitable for computer computations in CAD/CAM systems. This branch may be seen as a further development of
2163:
1799:
843:
653:
1409:
1523:
848:
273:
The core problems in computational geometry may be classified in different ways, according to various criteria. The following general classes may be distinguished.
2158:
1354:
281:
In the problems of this category, some input is given and the corresponding output needs to be constructed or found. Some fundamental problems of this type are:
1976:
1402:
1114:
2241:
2021:
351:
The computational complexity for this class of problems is estimated by the time and space (computer memory) required to solve a given problem instance.
2180:
456:
problem is to keep track of the convex hull, e.g., for the dynamically changing set of points, i.e., while the input points are inserted or deleted.
1528:
501:
applications the changing input data are often stored in dynamic data structures, which may be exploited to speed-up the point-in-polygon queries.
1937:
1234:
1036:
1353:
3254:
2958:
2930:
1280:
478:
Some problems may be treated as belonging to either of the categories, depending on the context. For example, consider the following problem.
444:. Any of the computational geometric problems may be converted into a dynamic one, at the cost of increased processing time. For example, the
2983:
1538:
489:
In many applications this problem is treated as a single-shot one, i.e., belonging to the first class. For example, in many applications of
2834:
2104:
171:
and is often considered a branch of computer graphics or CAD. The term "computational geometry" in this meaning has been in use since 1971.
1142:
1024:
S. Fortune and J.E. Hopcroft. "A note on Rabin's nearest-neighbor algorithm." Information
Processing Letters, 8(1), pp. 20—23, 1979
2988:
2260:
1558:
1553:
876:
494:
397:: Given a partitioning of the space into cells, produce a data structure that efficiently tells in which cell a query point is located.
2493:
992:
778:
3140:
2968:
2498:
1369:
1206:
951:
631:
3228:
2322:
1971:
1655:
1100:
28:
3249:
2616:
1718:
1478:
1198:
696:
518:
159:
2869:
2907:
2526:
2234:
1645:
1184:
1170:
409:: Given a set of objects in space, produce a data structure that efficiently tells which object a query ray intersects first.
345:
1274:
907:
684:
3049:
3026:
2756:
2746:
1650:
1543:
1305:
1248:
102:
3259:
3130:
2718:
2626:
2531:
2307:
2292:
2204:
1548:
1241:
1121:
1065:
902:
857:
437:
83:
813:
3218:
2953:
2451:
1590:
1255:
325:: Given a set of points, find a largest circle with its center inside of their convex hull and enclosing none of them.
3190:
2839:
2208:
1672:
1163:
1093:
861:
774:
110:
87:
3208:
3135:
3110:
2973:
2621:
2227:
2068:
2001:
1996:
1959:
1490:
1463:
1433:
1388:
1262:
1107:
675:
647:: a method for efficiently finding two-dimensional objects represented by discrete points that have undergone an
291:
3059:
2892:
2478:
2347:
1925:
1920:
1829:
1789:
1505:
758:
413:
If the search space is fixed, the computational complexity for this class of problems is usually estimated by:
400:
1128:
449:
3120:
3054:
2945:
2761:
2421:
2114:
706:
663:
620:
441:
328:
689:
3185:
3016:
2897:
2654:
2649:
2119:
2109:
2083:
1905:
1900:
1895:
1890:
1848:
1811:
1757:
1483:
1451:
871:
819:
808:
768:
763:
724:
638:
596:
406:
394:
313:
297:
55:
203:
Some of these problems seem so simple that they were not regarded as problems at all until the advent of
3155:
3125:
3115:
3011:
2925:
2801:
2741:
2708:
2698:
2581:
2546:
2536:
2473:
2342:
2317:
2312:
2277:
2036:
2016:
1954:
1883:
1662:
1640:
1615:
1515:
1227:
1058:
980:
853:
804:
794:
648:
498:
466:
the time and space to modify the searched data structure after an incremental change in the search space
334:
79:
560:
Application areas of computational geometry include shipbuilding, aircraft, and automotive industries.
391:: Preprocess a set of points, in order to efficiently count the number of points inside a query region.
305:: Given a set of points, partition the space according to which points are closest to the given points.
1325:
2915:
2887:
2859:
2854:
2683:
2659:
2611:
2594:
2589:
2571:
2561:
2556:
2518:
2468:
2463:
2380:
2326:
2194:
2088:
2073:
1988:
1915:
1878:
1873:
1863:
1623:
1577:
1384:
1213:
1079:
700:
679:
578:
550:
322:
250:
209:
168:
136:
3180:
3105:
3021:
3006:
2771:
2551:
2508:
2503:
2400:
2390:
2362:
2063:
1932:
1843:
1730:
1701:
1425:
1287:
1156:
931:
897:
669:
626:
584:
453:
403:: Preprocess a set of points, in order to efficiently find which point is closest to a query point.
378:
140:
3145:
3044:
2920:
2877:
2786:
2728:
2713:
2703:
2488:
2287:
2200:
1853:
1839:
1821:
1804:
1784:
1767:
1677:
1500:
1220:
935:
892:
827:
785:
752:
570:
542:
506:
374:
308:
230:
144:
106:
288:: Given a set of points, find the smallest convex polyhedron/polygon containing all the points.
74:
The main impetus for the development of computational geometry as a discipline was progress in
3165:
3095:
3074:
3036:
2844:
2811:
2791:
2483:
2395:
2269:
2026:
1762:
1740:
1667:
1628:
1605:
988:
947:
886:
734:
712:
644:
604:
490:
118:
75:
184:
The primary goal of research in combinatorial computational geometry is to develop efficient
2998:
2882:
2849:
2644:
2566:
2455:
2441:
2436:
2385:
2372:
2297:
2250:
1944:
1735:
1723:
1706:
1684:
1633:
1585:
1446:
1315:
1072:
881:
755:: determine the area of a polygon whose vertices are described by ordered pairs in the plane
718:
554:
538:
482:
41:
3069:
2963:
2935:
2829:
2781:
2766:
2751:
2606:
2601:
2541:
2431:
2405:
2357:
2302:
2050:
2006:
1833:
1777:
1772:
1750:
1711:
1533:
1458:
943:
800:
738:
641:: computes the distance between every point in a grid and a discrete collection of points.
445:
388:
340:
302:
192:
for solving problems stated in terms of basic geometrical objects: points, line segments,
114:
98:
86:), but many problems in computational geometry are classical in nature, and may come from
546:
331:: Connect two points in a Euclidean space (with polyhedral obstacles) by a shortest path.
581:: find the pair of points (from a set of points) with the smallest distance between them
3175:
3079:
2978:
2824:
2796:
1694:
1149:
866:
742:
590:
234:
189:
377:
part, which varies over the problem instances. The search space typically needs to be
3243:
3064:
2352:
2011:
1966:
1949:
1595:
1468:
1394:
360:
17:
225:
One could compute the distances between all the pairs of points, of which there are
3160:
2819:
2031:
1910:
1689:
1600:
1495:
1086:
1135:
1352:
316:: Given a set of points, find the two with the smallest distance from each other.
3150:
2776:
2688:
2142:
2058:
1269:
789:
746:
728:
610:
600:
285:
147:
dates the first use of the term "computational geometry" in this sense by 1975.
3170:
3100:
2693:
2426:
2282:
2078:
657:
197:
1372:
was created from a revision of this article dated 17 September 2013
1310:
463:
the time and space required to construct the data structure to be searched in
417:
the time and space required to construct the data structure to be searched in
221:
points in the plane, find the two with the smallest distance from each other.
2675:
2636:
1441:
1316:"Strategic Directions in Computational Geometry—Working Group Report" (1996)
912:
615:
185:
45:
771:(also known as Delaunay refinement): create quality Delaunay triangulations
505:
the whole sequence of N queries, rather than for a single query. See also "
2736:
1300:
459:
The computational complexity for this class of problems is estimated by:
204:
94:
49:
587:
algorithms: check for the collision or intersection of two given solids
193:
2126:
The
Unreasonable Effectiveness of Mathematics in the Natural Sciences
1745:
1563:
493:
a common problem is to find which area on the screen is clicked by a
452:
problem by providing for addition and/or deletion of the points. The
788:: reconstruct two-dimensional surface geometry from an unstructured
2219:
721:
algorithms: tests whether a given point lies within a given polygon
257:) expected time, as well as a deterministic algorithm that takes O(
534:
Core problems are curve and surface modelling and representation.
553:
curves and surfaces. An important non-parametric approach is the
373:, the input consists of two parts: the search space part and the
71:) may be the difference between days and seconds of computation.
1192:
International
Journal of Computational Geometry and Applications
1009:
A simple randomized sieve algorithm for the closest-pair problem
2223:
2181:
European
Community on Computational Methods in Applied Sciences
1398:
93:
Other important applications of computational geometry include
1178:
IEEE Transactions on
Pattern Analysis and Machine Intelligence
1012:
485:: Decide whether a point is inside or outside a given polygon.
381:, in a way that multiple queries can be answered efficiently.
294:: Find the intersections between a given set of line segments.
2176:
International
Council for Industrial and Applied Mathematics
1350:
424:
For the case when the search space is allowed to vary, see "
956:. 1st edition; 2nd printing, corrected and expanded, 1988.
469:
the time (and sometimes an extra space) to answer a query.
420:
the time (and sometimes an extra space) to answer queries.
105:(GIS) (geometrical location and search, route planning),
337:: Given a polygon, partition its interior into triangles
797:
algorithms: decompose a polygon into a set of triangles
229:, then pick the pair with the smallest distance. This
1795:
Numerical methods for ordinary differential equations
2171:
Société de Mathématiques
Appliquées et Industrielles
2164:
Japan
Society for Industrial and Applied Mathematics
1800:
Numerical methods for partial differential equations
1330:
816:: create voronoi diagram in any number of dimensions
3088:
3035:
2997:
2944:
2906:
2868:
2810:
2727:
2673:
2635:
2580:
2517:
2450:
2414:
2371:
2335:
2268:
2151:
2135:
2097:
2049:
1987:
1862:
1820:
1614:
1576:
1514:
1432:
1320:
844:
List of combinatorial computational geometry topics
709:: find the nearest point or points to a query point
666:: an algorithm for point location in triangulations
1273:; featured the "Computational Geometry Column" by
715:: make the most efficient use of material or space
678:: finding whether lines intersect, usually with a
727:algorithms: finds the transformation between two
124:The main branches of computational geometry are:
1326:(Annual) Winter School on Computational Geometry
1048:Combinatorial/algorithmic computational geometry
656:: determining the smallest distance between two
139:entities. A groundlaying book in the subject by
1101:Computational Geometry: Theory and Applications
849:List of numerical computational geometry topics
384:Some fundamental geometric query problems are:
2159:Society for Industrial and Applied Mathematics
109:design (IC geometry design and verification),
2259:Note: This template roughly follows the 2012
2235:
1410:
78:and computer-aided design and manufacturing (
8:
1977:Supersymmetric theory of stochastic dynamics
913:Wikiversity:Computer-aided geometric design
2242:
2228:
2220:
1984:
1511:
1417:
1403:
1395:
654:Gilbert–Johnson–Keerthi distance algorithm
672:: an algorithm to smooth a polygonal mesh
1380:, and does not reflect subsequent edits.
1363:
966:A.R. Forrest, "Computational geometry",
940:Computational Geometry - An Introduction
908:Wikiversity:Topic:Computational geometry
537:The most important instruments here are
135:, which deals with geometric objects as
1235:Journal of Computer and System Sciences
1037:List of books in computational geometry
923:
2959:Knowledge representation and reasoning
2984:Philosophy of artificial intelligence
1143:Discrete & Computational Geometry
425:
7:
2303:Energy consumption (Green computing)
180:Combinatorial computational geometry
129:Combinatorial computational geometry
2989:Distributed artificial intelligence
2261:ACM Computing Classification System
1011:. Inf. Comput., 118(1):34—37,1995 (
877:Computer representation of surfaces
779:constrained Delaunay triangulations
265:) time, have also been discovered.
2494:Integrated development environment
1426:Industrial and applied mathematics
1136:Computing in Geometry and Topology
1122:Computer Graphics and Applications
741:pairs of points and vertices on a
448:problem may be converted into the
25:
2969:Automated planning and scheduling
2499:Software configuration management
1656:Stochastic differential equations
1321:Journal of Computational Geometry
1207:Journal of Computational Geometry
3223:
3213:
3204:
3203:
1972:Supersymmetric quantum mechanics
1362:
1214:Journal of Differential Geometry
569:This section is an excerpt from
513:Numerical computational geometry
151:Numerical computational geometry
48:which can be stated in terms of
29:Computational Geometry (journal)
3214:
2617:Computational complexity theory
1854:Stochastic variational calculus
1646:Ordinary differential equations
1199:Journal of Combinatorial Theory
1115:Computer Aided Geometric Design
970:, 321, series 4, 187-195 (1971)
697:Minimum bounding box algorithms
529:computer-aided geometric design
519:computer-aided geometric design
436:Yet another major class is the
160:computer-aided geometric design
2401:Network performance evaluation
1651:Partial differential equations
1524:Arbitrary-precision arithmetic
1185:Information Processing Letters
1171:IEEE Transactions on Computers
985:Optical Computational Geometry
346:Boolean operations on polygons
103:geographic information systems
1:
3255:Computational fields of study
2772:Multimedia information system
2757:Geographic information system
2747:Enterprise information system
2336:Computer systems organization
1539:Interactive geometry software
1164:IEEE Transactions on Graphics
701:oriented minimum bounding box
571:List of algorithms § Geometry
523:This branch is also known as
207:. Consider, for example, the
113:(CAE) (mesh generation), and
3131:Computational social science
2719:Theoretical computer science
2532:Software development process
2308:Electronic design automation
2293:Very Large Scale Integration
1306:Computational Geometry Pages
1281:Theoretical Computer Science
1066:ACM Transactions on Graphics
903:Robust geometric computation
639:Euclidean distance transform
632:Kirkpatrick–Seidel algorithm
2954:Natural language processing
2742:Information storage systems
1591:Computational number theory
1554:Numerical-analysis software
1256:Pattern Recognition Letters
3276:
2870:Human–computer interaction
2840:Intrusion detection system
2752:Social information systems
2737:Database management system
1331:Computational Geometry Lab
1007:S. Khuller and Y. Matias.
968:Proc. Royal Society London
568:
516:
358:
111:computer-aided engineering
101:and visibility problems),
88:mathematical visualization
34:Branch of computer science
26:
3199:
3136:Computational engineering
3111:Computational mathematics
2257:
2189:
1997:Algebra of physical space
1464:Automated theorem proving
1263:SIAM Journal on Computing
1108:Communications of the ACM
703:enclosing a set of points
685:Bentley–Ottmann algorithm
676:Line segment intersection
593:: identify surface points
371:geometric search problems
355:Geometric query problems
292:Line segment intersection
3146:Computational healthcare
3141:Differentiable computing
3060:Graphics processing unit
2479:Domain-specific language
2348:Computational complexity
1790:Numerical linear algebra
889:(combinatorial geometry)
822:: create voronoi diagram
731:to optimally align them.
367:geometric query problems
56:Computational complexity
44:devoted to the study of
3121:Computational chemistry
3055:Photograph manipulation
2946:Artificial intelligence
2762:Decision support system
1529:Finite element analysis
1479:Constraint satisfaction
1129:Computer Graphics World
814:Bowyer–Watson algorithm
775:Chew's second algorithm
707:Nearest neighbor search
664:Jump-and-Walk algorithm
621:Gift wrapping algorithm
450:dynamic range searching
442:dynamic data structures
329:Euclidean shortest path
319:Farthest pair of points
3250:Computational geometry
3186:Educational technology
3017:Reinforcement learning
2767:Process control system
2665:Computational geometry
2655:Algorithmic efficiency
2650:Analysis of algorithms
2298:Systems on Chip (SoCs)
2084:Mathematical economics
1758:Multivariable calculus
1641:Differential equations
1484:Constraint programming
1474:Computational geometry
1358:
1338:Listen to this article
1301:Computational Geometry
872:Computational topology
809:Delaunay triangulation
764:Delaunay triangulation
725:Point set registration
597:Convex hull algorithms
395:Point location problem
314:Closest pair of points
298:Delaunay triangulation
38:Computational geometry
3156:Electronic publishing
3126:Computational biology
3116:Computational physics
3012:Unsupervised learning
2926:Distributed computing
2802:Information retrieval
2709:Mathematical analysis
2699:Mathematical software
2582:Theory of computation
2547:Software construction
2537:Requirements analysis
2415:Software organization
2343:Computer architecture
2313:Hardware acceleration
2278:Printed circuit board
2037:Supersymmetry algebra
2022:Representation theory
2017:Renormalization group
1663:Differential geometry
1544:Optimization software
1516:Mathematical software
1357:
1228:Journal of Algorithms
1059:ACM Computing Surveys
795:Polygon triangulation
690:Shamos–Hoey algorithm
649:affine transformation
335:Polygon triangulation
251:Randomized algorithms
27:For the journal, see
18:Geometric computation
2916:Concurrent computing
2888:Ubiquitous computing
2860:Application security
2855:Information security
2684:Discrete mathematics
2660:Randomized algorithm
2612:Computability theory
2590:Model of computation
2562:Software maintenance
2557:Software engineering
2519:Software development
2469:Programming language
2464:Programming paradigm
2381:Network architecture
2089:Mathematical finance
2074:Social choice theory
1989:Algebraic structures
1938:in quantum mechanics
1874:Analytical mechanics
1840:Stochastic processes
1812:Variational calculus
1624:Approximation theory
1549:Statistical software
1389:More spoken articles
1080:Advances in Geometry
680:sweep line algorithm
579:Closest pair problem
369:, commonly known as
323:Largest empty circle
210:Closest pair problem
169:descriptive geometry
133:algorithmic geometry
3260:Geometry processing
3191:Document management
3181:Operations research
3106:Enterprise software
3022:Multi-task learning
3007:Supervised learning
2729:Information systems
2552:Software deployment
2509:Software repository
2363:Real-time computing
2064:Operations research
1933:Perturbation theory
1731:Multilinear algebra
1702:Functional analysis
1559:Numerical libraries
1491:Computational logic
1288:The Visual Computer
1249:Pattern Recognition
1157:Geometriae Dedicata
932:Franco P. Preparata
820:Fortune's Algorithm
769:Ruppert's algorithm
670:Laplacian smoothing
585:Collision detection
543:parametric surfaces
525:geometric modelling
454:dynamic convex hull
2974:Search methodology
2921:Parallel computing
2878:Interaction design
2787:Computing platform
2714:Numerical analysis
2704:Information theory
2489:Software framework
2452:Software notations
2391:Network components
2288:Integrated circuit
2201:Mathematics portal
2098:Other applications
1822:Probability theory
1805:Validated numerics
1785:Numerical analysis
1678:Geometric analysis
1668:Differential forms
1501:Information theory
1359:
1311:Geometry In Action
1242:Management Science
1221:Journal of the ACM
981:Yevgeny B. Karasik
936:Michael Ian Shamos
893:Space partitioning
828:Quasitriangulation
786:Marching triangles
753:Shoelace algorithm
599:: determining the
564:List of algorithms
507:amortized analysis
309:Linear programming
165:geometric modeling
107:integrated circuit
3237:
3236:
3166:Electronic voting
3096:Quantum Computing
3089:Applied computing
3075:Image compression
2845:Hardware security
2835:Security services
2792:Digital marketing
2572:Open-source model
2484:Modeling language
2396:Network scheduler
2217:
2216:
2051:Decision sciences
2045:
2044:
2027:Spacetime algebra
1719:Harmonic analysis
1685:Dynamical systems
1629:Clifford analysis
1606:Discrete geometry
1572:
1571:
1355:
898:Tricomplex number
887:Discrete geometry
777:: create quality
735:Rotating calipers
713:Nesting algorithm
645:Geometric hashing
539:parametric curves
491:computer graphics
119:3D reconstruction
76:computer graphics
16:(Redirected from
3267:
3227:
3226:
3217:
3216:
3207:
3206:
3027:Cross-validation
2999:Machine learning
2883:Social computing
2850:Network security
2645:Algorithm design
2567:Programming team
2527:Control variable
2504:Software library
2442:Software quality
2437:Operating system
2386:Network protocol
2251:Computer science
2244:
2237:
2230:
2221:
2002:Feynman integral
1985:
1945:Potential theory
1834:random variables
1724:Fourier analysis
1707:Operator algebra
1634:Clifford algebra
1586:Computer algebra
1512:
1419:
1412:
1405:
1396:
1379:
1377:
1366:
1365:
1356:
1346:
1344:
1339:
1094:Ars Combinatoria
1073:Acta Informatica
1025:
1022:
1016:
1005:
999:
998:
977:
971:
964:
958:
957:
928:
882:Digital geometry
801:Voronoi diagrams
737:: determine all
719:Point in polygon
627:Chan's algorithm
555:level-set method
483:Point in polygon
438:dynamic problems
432:Dynamic problems
426:Dynamic problems
401:Nearest neighbor
233:algorithm takes
155:machine geometry
42:computer science
21:
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3176:Word processing
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3070:Virtual reality
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2993:
2964:Computer vision
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2936:Multiprocessing
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2864:
2830:Security hacker
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2782:Digital library
2723:
2674:Mathematics of
2669:
2631:
2607:Automata theory
2602:Formal language
2576:
2542:Software design
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2446:
2432:Virtual machine
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2406:Network service
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2358:Embedded system
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2213:
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2007:Poisson algebra
1983:
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1712:Operator theory
1610:
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1534:Tensor software
1510:
1459:Automata theory
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1370:This audio file
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1275:Joseph O'Rourke
1050:
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1031:Further reading
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944:Springer-Verlag
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840:
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623:or Jarvis march
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476:
446:range searching
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389:Range searching
363:
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341:Mesh generation
303:Voronoi diagram
279:
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269:Problem classes
190:data structures
182:
115:computer vision
99:motion planning
40:is a branch of
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3080:Solid modeling
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2979:Control method
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2825:Formal methods
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2797:World Wide Web
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3161:Cyberwarfare
2820:Cryptography
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2207: /
2203: /
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2069:Optimization
2032:Superalgebra
1891:Field theory
1864:Mathematical
1842: /
1690:Chaos theory
1673:Gauge theory
1601:Graph theory
1496:Cryptography
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3171:Video games
3151:Digital art
2908:Concurrency
2777:Data mining
2689:Probability
2422:Interpreter
2209:topics list
2143:Mathematics
2059:Game theory
1960:Topological
1926:Topological
1921:Statistical
1884:Hamiltonian
1270:SIGACT News
1053:decreased.
790:point cloud
747:convex hull
699:: find the
611:Graham scan
601:convex hull
407:Ray tracing
286:Convex hull
231:brute-force
163:(CAGD), or
3244:Categories
3229:Glossaries
3101:E-commerce
2694:Statistics
2637:Algorithms
2595:Stochastic
2427:Middleware
2283:Peripheral
2115:Psychology
2079:Statistics
1879:Lagrangian
1506:Statistics
1442:Algorithms
1385:Audio help
1376:2013-09-17
1201:, Series B
919:References
729:point sets
607:of points
545:, such as
474:Variations
359:See also:
186:algorithms
46:algorithms
3050:Rendering
3045:Animation
2676:computing
2627:Semantics
2318:Processor
2120:Sociology
2110:Chemistry
1906:Effective
1901:Conformal
1896:Classical
1768:Geometric
1741:Geometric
739:antipodal
616:Quickhull
205:computers
198:polyhedra
141:Preparata
3209:Category
3037:Graphics
2812:Security
2474:Compiler
2373:Networks
2270:Hardware
2195:Category
1844:analysis
1763:Exterior
1736:Exterior
1616:Analysis
1578:Discrete
1452:analysis
1387: ·
1043:Journals
983:(2019).
938:(1985).
838:See also
531:(CAGD).
261:log log
227:n(n-1)/2
194:polygons
137:discrete
95:robotics
63:) and O(
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3219:Outline
2205:outline
2136:Related
2105:Biology
1955:Bosonic
1916:Quantum
1866:physics
1832: (
1564:Solvers
1374: (
1345:minutes
660:shapes.
495:pointer
200:, etc.
1778:Vector
1773:Tensor
1751:Vector
1746:Tensor
1447:design
991:
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658:convex
551:spline
217:Given
145:Shamos
2622:Logic
2456:tools
1911:Gauge
603:of a
375:query
2454:and
2327:Form
2323:Size
989:ISBN
948:ISBN
934:and
805:dual
541:and
527:and
245:log
188:and
143:and
67:log
1013:PDF
862:CAE
858:CAM
854:CAD
807:of
745:or
605:set
509:".
499:CAD
428:".
365:In
249:).
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