Version 5.0 The LEDA User Manual

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dictionary . . . . . . . . . . . . . . . . 152 edge set . . . . . . . . . . . . . . . . . . . . . . . . . 303 EdgeIt . . . . . . . . . . . . . . . . . . . . . . . . . . 375 GeoWin . . . . . . . . . . . . . . . . . . . . . . . . .698 InAdjIt . . . . . . . . . . . . . . . . . . . . . . . . . 382 int set . . . . . . . . . . . . . . . . . . . . . . . . . . 139 interval set . . . . . . . . . . . . . . . . . . 548 list . . . . . . . . . . . . . . . . . . . . . . . . . 127 node list . . . . . . . . . . . . . . . . . . . . . . . . 304 node pq . . . . . . . . . . . . . . . . . . . . . 307 node set . . . . . . . . . . . . . . . . . . . . . . . . .302 OutAdjIt . . . . . . . . . . . . . . . . . . . . . . . . 379 p dictionary . . . . . . . . . . . . . . 163 p queue . . . . . . . . . . . . . . . . . . . 176 POINT SET . . . . . . . . . . . . . . . . . . . . 545 pp dictionary. . . . . . .165 rat segment set . . . . . . . . . . . . . . 552 segment set . . . . . . . . . . . . . . . . . . 550 set . . . . . . . . . . . . . . . . . . . . . . . . . .136 slist. . . . . . . . . . . . . . . . . . . . . . . . .135 sortseq . . . . . . . . . . . . . . . . . . . 170 string . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 insert at(...) sortseq . . . . . . . . . . . . . . . . . . . 170 insert reverse edges() graph . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 inside(...) circle . . . . . . . . . . . . . . . . . . . . . . . . . . . 429 d3 rat sphere . . . . . . . . . . . . . . . . . . . . 594 d3 sphere . . . . . . . . . . . . . . . . . . . . . . . 570 GEN POLYGON . . . . . . . . . . . . . . . 442 POLYGON . . . . . . . . . . . . . . . . . . . . . 436 r circle gen polygon . . . . . . . . . . . . . .537 r circle polygon . . . . . . . . . . . . . . . . . .532 rat circle . . . . . . . . . . . . . . . . . . . . . . . . 468 rat rectangle . . . . . . . . . . . . . . . . . . . . .474 rat triangle . . . . . . . . . . . . . . . . . . . . . .471 real circle . . . . . . . . . . . . . . . . . . . . . . . 494 real rectangle . . . . . . . . . . . . . . . . . . . . 501 real triangle . . . . . . . . . . . . . . . . . . . . . 498 rectangle . . . . . . . . . . . . . . . . . . . . . . . . 448 triangle . . . . . . . . . . . . . . . . . . . . . . . . . 445 inside circle(...) . . . . . . . . . . . . . . . . . 415, 480 inside or contains(...) rat rectangle . . . . . . . . . . . . . . . . . . . . .474 real rectangle . . . . . . . . . . . . . . . . . . . . 501 rectangle . . . . . . . . . . . . . . . . . . . . . . . . 448 inside sphere(...) . . . . . . . . . . . . . . . . 559, 579 insphere(...) d3 rat simplex . . . . . . . . . . . . . . . . . . .597 d3 simplex . . . . . . . . . . . . . . . . . . . . . . 573 int item(...) window . . . . . . . . . . . . . . . . . . . . . 629–631 int set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 integer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 integer matrix . . . . . . . . . . . . . . . . . . . . . . .100 integer vector . . . . . . . . . . . . . . . . . . . . . . . . 98 integrate function(...). . . . . . . . . . . . . . . .116 intersect(...) d int set . . . . . . . . . . . . . . . . . . . . . . . . .141 int set . . . . . . . . . . . . . . . . . . . . . . . . . . 139 set . . . . . . . . . . . . . . . . . . . . . . . . . .136 intersect halfplane(...) POLYGON . . . . . . . . . . . . . . . . . . . . . 434 intersection(...) circle . . . . . . . . . . . . . . . . . . . . . . . . . . . 430 d3 line . . . . . . . . . . . . . . . . . . . . . . . . . . 566 d3 plane . . . . . . . . . . . . . . . . . . . . . . . . 568 d3 rat line . . . . . . . . . . . . . . . . . .586, 587 d3 rat plane . . . . . . . . . . . . . . . . . . . . . 592 d3 rat ray . . . . . . . . . . . . . . . . . . . . . . . 583 d3 rat segment . . . . . . . . . . . . . . . . . . 589 d3 ray . . . . . . . . . . . . . . . . . . . . . . . . . . 561 d3 segment . . . . . . . . . . . . . . . . . . . . . .564 GEN POLYGON . . . . . . . . . . 441, 442 interval set . . . . . . . . . . . . . . . . . . 548 line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425 POLYGON . . . . . . . . . . . . . . . . . . . . . 434 r circle gen polygon . . . . 535, 536, 538 r circle point . . . . . . . . . . . . . . . . . . . . 522 r circle polygon . . . . . . . . . . . . . . . . . .530 r circle segment . . . . . . . . . . . . 525, 526 rat line . . . . . . . . . . . . . . . . . . . . . . . . . .464 rat ray . . . . . . . . . . . . . . . . . . . . . . . . . . 461 rat rectangle . . . . . . . . . . . . . . . .475, 476 rat segment . . . . . . . . . . . . . . . . . . . . . 458 rat segment set . . . . . . . . . 552, 553 rat triangle . . . . . . . . . . . . . . . . . . . . . .471 ray . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .422 real circle . . . . . . . . . . . . . . . . . . . . . . . 495 real line . . . . . . . . . . . . . . . . . . . . . . . . . 490 real ray . . . . . . . . . . . . . . . . . . . . . . . . . 487 real rectangle . . . . . . . . . . . . . . . 502, 503 real segment . . . . . . . . . . . . . . . . 483, 484
eal triangle . . . . . . . . . . . . . . . . . . . . . 498 rectangle . . . . . . . . . . . . . . . . . . . . . . . . 449 segment . . . . . . . . . . . . . . . . . . . . . . . . . 419 segment set . . . . . . . . . . . . . . . . . . 551 triangle . . . . . . . . . . . . . . . . . . . . . . . . . 445 intersection half...(...) r circle polygon . . . . . . . . . . . . . . . . . .530 intersection of l...(...) d3 rat segment . . . . . . . . . . . . . . . . . . 589 d3 segment . . . . . . . . . . . . . . . . . . . . . .564 rat segment . . . . . . . . . . . . . . . . . . . . . 458 real segment . . . . . . . . . . . . . . . . . . . . .484 segment . . . . . . . . . . . . . . . . . . . . . . . . . 419 intersection sorted(...) rat segment set . . . . . . . . . . . . . . 553 segment set . . . . . . . . . . . . . . . . . . 551 interval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 interval set . . . . . . . . . . . . . . . . . . . . . . 548 inv() matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 real matrix . . . . . . . . . . . . . . . . . . . . . . 113 inverse() rational . . . . . . . . . . . . . . . . . . . . . . . . . . 68 inverse(...) . . . . . . . . . . . . . . . . . . . . . . . . . . 102 residual . . . . . . . . . . . . . . . . . . . . . . 86, 89 invert() rational . . . . . . . . . . . . . . . . . . . . . . . . . . 68 ipow2(...) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 is a point() interval . . . . . . . . . . . . . . . . . . . . . . . . . . 83 is active(...) GeoWin . . . . . . . . . . . . . . . . . . . . . . . . .681 Is Acyclic(...). . . . . . . . . . . . . . . . . . . . . . . .317 Is Biconnected(...) . . . . . . . . . . . . . . . . . . . 317 is bidirected() graph . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 Is Bidirected(...). . . . . . . . . . . . . . . . . . . . .317 Is Bipartite(...) . . . . . . . . . . . . . . . . . . . . . . 318 is call enabled(...) GraphWin . . . . . . . . . . . . . . . . . . . . . . 656 Is CCW Convex Fac...(...). . . . . . . . . . . .513 Is CCW Ordered(...) . . . . . . . 361, 362, 512 Is CCW Ordered Pl...(...) . . . . . . . . . . . . 513 Is CCW Weakly Con...(...) . . . . . . . . . . . 513 Is CCW Weakly Ord...(...) . . . . . . 512, 513 Is Connected(...) . . . . . . . . . . . . . . . . . . . . 317 is convex() GEN POLYGON . . . . . . . . . . . . . . . 440 POLYGON . . . . . . . . . . . . . . . . . . . . . 433 r circle gen polygon . . . . . . . . . . . . . .535 r circle polygon . . . . . . . . . . . . . . . . . .530 Is Convex Subdivi...(...). . . . . . . . . . . . . .508 Is CW Convex Face...(...) . . . . . . . . . . . . 513 Is CW Weakly Conv...(...) . . . . . . . . . . . 513 is degenerate() circle . . . . . . . . . . . . . . . . . . . . . . . . . . . 429 d3 rat simplex . . . . . . . . . . . . . . . . . . .596 d3 rat sphere . . . . . . . . . . . . . . . . . . . . 594 d3 simplex . . . . . . . . . . . . . . . . . . . . . . 572 d3 sphere . . . . . . . . . . . . . . . . . . . . . . . 570 r circle segment . . . . . . . . . . . . . . . . . 524 rat circle . . . . . . . . . . . . . . . . . . . . . . . . 468 rat rectangle . . . . . . . . . . . . . . . . . . . . .474 rat triangle . . . . . . . . . . . . . . . . . . . . . .471 real circle . . . . . . . . . . . . . . . . . . . . . . . 494 real rectangle . . . . . . . . . . . . . . . . . . . . 501 real triangle . . . . . . . . . . . . . . . . . . . . . 498 rectangle . . . . . . . . . . . . . . . . . . . . . . . . 448 triangle . . . . . . . . . . . . . . . . . . . . . . . . . 444 Is Delaunay Diagram(...) . . . . . . . . . . . . 509 Is Delaunay Trian...(...) . . . . . . . . . . . . . . 509 is diagram dart(...) POINT SET . . . . . . . . . . . . . . . . . . . . 544 is diagram edge(...) POINT SET . . . . . . . . . . . . . . . . . . . . 544 is directed() graph . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 is directory(...) . . . . . . . . . . . . . . . . . . . . . . . 38 is empty() CryptByteString . . . . . . . . . . . . . . . . .236 r circle gen polygon . . . . . . . . . . . . . .535 r circle polygon . . . . . . . . . . . . . . . . . .529 is enabled(...) window . . . . . . . . . . . . . . . . . . . . .635, 636 is file(...) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 is finite() interval . . . . . . . . . . . . . . . . . . . . . . . . . . 83 is full() r circle gen polygon . . . . . . . . . . . . . .535 r circle polygon . . . . . . . . . . . . . . . . . .529 is full circle() r circle segment . . . . . . . . . . . . . . . . . 524 is general() real . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
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Version 5.0 The LEDA User Manual Al
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4.14 Socket Streambuffer ( socket s
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9.11 Move-To-Front Coder II ( MTF2C
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13.1.2 Handles and Iterators . . .
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16.7 Simplices in 3D-Space ( d3 sim
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License Terms and Availability Any
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7. LEDA is available from Algorithm
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Chapter 2 Basics An extended versio
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XYZ y(x1, ... ,xt); ,tk > and uses
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2.3.1 Linear Orders Many data types
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dictionary D0; // default ordering
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2.3.3 Implementation Parameters Man
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lookup returned the location where
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list::iterator defines the iterator
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• internal (LEDA/incl/internal/)
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string s(const char ∗ p); string
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ool bool bool bool istream& ostream
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string buffer, i.e., all output ope
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andom source& S ≫ char& x random
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int R.set weight(int i, int g) sets
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4.10 Memory Allocator ( leda alloca
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4.11 Error Handling ( error ) LEDA
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4.12 Files and Directories ( file )
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4.13 Sockets ( leda socket ) 1. Def
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ool S.receive string(string& s) rec
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ool sb.failed( ) returns whether a
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4.15 Some Useful Functions ( misc )
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4.16 Timer ( timer ) 1. Definition
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unsigned fibonacci(unsigned n) { st
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unsigned fibonacci(unsigned n) { st
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int Hash(const two tuple& p) hash f
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3. Creation four tuple p; creates a
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4.21 A date interface ( date ) 1. D
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3. Creation date D; creates an inst
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string D.get month name( ) returns
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Now we show an example in which dif
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integer integer a(const char ∗ s)
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5.2 Rational Numbers ( rational ) 1
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5.3 The data type bigfloat ( bigflo
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ounding modes bigfloat :: get round
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ostream& ostream& os ≪ const bigf
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double x.get double error( ) bigflo
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int int real roots(const Polynomial
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√ y v = b 1 c 2 + b 2 c 1 ± sign
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5.5 Interval Arithmetic in LEDA ( i
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void x.set midpoint(VOLATILE I doub
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5.7 The mod kernel of type residual
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int residual :: required primetable
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5.9 A Floating Point Filter ( float
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5.10 Double-Valued Vectors ( vector
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double v.zcoord( ) returns the seco
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matrix matrix matrix vector M + con
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5.12 Vectors with Integer Entries (
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5.13 Matrices with Integer Entries
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integer matrix inverse(const intege
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distinct representatives and linear
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at vector v(const array& A); introd
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int compare by angle(const rat vect
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5.15 Real-Valued Vectors ( real vec
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int compare by angle(const real vec
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eal matrix M + const real matrix& M
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5.17.2 Integration double integrate
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array A(int low, const E& x, const
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int A.binary locate(int (∗cmp)(co
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6.3 Stacks ( stack ) 1. Definition
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6.5 Bounded Stacks ( b stack ) 1. D
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6.7 Linear Lists ( list ) 1. Defini
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const E& L.pop front( ) same as L.p
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Sorting and Searching void L.sort(i
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Input and Output void L.read(istrea
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6.8 Singly Linked Lists ( slist ) 1
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6.9 Sets ( set ) 1. Definition An i
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4. Implementation Sets are implemen
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int set S | const int set& T return
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d int set S − const d int set& T
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6.12 Partitions ( partition ) 1. De
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6.13 Parameterized Partitions ( Par
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void D.evert(vertex v) makes v the
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4. Implementation Dynamic collectio
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dictionary D(int (∗cmp)(const K&
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7.2 Dictionary Arrays ( d array ) 1
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{ d_array dic; dic["hello"] = "hall
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ool A.empty( ) returns true if A is
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Note that it is not possible to ite
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void M.clear( ) clears M by making
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p dictionary D.change inf(p dic ite
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void D.del(const K& k) deletes the
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3. Creation sortseq S; creates an i
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seq item S.max item( ) returns the
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Iteration forall items(it, S) { “
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Chapter 8 Priority Queues 8.1 Prior
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6. Example Dijkstra’s Algorithm (
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int Q.size( ) returns the size of Q
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Assume that you want to send the fi
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9.1 Adaptive Arithmetic Coder ( A0C
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uint32 C.get scale threshold( ) uin
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uint32 C.decode memory chunk(const
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3. Creation PPMIICoder C(streambuf
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9.4 Deflation/Inflation Coder ( Def
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void C.set compression level(int le
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void void C.set src stream(streambu
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streambuf ∗ C.get src stream( ) r
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streambuf ∗ C.get src stream( ) r
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uint32 C.decode memory chunk(const
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uint32 C.encode memory chunk(const
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9.10 Move-To-Front Coder ( MTFCoder
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9.11 Move-To-Front Coder II ( MTF2C
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9.12 RLE for Runs of Zero ( RLE0Cod
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9.13 Checksummers ( checksummer bas
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ool C.checksum is valid( ) returns
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9.19 Encoding Output Stream ( encod
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ostream& os.seekp(streamoff off , i
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9.23 Coder Pipes ( CoderPipe2 ) 1.
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void C.set coder1(Coder1 ∗ c1 , b
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void void C.set src stream(streambu
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3. Operations Standard Operations v
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string out_file1 = tmp_file_name(),
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void mb.truncate(streamsize n) also
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e able to change your message witho
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Then you can use the CryptAutoDecod
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10.1 Secure Byte String ( CryptByte
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CryptKey k(const byte ∗ bytes, ui
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10.3 Encryption and Decryption with
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10.4 Example for a Stream-Cipher (
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uint16 void C.get accepted key size
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3. Operations Standard Operations v
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10.6 Automatic Decoder supporting C
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void C.add keys in file(const char
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secure socket streambuf sb(leda soc
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Chapter 11 Graphs and Related Data
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2. Creation graph G; creates an obj
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edge G.first in edge(node v) return
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void G.hide node(node v) removes no
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void G.bucket sort nodes(int l, int
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edge G.new map edge(edge e1 , edge
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edge edge edge G.new edge(node v, e
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void void G.print(string s, ostream
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graph algorithms, i.e., algorithms
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void void G.sort nodes(const list&
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• Opposite Graphs (opposite graph
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4. Operations The interface consist
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int main () { static_graph G; array
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3. Implementation see section 11.2.
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list M.triangulate( ) triangulates
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void M.assign(face f, const ftype&
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void A.init(const graph t& G, int n
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ool M.use node data(const graph t&
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ool M.use edge data(const graph t&
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E& M[face f] returns the variable M
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4. Implementation Node matrices for
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4. Implementation Node maps are imp
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11.17 Sets of Edges ( edge set ) 1.
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node L.cyclic pred(node v) returns
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11.20 Node Priority Queues ( node p
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11.21 Bounded Node Priority Queues
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11.22 Graph Generators ( graph gen
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uedges. For n > 3, a random maximal
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void random planar graph(graph& G,
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ool Is Bidirected(const graph& G) r
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list Delete Loops(graph& G) returns
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11.25 Dynamic Markov Chains ( dynam
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has a source and a target. These ar
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void parser.append(const char ∗ k
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11.27 The LEDA graph input/output f
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arithmetic demand for each function
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GRAPH TRANSITIVE CLOSURE(const gra
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template bool SHORTEST PATH T(cons
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template bool ALL PAIRS SHORTEST P
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The algorithms have the following a
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inline NT MAX FLOW GRH T(const grap
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12.5 Minimum Cut ( min cut ) A cut
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that the bipartition (A, B) is give
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The pre-instantiations for number t
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template bool CHECK MIN WEIGHT ASS
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in general graph. You may skip the
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Worst-Case Running Time: All functi
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list MIN WEIGHT PERFECT MATCHING T(
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12.10 Stable Matching ( stable matc
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12.11 Minimum Spanning Trees ( min
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12.13 Algorithms for Planar Graphs
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ool bool Is CCW Ordered(const graph
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ool void void void TUTTE EMBEDDING(
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Chapter 13 Graphs and Iterators 13.
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The purpose of each iterator is the
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template void set_and_check (graph
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In addition to the algorithm mentio
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13.3 Edge Iterators ( EdgeIt ) 1. D
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#include < LEDA/graph/graph iterato
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OutAdjIt OutAdjIt OutAdjIt it(const
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OutAdjIt& −−it performs one ste
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ool it.eol( ) returns !it.valid( )
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void it.del( ) deletes the marked l
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3. Operations void fc.init(const le
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We would have to write something li
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Equal is a class that compares two
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used only as a “Trojan horse,”
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typename DataAccessor :: value type
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13.14 Constant Accessors ( constant
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13.16 Node Attribute Accessors ( no
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GIT BFS< OutAdjIt, Queuetype, Mark
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3. dfs grow depth: a new adjacency
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• indegree stores for every node
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• Mark is a data accessor that ha
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OutAdjIt algorithm.curr adj( ) retu
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14.1 Points ( point ) 1. Definition
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point p.reflect(const point& q, con
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ool contained in simplex(const arra
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4. Operations point s.start( ) retu
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segment s.rotate90(const point& q,
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double r.direction( ) returns the d
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14.4 Straight Lines ( line ) 1. Def
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line l.translate(const vector& v) r
Page 440 and 441:
14.5 Circles ( circle ) 1. Definiti
Page 442 and 443:
circle C + const vector& v returns
Page 444 and 445:
14.6 Polygons ( POLYGON ) 1. Defini
Page 446 and 447:
const list& P.segments( ) returns t
Page 448 and 449:
ool P.inside(const POINT & p) bool
Page 450 and 451:
14.7 Generalized Polygons ( GEN POL
Page 452 and 453:
GEN POLYGON GEN POLYGON :: make wea
Page 454 and 455:
int P.side of(const POINT & p) regi
Page 456 and 457:
14.8 Triangles ( triangle ) 1. Defi
Page 458 and 459:
triangle t.rotate90(const point& q,
Page 460 and 461:
double r.height( ) returns the heig
Page 462 and 463:
14.10 Rational Points ( rat point )
Page 464 and 465:
at point p.reflect(const rat point&
Page 466 and 467:
int side of halfspace(const rat poi
Page 468 and 469:
at segment s(const segment& s1 , in
Page 470 and 471:
ational s.y abs( ) returns the y-ab
Page 472 and 473:
14.12 Rational Rays ( rat ray ) 1.
Page 474 and 475:
ool r.contains(const rat segment& s
Page 476 and 477:
void l.normalize( ) simplifies the
Page 478 and 479:
at line p bisector(const rat point&
Page 480 and 481:
at circle C(const circle& c, int pr
Page 482 and 483:
14.15 Rational Triangles ( rat tria
Page 484 and 485:
at triangle t − const rat vector&
Page 486 and 487:
list r.vertices( ) returns the vert
Page 488 and 489:
list r.intersection(const rat recta
Page 490 and 491:
int p.orientation(const real point&
Page 492 and 493:
eal area(const real point& a, const
Page 494 and 495:
14.18 Real Segments ( real segment
Page 496 and 497:
ool s.intersection(const real segme
Page 498 and 499:
14.19 Real Rays ( real ray ) 1. Def
Page 500 and 501:
Non-Member Functions int orientatio
Page 502 and 503:
4. Operations real point l.point1(
Page 504 and 505:
int cmp slopes(const real line& l1
Page 506 and 507:
eal circle C(const circle& c, int p
Page 508 and 509:
ool radical axis(const real circle&
Page 510 and 511:
eal point t.point3( ) returns the t
Page 512 and 513:
14.23 Iso-oriented Real Rectangles
Page 514 and 515:
eal rectangle r.translate(real dx,
Page 516 and 517:
14.24 Geometry Algorithms ( geo alg
Page 518 and 519:
edge TRIANGULATE PLANE MAP(GRAPH &
Page 520 and 521:
gen polygon MINKOWSKI SUM(const pol
Page 522 and 523:
ool MIN WIDTH ANNULUS(const list& L
Page 524 and 525:
double CLOSEST PAIR(list& L, point&
Page 526 and 527:
14.25 Transformation ( TRANSFORM )
Page 528 and 529:
TRANSFORM reflection(const POINT& q
Page 530 and 531:
void random points in unit cube(int
Page 532 and 533:
void random points on unit circle(i
Page 534 and 535:
const rat point& p.to rat point( )
Page 536 and 537:
circle segment cs(const rat circle&
Page 538 and 539:
list cs.intersection(const r circle
Page 540 and 541:
14.29 Polygons with circular edges
Page 542 and 543:
CHECK TYPE P.check simplicity( ) ch
Page 544 and 545:
ool P.inside(const r circle point&
Page 546 and 547:
circle gen polygon P (KIND k); crea
Page 548 and 549:
list P.intersection(const rat line&
Page 550 and 551:
double P.approximate area( ) approx
Page 552 and 553:
const I& D.inf(dic2 item it) return
Page 554 and 555:
15.2 Point Sets and Delaunay Triang
Page 556 and 557:
ool T.is hull edge(edge e) as above
Page 558 and 559:
list T.range search(node v, const P
Page 560 and 561:
15.3 Sets of Intervals ( interval s
Page 562 and 563:
15.4 Sets of Parallel Segments ( se
Page 564 and 565:
15.5 Sets of Parallel Rational Segm
Page 566 and 567:
15.6 Planar Subdivisions ( subdivis
Page 568 and 569:
16.1 Points in 3D-Space ( d3 point
Page 570 and 571:
d3 point midpoint(const d3 point& a
Page 572 and 573:
ool outside sphere(const d3 point&
Page 574 and 575:
ool bool r.project xz(ray& m) if th
Page 576 and 577:
segment s.project xy( ) returns the
Page 578 and 579:
ool l.project(const d3 point& p, co
Page 580 and 581:
double p.sqr dist(const d3 point& q
Page 582 and 583:
16.6 Spheres in 3D-Space ( d3 spher
Page 584 and 585:
16.7 Simplices in 3D-Space ( d3 sim
Page 586 and 587:
16.8 Rational Points in 3D-Space (
Page 588 and 589:
d3 rat point p.translate(const rat
Page 590 and 591:
ool coplanar(const d3 rat point& a,
Page 592 and 593:
d3 rat point random d3 rat point in
Page 594 and 595:
void random d3 rat points on segmen
Page 596 and 597:
ool r.project xy(rat ray& m) bool r
Page 598 and 599:
ool l.project yz(rat line& m) if th
Page 600 and 601:
16.11 Rational Segments in 3D-Space
Page 602 and 603:
d3 rat segment s + const rat vector
Page 604 and 605:
d3 plane p.to float( ) returns a fl
Page 606 and 607:
16.13 Rational Spheres ( d3 rat sph
Page 608 and 609:
16.14 Rational Simplices ( d3 rat s
Page 610 and 611:
16.15 3D Convex Hull Algorithms ( d
Page 613 and 614:
Chapter 17 Graphics This section de
Page 615 and 616:
17.2 Windows ( window ) 1. Definiti
Page 617 and 618:
18. The buttons per line parameter
Page 619 and 620:
void W.display(window& W 0 , int x,
Page 621 and 622:
void W.set show coord object(const
Page 623 and 624:
int W.menu bar height( ) returns th
Page 625 and 626:
void W.draw ray(point p, point q, l
Page 627 and 628:
void W.draw filled ellipse(double x
Page 629 and 630:
void void void void void W.draw rou
Page 631 and 632:
void void void W.draw edge(double x
Page 633 and 634:
void W.screenshot(string fname, boo
Page 635 and 636:
int W.read mouse seg(const point& p
Page 637 and 638:
int W.read event(int& val, double&
Page 639 and 640:
window& W ≫ segment& s reads a se
Page 641 and 642:
panel item W.bool item(string s, bo
Page 643 and 644:
panel item W.int item(string s, int
Page 645 and 646:
int W.button(string s, const char
Page 647 and 648:
int W.button(string s, window& M, c
Page 649 and 650:
void void void W.redraw panel(panel
Page 651 and 652:
17.4 Menues ( menu ) 1. Definition
Page 653 and 654:
17.5 Postscript Files ( ps file ) 1
Page 655 and 656:
shape: the shape of the node (type
Page 657 and 658:
void gw.display(int x, int y) displ
Page 659 and 660:
param type gw.set param(node v, par
Page 661 and 662:
string gw.set edge index format(str
Page 663 and 664:
void void gw.transform layout(node
Page 665 and 666:
int bool bool gw.load layout(istrea
Page 667 and 668:
void void gw.set edge slider handle
Page 669 and 670:
int bool bool bool bool bool bool g
Page 671 and 672:
void gw.restore all attributes( ) .
Page 673 and 674:
6. edge index format format This li
Page 675 and 676:
of GraphWin) are 0 (central pos) 1
Page 677 and 678:
17.7.1 A complete example LEDA.GRAP
Page 679 and 680:
17.8 Geometry Windows ( GeoWin ) 1.
Page 681 and 682:
0 will be drawn on top in the order
Page 683 and 684:
geowin new scene and geowin get obj
Page 685 and 686:
e inserted in the result scene. In
Page 687 and 688:
geo_scene sc_points = gw.new_scene(
Page 689 and 690:
} }; int main() { GeoWin gw; list L
Page 691 and 692:
virtual bool is_running(const GeoWi
Page 693 and 694:
geo scene void int GW.get scene wit
Page 695 and 696:
color GW.get fill color(geo scene s
Page 697 and 698:
void∗ GW.set client data(geo scen
Page 699 and 700:
color GW.set obj color(GeoBaseScene
Page 701 and 702:
template string GW.set obj label(G
Page 703 and 704:
string string GW.get bg pixmap( ) r
Page 705 and 706:
• A DRAG (button not released)
Page 707 and 708:
template bool GW.set post del hand
Page 709 and 710:
geowin_gui_rat_transform geowin_gui
Page 711 and 712:
ool GW.del(geo scenegroup GS , geo
Page 713 and 714:
void GW.set d3 fcn(geo scene sc, vo
Page 715 and 716:
17.9 Windows for 3d visualization (
Page 717 and 718:
int D.move( ) animates the contents
Page 719 and 720:
Chapter 18 Implementations 18.1 Lis
Page 721 and 722:
void clear(); int size() const; };
Page 723:
18.2.3 Sorted Sequences Any class s
Page 726 and 727:
libGeoW is the LEDA library providi
Page 728 and 729:
(b) Type VCVARS32 (VSVARS32). 2. Go
Page 730 and 731:
LEDA MEMORY STD: If this is set, th
Page 732 and 733:
When using graphics on Solaris syst
Page 734 and 735:
(7) Double click on prog.cpp If you
Page 736 and 737:
• extend LIB by Otherwise add ne
Page 738 and 739:
and at least one of the following d
Page 740 and 741:
• Copy leda .dll to the bin\ subd
Page 742 and 743:
Preparations To install LEDA you on
Page 744 and 745:
• libg .lib libl .lib for program
Page 746 and 747:
cl -TP prog.c Programs using grap
Page 748 and 749: Automatic Setting Include header fi
Page 750 and 751: The default value is ”/MLd”, al
Page 752 and 753: 2. Windows 95/98: (a) Add the line
Page 754 and 755: Preparations To install LEDA you on
Page 756 and 757: A.16 Platforms When this manual was
Page 758 and 759: (b) For objects x and y of an indep
Page 760 and 761: A and B are different objects: A ==
Page 762 and 763: if (p.y > q.y) return 1; return 0;
Page 764 and 765: partypes={no, yes} Determines how p
Page 766 and 767: Stacks ( stack ) 1. Definition An i
Page 769 and 770: Bibliography [1] H. Alt, N. Blum, K
Page 771 and 772: [31] I. Fary: “On Straight Line R
Page 773 and 774: [67] M. Mignotte: Mathematics for C
Page 775 and 776: Index Symbols L A TEX . . . . . . .
Page 777 and 778: adj nodes(...) graph . . . . . . .
Page 779 and 780: circle gen polygon . . . . . . . .
Page 781 and 782: at ray . . . . . . . . . . . . . .
Page 783 and 784: CBCCoder< BlkCipher > . . . . . . .
Page 785 and 786: disconnect() leda socket . . . . .
Page 787 and 788: edges() GEN POLYGON . . . . . . . .
Page 789 and 790: finger locate pre...(...) sortseq .
Page 791 and 792: checksummer base . . . . . . . . .
Page 793 and 794: OMACCoder< BlkCipher > . . . . . .
Page 795 and 796: get stack() GIT DFS . . . . . . . .
Page 797: in pred(...) graph . . . . . . . .
Page 801 and 802: at segment . . . . . . . . . . . .
Page 803 and 804: eal rectangle . . . . . . . . . . .
Page 805 and 806: mw matching . . . . . . . . . . . .
Page 807 and 808: outdeg(...) graph . . . . . . . . .
Page 809 and 810: pos(...) POINT SET . . . . . . . .
Page 811 and 812: eal matrix . . . . . . . . . . . .
Page 813 and 814: FaceIt . . . . . . . . . . . . . .
Page 815 and 816: save gw(...) GraphWin . . . . . . .
Page 817 and 818: set edge index fo...(...) GraphWin
Page 819 and 820: GeoWin . . . . . . . . . . . . . .
Page 821 and 822: DeflateCoder . . . . . . . . . . .
Page 823 and 824: planar map . . . . . . . . . . . .
Page 825 and 826: d3 rat point . . . . . . . . . . .
Page 827 and 828: GraphWin . . . . . . . . . . . . .
Page 829 and 830: at segment . . . . . . . . . . . .
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