From a28d3c6ba5ab9687626992cc0402c4399c76ecaf Mon Sep 17 00:00:00 2001 From: vrouvrea Date: Tue, 15 Mar 2016 14:23:19 +0000 Subject: In Delaunay_triangulation_off_io.h, constructing the Triangulation from a vector of Points is a more efficient way (instead of inserting points on the fly). As consequence, the documentation needs to be rewritten as the points index are changed. git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/alphashapes@1046 636b058d-ea47-450e-bf9e-a15bfbe3eedb Former-commit-id: bdb0196b61418a983cfaf7f6781a3a2906e8b136 --- src/Alpha_complex/doc/Intro_alpha_complex.h | 8 +- src/Alpha_complex/doc/alpha_complex_doc.ipe | 371 ++++++++++----- src/Alpha_complex/doc/alpha_complex_doc.png | Bin 49973 -> 25150 bytes src/Alpha_complex/doc/alpha_complex_doc_135.ipe | 514 --------------------- src/Alpha_complex/doc/alpha_complex_doc_135.png | Bin 80794 -> 0 bytes src/Alpha_complex/doc/alpha_complex_doc_421.ipe | 514 +++++++++++++++++++++ src/Alpha_complex/doc/alpha_complex_doc_421.png | Bin 0 -> 100798 bytes .../doc/alpha_complex_representation.ipe | 14 +- .../doc/alpha_complex_representation.png | Bin 16737 -> 14628 bytes 9 files changed, 771 insertions(+), 650 deletions(-) delete mode 100644 src/Alpha_complex/doc/alpha_complex_doc_135.ipe delete mode 100644 src/Alpha_complex/doc/alpha_complex_doc_135.png create mode 100644 src/Alpha_complex/doc/alpha_complex_doc_421.ipe create mode 100644 src/Alpha_complex/doc/alpha_complex_doc_421.png (limited to 'src/Alpha_complex/doc') diff --git a/src/Alpha_complex/doc/Intro_alpha_complex.h b/src/Alpha_complex/doc/Intro_alpha_complex.h index 0987e0e7..deecf93f 100644 --- a/src/Alpha_complex/doc/Intro_alpha_complex.h +++ b/src/Alpha_complex/doc/Intro_alpha_complex.h @@ -112,19 +112,19 @@ namespace alphacomplex { * * \subsubsection dimension2 Dimension 2 * - * From the example above, it means the algorithm looks into each triangle ([1,2,3], [2,3,4], [1,3,5], ...), + * From the example above, it means the algorithm looks into each triangle ([4,2,1], [2,4,6], [4,5,6], ...), * computes the filtration value of the triangle, and then propagates the filtration value as described * here : - * \image html "alpha_complex_doc_135.png" "Filtration value propagation example" + * \image html "alpha_complex_doc_421.png" "Filtration value propagation example" * * \subsubsection dimension1 Dimension 1 * - * Then, the algorithm looks into each edge ([1,2], [2,3], [1,3], ...), + * Then, the algorithm looks into each edge ([1,2], [4,2], [4,1], ...), * computes the filtration value of the edge (in this case, propagation will have no effect). * * \subsubsection dimension0 Dimension 0 * - * Finally, the algorithm looks into each vertex ([1], [2], [3], [4], [5], [6] and [7]) and + * Finally, the algorithm looks into each vertex ([0], [1], [2], [3], [4], [5] and [6]) and * sets the filtration value (0 in case of a vertex - propagation will have no effect). * * \subsubsection nondecreasing Non decreasing filtration values diff --git a/src/Alpha_complex/doc/alpha_complex_doc.ipe b/src/Alpha_complex/doc/alpha_complex_doc.ipe index e74f9bc4..99bd05af 100644 --- a/src/Alpha_complex/doc/alpha_complex_doc.ipe +++ b/src/Alpha_complex/doc/alpha_complex_doc.ipe @@ -1,7 +1,7 @@ - + @@ -253,13 +253,13 @@ h 320 580 l Delaunay triangulation -0 -1 -2 -3 -4 -5 -6 +2 +6 +4 +5 +1 +3 +0 280 660 m 300 710 l @@ -278,161 +278,282 @@ h 320 580 l 280 660 l -0 -1 -2 -2 -1 -2 -2 -3 -3 -3 -3 -4 -4 -4 -4 -6 -6 -6 -6 -6 -6 -5 -6 -5 - + 4 0 0 4 320 704 e - + 322.919 706.788 m 317.189 701.058 l 317.189 701.203 l - + 317.551 706.934 m 322.629 701.058 l - -230 680 m -240 670 l + +240 620 m +220 600 l - -230 680 m -240 670 l + +240 620 m +220 640 l - -230 680 m -240 670 l +Simplex tree structure + +280 630 m +170 630 l - -230 680 m -240 670 l + +280 610 m +170 610 l - -230 680 m -220 670 l + + + + + + + +3 + +300 688 m +300 676 l +312 676 l +312 688 l +h - -230 680 m -230 670 l + +300 688 m +300 676 l +312 676 l +312 688 l +h - -220 660 m -220 650 l +4 +3 + +300 688 m +300 676 l +312 676 l +312 688 l +h - -230 660 m -230 650 l + +300 688 m +300 676 l +312 676 l +312 688 l +h - -260 680 m -260 670 l +4 +1 + +300 688 m +300 676 l +312 676 l +312 688 l +h - -260 660 m -260 650 l + +300 688 m +300 676 l +312 676 l +312 688 l +h - -300 680 m -300 670 l +5 + +300 688 m +300 676 l +312 676 l +312 688 l +h - -300 680 m -290 670 l +5 +3 + +300 688 m +300 676 l +312 676 l +312 688 l +h - -290 660 m -290 650 l + +300 688 m +300 676 l +312 676 l +312 688 l +h - -300 660 m -300 650 l +4 +2 + +300 688 m +300 676 l +312 676 l +312 688 l +h - -330 680 m -330 670 l + +300 688 m +300 676 l +312 676 l +312 688 l +h - -350 680 m -350 670 l +4 +6 + +300 688 m +300 676 l +312 676 l +312 688 l +h - -350 660 m -350 650 l +4 + +300 688 m +300 676 l +312 676 l +312 688 l +h - -320 700 m -240 690 l + +300 688 m +300 676 l +312 676 l +312 688 l +h - -320 700 m -270 690 l +6 +6 + +300 688 m +300 676 l +312 676 l +312 688 l +h - -320 700 m -310 690 l +5 + +300 688 m +300 676 l +312 676 l +312 688 l +h - -320 700 m -330 690 l + +300 688 m +300 676 l +312 676 l +312 688 l +h - -320 700 m -350 690 l +6 + +300 688 m +300 676 l +312 676 l +312 688 l +h - -320 700 m -380 690 l +6 + +292 716 m +292 728 l +316 728 l +316 716 l +h - -320 700 m -400 690 l + +316 716 m +316 728 l +340 728 l +340 716 l +h - -240 620 m -220 600 l + +340 716 m +340 728 l +364 728 l +364 716 l +h - -240 620 m -220 640 l + +364 716 m +364 728 l +388 728 l +388 716 l +h + + +388 716 m +388 728 l +412 728 l +412 716 l +h + + +412 716 m +412 728 l +436 728 l +436 716 l +h + + +436 716 m +436 728 l +460 728 l +460 716 l +h + +0 +1 +2 +3 +4 +5 +6 + +436 708 m +436 716 l + + +364 708 m +364 716 l + + +364 688 m +364 696 l + + +320 688 m +320 696 l + + +296 708 m +308 716 l +308 716 l + + +264 688 m +268 696 l + + +292 688 m +292 696 l + + +388 736 m +388 728 l -Simplex tree structure -280 630 m -170 630 l +372 612 m +376 620 l -280 610 m -170 610 l +448 612 m +448 620 l - - - - - - - diff --git a/src/Alpha_complex/doc/alpha_complex_doc.png b/src/Alpha_complex/doc/alpha_complex_doc.png index c9eab275..cfe3ede6 100644 Binary files a/src/Alpha_complex/doc/alpha_complex_doc.png and b/src/Alpha_complex/doc/alpha_complex_doc.png differ diff --git a/src/Alpha_complex/doc/alpha_complex_doc_135.ipe b/src/Alpha_complex/doc/alpha_complex_doc_135.ipe deleted file mode 100644 index 5d1d29d4..00000000 --- a/src/Alpha_complex/doc/alpha_complex_doc_135.ipe +++ /dev/null @@ -1,514 +0,0 @@ - - - - - - - -0 0 m --1 0.333 l --1 -0.333 l -h - - - - -0 0 m --1 0.333 l --1 -0.333 l -h - - - - -0.6 0 0 0.6 0 0 e -0.4 0 0 0.4 0 0 e - - - - -0.6 0 0 0.6 0 0 e - - - - - -0.5 0 0 0.5 0 0 e - - -0.6 0 0 0.6 0 0 e -0.4 0 0 0.4 0 0 e - - - - - --0.6 -0.6 m -0.6 -0.6 l -0.6 0.6 l --0.6 0.6 l -h --0.4 -0.4 m -0.4 -0.4 l -0.4 0.4 l --0.4 0.4 l -h - - - - --0.6 -0.6 m -0.6 -0.6 l -0.6 0.6 l --0.6 0.6 l -h - - - - - --0.5 -0.5 m -0.5 -0.5 l -0.5 0.5 l --0.5 0.5 l -h - - --0.6 -0.6 m -0.6 -0.6 l -0.6 0.6 l --0.6 0.6 l -h --0.4 -0.4 m -0.4 -0.4 l -0.4 0.4 l --0.4 0.4 l -h - - - - - - --0.43 -0.57 m -0.57 0.43 l -0.43 0.57 l --0.57 -0.43 l -h - - --0.43 0.57 m -0.57 -0.43 l -0.43 -0.57 l --0.57 0.43 l -h - - - - - -0 0 m --1 0.333 l --1 -0.333 l -h - - - - -0 0 m --1 0.333 l --0.8 0 l --1 -0.333 l -h - - - - -0 0 m --1 0.333 l --0.8 0 l --1 -0.333 l -h - - - - --1 0.333 m -0 0 l --1 -0.333 l - - - - -0 0 m --1 0.333 l --1 -0.333 l -h --1 0 m --2 0.333 l --2 -0.333 l -h - - - - -0 0 m --1 0.333 l --1 -0.333 l -h --1 0 m --2 0.333 l --2 -0.333 l -h - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -320 580 m -350 520 l -290 530 l -320 580 l -320 580 l - - -320 580 m -280 660 l -290 530 l -320 580 l -320 580 l - - -320 580 m -370 580 l -350 520 l -320 580 l - -Cell [4,2,0] -0 -1 -2 -3 -4 -5 -6 - -280 660 m -300 710 l -370 690 l -280 660 l - - -320 580 m -370 690 l -370 580 l -320 580 l - - -280 660 m -370 690 l -320 580 l -280 660 l - - -77.2727 0 0 77.2727 243.636 591.818 e - - -243.428 591.569 m -186.061 643.28 l - -$\alpha_{420}$ - -320 580 m -350 520 l -290 530 l -320 580 l -320 580 l - - -320 580 m -280 660 l -290 530 l -320 580 l -320 580 l - - -320 580 m -370 580 l -350 520 l -320 580 l - -[2,0] is Gabriel $\rightarrow$ $\alpha_{20}$ is not$\\$ -modified (NaN) - -0 -2 -3 -4 -5 -6 - -280 660 m -300 710 l -370 690 l -280 660 l - - -320 580 m -370 690 l -370 580 l -320 580 l - - -280 660 m -370 690 l -320 580 l -280 660 l - -$\alpha_{20}$ - -290 530 m -320 580 l - - -29.1548 0 0 29.1548 305 555 e - - -304.883 555.015 m -334.509 555.015 l - - -320 580 m -350 520 l -290 530 l -320 580 l -320 580 l - - -320 580 m -280 660 l -290 530 l -320 580 l -320 580 l - - -320 580 m -370 580 l -350 520 l -320 580 l - -[0,4] is not Gabriel $\rightarrow$ $\alpha_{40} = \alpha_{420}$ -0 -3 -5 -6 - -280 660 m -300 710 l -370 690 l -280 660 l - - -320 580 m -370 690 l -370 580 l -320 580 l - - -280 660 m -370 690 l -320 580 l -280 660 l - -$\alpha_{40}$ - -290 530 m -280 660 l - - -320 580 m -350 520 l -290 530 l -320 580 l -320 580 l - - -320 580 m -280 660 l -290 530 l -320 580 l -320 580 l - - -320 580 m -370 580 l -350 520 l -320 580 l - -0 -1 -2 -3 -5 -6 - -280 660 m -300 710 l -370 690 l -280 660 l - - -320 580 m -370 690 l -370 580 l -320 580 l - - -280 660 m -370 690 l -320 580 l -280 660 l - -$\alpha_{42}$ -4 - -406.093 497.775 m -446.094 418.092 l - - -44.5799 0 0 44.5799 425.934 457.774 e - - -425.854 457.774 m -470.795 457.774 l - -[2,4] is Gabriel $\rightarrow$ $\alpha_{42}$ is not modified (NaN) - - -205.028 596.091 m -110.946 544.02 l - - -280.768 588.99 m -280.768 547.57 l - - -341.123 594.316 m -413.904 554.079 l - -For all faces of [4,2,0] -N.B. : is Gabriel on a single point has no sense. -Dimension =2 - $\sigma$ = [4,2,0] - -247.333 430.892 m -311.764 430.892 l - - - - - - - - - - - - - - -1 - - - - - -4 - - -1 - - -2 - -65.192 0 0 65.192 285 595 e - - - - - - - - - - - - - diff --git a/src/Alpha_complex/doc/alpha_complex_doc_135.png b/src/Alpha_complex/doc/alpha_complex_doc_135.png deleted file mode 100644 index ef7187f7..00000000 Binary files a/src/Alpha_complex/doc/alpha_complex_doc_135.png and /dev/null differ diff --git a/src/Alpha_complex/doc/alpha_complex_doc_421.ipe b/src/Alpha_complex/doc/alpha_complex_doc_421.ipe new file mode 100644 index 00000000..727816c5 --- /dev/null +++ b/src/Alpha_complex/doc/alpha_complex_doc_421.ipe @@ -0,0 +1,514 @@ + + + + + + + +0 0 m +-1 0.333 l +-1 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-1 -0.333 l +h + + + + +0.6 0 0 0.6 0 0 e +0.4 0 0 0.4 0 0 e + + + + +0.6 0 0 0.6 0 0 e + + + + + +0.5 0 0 0.5 0 0 e + + +0.6 0 0 0.6 0 0 e +0.4 0 0 0.4 0 0 e + + + + + +-0.6 -0.6 m +0.6 -0.6 l +0.6 0.6 l +-0.6 0.6 l +h +-0.4 -0.4 m +0.4 -0.4 l +0.4 0.4 l +-0.4 0.4 l +h + + + + +-0.6 -0.6 m +0.6 -0.6 l +0.6 0.6 l +-0.6 0.6 l +h + + + + + +-0.5 -0.5 m +0.5 -0.5 l +0.5 0.5 l +-0.5 0.5 l +h + + +-0.6 -0.6 m +0.6 -0.6 l +0.6 0.6 l +-0.6 0.6 l +h +-0.4 -0.4 m +0.4 -0.4 l +0.4 0.4 l +-0.4 0.4 l +h + + + + + + +-0.43 -0.57 m +0.57 0.43 l +0.43 0.57 l +-0.57 -0.43 l +h + + +-0.43 0.57 m +0.57 -0.43 l +0.43 -0.57 l +-0.57 0.43 l +h + + + + + +0 0 m +-1 0.333 l +-1 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-0.8 0 l +-1 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-0.8 0 l +-1 -0.333 l +h + + + + +-1 0.333 m +0 0 l +-1 -0.333 l + + + + +0 0 m +-1 0.333 l +-1 -0.333 l +h +-1 0 m +-2 0.333 l +-2 -0.333 l +h + + + + +0 0 m +-1 0.333 l +-1 -0.333 l +h +-1 0 m +-2 0.333 l +-2 -0.333 l +h + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +320 580 m +350 520 l +290 530 l +320 580 l +320 580 l + + +320 580 m +280 660 l +290 530 l +320 580 l +320 580 l + + +320 580 m +370 580 l +350 520 l +320 580 l + +Cell [4,2,1] +2 +6 +4 +5 +1 +3 +0 + +280 660 m +300 710 l +370 690 l +280 660 l + + +320 580 m +370 690 l +370 580 l +320 580 l + + +280 660 m +370 690 l +320 580 l +280 660 l + + +77.2727 0 0 77.2727 243.636 591.818 e + + +243.428 591.569 m +186.061 643.28 l + +$\alpha_{421}$ + +320 580 m +350 520 l +290 530 l +320 580 l +320 580 l + + +320 580 m +280 660 l +290 530 l +320 580 l +320 580 l + + +320 580 m +370 580 l +350 520 l +320 580 l + +[4,2] is Gabriel $\rightarrow$ $\alpha_{42}$ is not$\\$ +modified (NaN) + +2 +4 +5 +1 +3 +0 + +280 660 m +300 710 l +370 690 l +280 660 l + + +320 580 m +370 690 l +370 580 l +320 580 l + + +280 660 m +370 690 l +320 580 l +280 660 l + +$\alpha_{42}$ + +290 530 m +320 580 l + + +29.1548 0 0 29.1548 305 555 e + + +304.883 555.015 m +334.509 555.015 l + + +320 580 m +350 520 l +290 530 l +320 580 l +320 580 l + + +320 580 m +280 660 l +290 530 l +320 580 l +320 580 l + + +320 580 m +370 580 l +350 520 l +320 580 l + +[2,1] is not Gabriel $\rightarrow$ $\alpha_{21} = \alpha_{421}$ +2 +5 +3 +0 + +280 660 m +300 710 l +370 690 l +280 660 l + + +320 580 m +370 690 l +370 580 l +320 580 l + + +280 660 m +370 690 l +320 580 l +280 660 l + +$\alpha_{12}$ + +290 530 m +280 660 l + + +320 580 m +350 520 l +290 530 l +320 580 l +320 580 l + + +320 580 m +280 660 l +290 530 l +320 580 l +320 580 l + + +320 580 m +370 580 l +350 520 l +320 580 l + +2 +6 +4 +5 +3 +0 + +280 660 m +300 710 l +370 690 l +280 660 l + + +320 580 m +370 690 l +370 580 l +320 580 l + + +280 660 m +370 690 l +320 580 l +280 660 l + +$\alpha_{41}$ +1 + +406.093 497.775 m +446.094 418.092 l + + +44.5799 0 0 44.5799 425.934 457.774 e + + +425.854 457.774 m +470.795 457.774 l + +[4,1] is Gabriel $\rightarrow$ $\alpha_{41}$ is not modified (NaN) + + +205.028 596.091 m +110.946 544.02 l + + +280.768 588.99 m +280.768 547.57 l + + +341.123 594.316 m +413.904 554.079 l + +For all faces of [4,2,1] +N.B. : is Gabriel on a single point has no sense. +Dimension =2 - $\sigma$ = [4,2,1] + +247.333 430.892 m +311.764 430.892 l + + + + + + + + + + + + + + +6 + + + + + +1 + + +6 + + +4 + +65.192 0 0 65.192 285 595 e + + + + + + + + + + + + + diff --git a/src/Alpha_complex/doc/alpha_complex_doc_421.png b/src/Alpha_complex/doc/alpha_complex_doc_421.png new file mode 100644 index 00000000..1cce4402 Binary files /dev/null and b/src/Alpha_complex/doc/alpha_complex_doc_421.png differ diff --git a/src/Alpha_complex/doc/alpha_complex_representation.ipe b/src/Alpha_complex/doc/alpha_complex_representation.ipe index 8687d694..fead1661 100644 --- a/src/Alpha_complex/doc/alpha_complex_representation.ipe +++ b/src/Alpha_complex/doc/alpha_complex_representation.ipe @@ -251,13 +251,13 @@ h h Alpha complex -0 -1 -2 -3 -4 -5 -6 +2 +6 +4 +5 +1 +3 +0 58.1341 0 0 58.1341 218.925 692.601 e diff --git a/src/Alpha_complex/doc/alpha_complex_representation.png b/src/Alpha_complex/doc/alpha_complex_representation.png index 06e54c06..9833bff3 100644 Binary files a/src/Alpha_complex/doc/alpha_complex_representation.png and b/src/Alpha_complex/doc/alpha_complex_representation.png differ -- cgit v1.2.3