diff options
author | vrouvrea <vrouvrea@636b058d-ea47-450e-bf9e-a15bfbe3eedb> | 2018-03-05 13:38:57 +0000 |
---|---|---|
committer | vrouvrea <vrouvrea@636b058d-ea47-450e-bf9e-a15bfbe3eedb> | 2018-03-05 13:38:57 +0000 |
commit | b3a64294af818c977804c4b67a317782d872e2b5 (patch) | |
tree | 5877d208013369a58c71ae7128ae9292424e7a10 /src/Cech_complex/doc | |
parent | 3cd1e01f0b0d4fdb46f49ec640c389374ca2fe70 (diff) |
Fix doc and tests
git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/cechcomplex_vincent@3262 636b058d-ea47-450e-bf9e-a15bfbe3eedb
Former-commit-id: c76eb981f5960938221aa2498cb87b0707391733
Diffstat (limited to 'src/Cech_complex/doc')
-rw-r--r-- | src/Cech_complex/doc/Intro_cech_complex.h | 52 | ||||
-rw-r--r-- | src/Cech_complex/doc/cech_complex_representation.ipe | 160 | ||||
-rw-r--r-- | src/Cech_complex/doc/cech_complex_representation.png | bin | 15677 -> 54399 bytes | |||
-rw-r--r-- | src/Cech_complex/doc/cech_one_skeleton.ipe | 154 | ||||
-rw-r--r-- | src/Cech_complex/doc/cech_one_skeleton.png | bin | 12070 -> 29354 bytes |
5 files changed, 186 insertions, 180 deletions
diff --git a/src/Cech_complex/doc/Intro_cech_complex.h b/src/Cech_complex/doc/Intro_cech_complex.h index f2052763..8b6c7851 100644 --- a/src/Cech_complex/doc/Intro_cech_complex.h +++ b/src/Cech_complex/doc/Intro_cech_complex.h @@ -29,7 +29,7 @@ namespace cech_complex { /** \defgroup cech_complex Cech complex * - * \author Clément Maria, Pawel Dlotko, Vincent Rouvreau + * \author Vincent Rouvreau * * @{ * @@ -40,40 +40,54 @@ namespace cech_complex { * proximity graph that allows to construct a * <a target="_blank" href="https://en.wikipedia.org/wiki/Simplicial_complex">simplicial complex</a> * from it. - * The input can be a point cloud with a given distance function. + * The input shall be a point cloud in an Euclidean space. * - * The filtration value of each edge is computed from a user-given distance function. + * The filtration value of each edge of the `Gudhi::Proximity_graph` is computed from `Gudhi::Radius_distance` function. * - * All edges that have a filtration value strictly greater than a given threshold value are not inserted into - * the complex. + * All edges that have a filtration value strictly greater than a user given maximal radius value, \f$max\_radius\f$, + * are not inserted into the complex. * - * When creating a simplicial complex from this proximity graph, Cech inserts the proximity graph into the data - * structure, and then expands the simplicial complex when required. - * * Vertex name correspond to the index of the point in the given range (aka. the point cloud). * - * \image html "cech_complex_representation.png" "Cech complex proximity graph representation" - * - * On this example, as edges (4,5), (4,6) and (5,6) are in the complex, simplex (4,5,6) is added with the filtration - * value set with \f$max(filtration(4,5), filtration(4,6), filtration(5,6))\f$. - * And so on for simplex (0,1,2,3). + * \image html "cech_one_skeleton.png" "Cech complex proximity graph representation" * + * When creating a simplicial complex from this proximity graph, Cech inserts the proximity graph into the simplicial + * complex data structure, and then expands the simplicial complex when required. + * + * On this example, as edges \f$(x,y)\f$, \f$(y,z)\f$ and \f$(z,y)\f$ are in the complex, the minimal ball radius + * containing the points \f$(x,y,z)\f$ is computed. + * + * \f$(x,y,z)\f$ is inserted to the simplicial complex with the filtration value set with + * \f$mini\_ball\_radius(x,y,z))\f$ iff \f$mini\_ball\_radius(x,y,z)) \leq max\_radius\f$. + * + * And so on for higher dimensions. + * + * \image html "cech_complex_representation.png" "Cech complex expansion" + * + * The minimal ball radius computation is insured by + * <a target="_blank" href="https://people.inf.ethz.ch/gaertner/subdir/software/miniball.html"> + * the miniball software (V3.0)</a> - Smallest Enclosing Balls of Points - and distributed with GUDHI. + * + * Please refer to + * <a target="_blank" href="https://people.inf.ethz.ch/gaertner/subdir/texts/own_work/esa99_final.pdf"> + * the miniball software design description</a> for more information about this computation. + * * If the Cech_complex interfaces are not detailed enough for your need, please refer to - * <a href="_persistent_cohomology_2cech_persistence_step_by_step_8cpp-example.html"> - * cech_persistence_step_by_step.cpp</a> example, where the graph construction over the Simplex_tree is more detailed. + * <a href="_cech_complex_2cech_complex_step_by_step_8cpp-example.html"> + * cech_complex_step_by_step.cpp</a> example, where the graph construction over the Simplex_tree is more detailed. * - * \section cechpointsdistance Point cloud and distance function + * \section cechpointsdistance Point cloud * - * \subsection cechpointscloudexample Example from a point cloud and a distance function + * \subsection cechpointscloudexample Example from a point cloud * - * This example builds the proximity graph from the given points, threshold value, and distance function. + * This example builds the proximity graph from the given points, and maximal radius values. * Then it creates a `Simplex_tree` with it. * * Then, it is asked to display information about the simplicial complex. * * \include Cech_complex/cech_complex_example_from_points.cpp * - * When launching (Cech maximal distance between 2 points is 7.1, is expanded until dimension 2): + * When launching (Cech maximal distance between 2 points is 1., is expanded until dimension 2): * * \code $> ./Cech_complex_example_from_points * \endcode diff --git a/src/Cech_complex/doc/cech_complex_representation.ipe b/src/Cech_complex/doc/cech_complex_representation.ipe index 7f6028f4..c64d7596 100644 --- a/src/Cech_complex/doc/cech_complex_representation.ipe +++ b/src/Cech_complex/doc/cech_complex_representation.ipe @@ -1,7 +1,7 @@ <?xml version="1.0"?> <!DOCTYPE ipe SYSTEM "ipe.dtd"> <ipe version="70107" creator="Ipe 7.1.10"> -<info created="D:20150603143945" modified="D:20160928121844"/> +<info created="D:20150603143945" modified="D:20180223195207"/> <ipestyle name="basic"> <symbol name="arrow/arc(spx)"> <path stroke="sym-stroke" fill="sym-stroke" pen="sym-pen"> @@ -232,95 +232,99 @@ h <page> <layer name="alpha"/> <view layers="alpha" active="alpha"/> -<path layer="alpha" matrix="1 0 0 1 0 -8" fill="darkblue"> -109.771 601.912 m -159.595 601.797 l -140.058 541.915 l +<path layer="alpha" stroke="black" fill="darkcyan"> +48 640 m +80 672 l +48 672 l h </path> -<path matrix="1 0 0 1 0 -8" fill="darkblue"> -79.8776 552.169 m -109.756 601.699 l -139.812 542.209 l +<text matrix="1 0 0 1 -222.178 174.178" transformations="translations" pos="380 530" stroke="seagreen" type="label" width="70.886" height="8.307" depth="2.32" valign="baseline" size="large">Cech complex</text> +<text matrix="1 0 0 1 -212.333 10.6762" transformations="translations" pos="282.952 524.893" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">0</text> +<text matrix="1 0 0 1 -314.178 58.1775" transformations="translations" pos="352.708 510.349" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">1</text> +<text matrix="1 0 0 1 -194.178 -13.8225" transformations="translations" pos="310.693 578.759" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">2</text> +<text matrix="1 0 0 1 -226.178 18.1775" transformations="translations" pos="375.332 578.49" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">3</text> +<text matrix="1 0 0 1 -218.178 -21.8225" transformations="translations" pos="272.179 660.635" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">4</text> +<text matrix="1 0 0 1 -89.478 -87.9762" transformations="translations" pos="296.419 724.197" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">5</text> +<text matrix="1 0 0 1 -302.178 -13.8225" transformations="translations" pos="375.332 689.453" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">6</text> +<use name="mark/circle(sx)" pos="80 544" size="normal" stroke="black"/> +<use name="mark/circle(sx)" pos="48 576" size="normal" stroke="black"/> +<use name="mark/circle(sx)" pos="112 576" size="normal" stroke="black"/> +<use name="mark/fdisk(sfx)" pos="48 672" size="normal" stroke="black" fill="white"/> +<use name="mark/circle(sx)" pos="48 640" size="normal" stroke="black"/> +<use name="mark/circle(sx)" pos="48 672" size="normal" stroke="black"/> +<use name="mark/circle(sx)" pos="80 672" size="normal" stroke="black"/> +<use name="mark/circle(sx)" pos="144 672" size="normal" stroke="black"/> +<use name="mark/circle(sx)" pos="144 608" size="normal" stroke="black"/> +<use name="mark/circle(sx)" pos="200 640" size="normal" stroke="black"/> +<use matrix="1 0 0 1 -100 -96" name="mark/circle(sx)" pos="304 672" size="normal" stroke="darkgray"/> +<use matrix="1 0 0 1 -100 -96" name="mark/circle(sx)" pos="336 672" size="normal" stroke="darkgray"/> +<path matrix="1 0 0 1 -100 -96" stroke="darkgray"> +32 0 0 32 304 672 e +</path> +<path matrix="1 0 0 1 -100 -96" stroke="darkgray" pen="fat"> +304 672 m +336 672 l +</path> +<text matrix="1 0 0 1 -214.178 50.178" transformations="translations" pos="380 530" stroke="darkgray" type="label" width="80.052" height="8.302" depth="0" valign="baseline" size="large">Maximal radius</text> +<text matrix="1 0 0 1 -226.178 -13.8225" transformations="translations" pos="375.332 689.453" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">7</text> +<text matrix="1 0 0 1 -266.178 46.1775" transformations="translations" pos="375.332 689.453" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">8</text> +<text matrix="1 0 0 1 -334.178 -13.8225" transformations="translations" pos="375.332 689.453" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">9</text> +<path stroke="black"> +112 576 m +144 608 l +</path> +<path stroke="black"> +144 672 m +144 608 l +200 640 l h </path> -<path matrix="1 0 0 1 0 -8" fill="lightblue"> -69.8453 682.419 m -159.925 712.208 l -90.12 732.039 l +<path stroke="black" fill="darkcyan"> +48 576 m +112 576 l +80 544 l h </path> -<text matrix="1 0 0 1 -230.178 14.1775" transformations="translations" pos="380 530" stroke="seagreen" type="label" width="68.836" height="8.307" depth="2.32" valign="baseline" size="large">Rips complex</text> -<text matrix="1 0 0 1 -212.333 10.6762" transformations="translations" pos="282.952 524.893" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">0</text> -<text matrix="1 0 0 1 -210.178 14.1775" transformations="translations" pos="352.708 510.349" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">1</text> -<text matrix="1 0 0 1 -210.178 14.1775" transformations="translations" pos="310.693 578.759" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">2</text> -<text matrix="1 0 0 1 -210.178 14.1775" transformations="translations" pos="375.332 578.49" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">3</text> -<text matrix="1 0 0 1 -210.178 14.1775" transformations="translations" pos="272.179 660.635" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">4</text> -<text matrix="1 0 0 1 -209.478 4.0238" transformations="translations" pos="296.419 724.197" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">5</text> -<text matrix="1 0 0 1 -210.178 14.1775" transformations="translations" pos="375.332 689.453" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">6</text> -<path matrix="1 0 0 1 29.8225 14.1775" stroke="black" pen="heavier"> -60 710 m -40 660 l -</path> -<path matrix="1 0 0 1 29.8225 14.1775" stroke="black" pen="heavier"> -40 660 m -130 690 l -</path> -<path matrix="1 0 0 1 29.8225 14.1775" stroke="black" pen="heavier"> -130 690 m -60 710 l -</path> -<path matrix="1 0 0 1 29.8225 14.1775" stroke="black" pen="heavier"> -40 660 m -80 580 l -</path> -<path matrix="1 0 0 1 29.8225 14.1775" stroke="black" pen="heavier"> -80 580 m -130 580 l -130 580 l -</path> -<path matrix="1 0 0 1 29.8225 14.1775" stroke="black" pen="heavier"> -130 580 m -110 520 l -</path> -<path matrix="1 0 0 1 29.8225 14.1775" stroke="black" pen="heavier"> -110 520 m -50 530 l -50 530 l -50 530 l +<use name="mark/fdisk(sfx)" pos="112 728" size="normal" stroke="black"/> +<path stroke="black"> +80 672 m +144 672 l +112 728 l +h </path> -<path matrix="1 0 0 1 29.8225 14.1775" stroke="black" pen="heavier"> -50 530 m -80 580 l +<use name="mark/fdisk(sfx)" pos="112 728" size="normal" stroke="black" fill="white"/> +<use name="mark/fdisk(sfx)" pos="80 672" size="normal" stroke="black" fill="white"/> +<use name="mark/fdisk(sfx)" pos="144 672" size="normal" stroke="black" fill="white"/> +<path stroke="black" fill="darkcyan"> +48 576 m +48 640 l +32 608 l +h </path> -<path matrix="1 0 0 1 29.8225 14.1775" stroke="black" pen="heavier"> -130 580 m -130 690 l +<use name="mark/fdisk(sfx)" pos="200 640" size="normal" stroke="black" fill="white"/> +<use name="mark/fdisk(sfx)" pos="144 608" size="normal" stroke="black" fill="white"/> +<use name="mark/fdisk(sfx)" pos="112 576" size="normal" stroke="black" fill="white"/> +<use name="mark/fdisk(sfx)" pos="80 544" size="normal" stroke="black" fill="white"/> +<use name="mark/fdisk(sfx)" pos="48 576" size="normal" stroke="black" fill="white"/> +<use name="mark/fdisk(sfx)" pos="48 640" size="normal" stroke="black" fill="white"/> +<path stroke="darkcyan"> +32 0 0 32 80 576 e </path> -<use matrix="1 0 0 1 -209.478 4.0238" name="mark/fdisk(sfx)" pos="300 720" size="normal" stroke="black" fill="white"/> -<use matrix="1 0 0 1 -210.178 14.1775" name="mark/fdisk(sfx)" pos="280 660" size="normal" stroke="black" fill="white"/> -<use matrix="1 0 0 1 -210.178 14.1775" name="mark/fdisk(sfx)" pos="370 690" size="normal" stroke="black" fill="white"/> -<use matrix="1 0 0 1 -210.178 14.1775" name="mark/fdisk(sfx)" pos="370 580" size="normal" stroke="black" fill="white"/> -<use matrix="1 0 0 1 -210.178 14.1775" name="mark/fdisk(sfx)" pos="290 530" size="normal" stroke="black" fill="white"/> -<path matrix="1 0 0 1 -40 -16" stroke="black" pen="heavier"> -150.038 609.9 m -179.929 549.727 l +<path stroke="darkcyan"> +22.6274 0 0 22.6274 64 656 e </path> -<use matrix="1 0 0 1 -210.178 14.1775" name="mark/fdisk(sfx)" pos="320 580" size="normal" stroke="black" fill="white"/> -<use matrix="1 0 0 1 -210.178 14.1775" name="mark/fdisk(sfx)" pos="350 520" size="normal" stroke="black" fill="white"/> -<path stroke="black" pen="heavier"> -158.7 593.269 m -81.4925 544.805 l +<path stroke="darkorange"> +37.1429 0 0 37.1429 112 690.857 e </path> -<path matrix="1 0 0 1 -17.9662 -17.9662" stroke="gray"> -256.324 639.958 m -370.055 639.958 l +<path stroke="darkorange"> +37.1429 0 0 37.1429 162.857 640 e </path> -<path matrix="1 0 0 1 -17.9662 -17.9662" stroke="gray"> -56.8567 0 0 56.8567 313.217 639.756 e +<use name="mark/fdisk(sfx)" pos="32 608" size="normal" stroke="black"/> +<text matrix="1 0 0 1 -334.178 94.1775" transformations="translations" pos="352.708 510.349" stroke="black" type="label" width="9.963" height="6.42" depth="0" valign="baseline">10</text> +<path stroke="darkcyan"> +32 0 0 32 48 608 e </path> -<use matrix="1 0 0 1 52.1387 -98.0941" name="mark/fdisk(sfx)" pos="300 720" size="normal" stroke="gray" fill="white"/> -<use matrix="1 0 0 1 -61.4926 -98.0942" name="mark/fdisk(sfx)" pos="300 720" size="normal" stroke="gray" fill="white"/> -<text matrix="1 0 0 1 -26.6167 -33.2708" transformations="translations" pos="295.735 657.944" stroke="gray" type="label" width="63.374" height="6.926" depth="1.93" valign="baseline">Rips threshold</text> +<use name="mark/fdisk(sfx)" pos="204 576" size="normal" stroke="darkgray" fill="white"/> +<use name="mark/fdisk(sfx)" pos="236 576" size="normal" stroke="darkgray" fill="white"/> </page> </ipe> diff --git a/src/Cech_complex/doc/cech_complex_representation.png b/src/Cech_complex/doc/cech_complex_representation.png Binary files differindex e901d92e..4d103a56 100644 --- a/src/Cech_complex/doc/cech_complex_representation.png +++ b/src/Cech_complex/doc/cech_complex_representation.png diff --git a/src/Cech_complex/doc/cech_one_skeleton.ipe b/src/Cech_complex/doc/cech_one_skeleton.ipe index 3a35970c..345e6d7b 100644 --- a/src/Cech_complex/doc/cech_one_skeleton.ipe +++ b/src/Cech_complex/doc/cech_one_skeleton.ipe @@ -1,7 +1,7 @@ <?xml version="1.0"?> <!DOCTYPE ipe SYSTEM "ipe.dtd"> <ipe version="70107" creator="Ipe 7.1.10"> -<info created="D:20150603143945" modified="D:20160928130224"/> +<info created="D:20150603143945" modified="D:20180223195012"/> <ipestyle name="basic"> <symbol name="arrow/arc(spx)"> <path stroke="sym-stroke" fill="sym-stroke" pen="sym-pen"> @@ -232,95 +232,83 @@ h <page> <layer name="alpha"/> <view layers="alpha" active="alpha"/> -<path layer="alpha" matrix="1 0 0 1 0 -8" stroke="0"> -109.771 601.912 m -159.595 601.797 l -140.058 541.915 l +<text layer="alpha" matrix="1 0 0 1 -222.178 174.178" transformations="translations" pos="380 530" stroke="seagreen" type="label" width="84.053" height="8.307" depth="2.32" valign="baseline" size="large">Proximity graph</text> +<text matrix="1 0 0 1 -212.333 10.6762" transformations="translations" pos="282.952 524.893" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">0</text> +<text matrix="1 0 0 1 -314.178 58.1775" transformations="translations" pos="352.708 510.349" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">1</text> +<path matrix="1 0 0 1 -100 -96" stroke="darkgray" pen="fat"> +304 672 m +336 672 l +</path> +<text matrix="1 0 0 1 -194.178 -13.8225" transformations="translations" pos="310.693 578.759" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">2</text> +<text matrix="1 0 0 1 -226.178 18.1775" transformations="translations" pos="375.332 578.49" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">3</text> +<text matrix="1 0 0 1 -218.178 -21.8225" transformations="translations" pos="272.179 660.635" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">4</text> +<text matrix="1 0 0 1 -89.478 -87.9762" transformations="translations" pos="296.419 724.197" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">5</text> +<text matrix="1 0 0 1 -302.178 -13.8225" transformations="translations" pos="375.332 689.453" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">6</text> +<use name="mark/circle(sx)" pos="80 544" size="normal" stroke="black"/> +<use name="mark/circle(sx)" pos="48 576" size="normal" stroke="black"/> +<use name="mark/circle(sx)" pos="112 576" size="normal" stroke="black"/> +<use name="mark/circle(sx)" pos="48 640" size="normal" stroke="black"/> +<use name="mark/circle(sx)" pos="48 672" size="normal" stroke="black"/> +<use name="mark/circle(sx)" pos="80 672" size="normal" stroke="black"/> +<use name="mark/circle(sx)" pos="144 672" size="normal" stroke="black"/> +<use name="mark/circle(sx)" pos="144 608" size="normal" stroke="black"/> +<use name="mark/circle(sx)" pos="200 640" size="normal" stroke="black"/> +<use matrix="1 0 0 1 -100 -96" name="mark/circle(sx)" pos="336 672" size="normal" stroke="darkgray"/> +<path matrix="1 0 0 1 -100 -96" stroke="darkgray"> +32 0 0 32 304 672 e +</path> +<text matrix="1 0 0 1 -214.178 50.178" transformations="translations" pos="380 530" stroke="darkgray" type="label" width="80.052" height="8.302" depth="0" valign="baseline" size="large">Maximal radius</text> +<text matrix="1 0 0 1 -226.178 -13.8225" transformations="translations" pos="375.332 689.453" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">7</text> +<text matrix="1 0 0 1 -266.178 46.1775" transformations="translations" pos="375.332 689.453" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">8</text> +<text matrix="1 0 0 1 -334.178 -13.8225" transformations="translations" pos="375.332 689.453" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">9</text> +<path stroke="black"> +112 576 m +144 608 l +</path> +<path stroke="black"> +144 672 m +144 608 l +200 640 l h </path> -<path matrix="1 0 0 1 0 -8" stroke="0"> -79.8776 552.169 m -109.756 601.699 l -139.812 542.209 l +<path stroke="black"> +48 640 m +80 672 l +48 672 l h </path> -<path matrix="1 0 0 1 0.665417 -8.66542" stroke="0"> -69.8453 682.419 m -159.925 712.208 l -90.12 732.039 l +<path stroke="black"> +48 576 m +112 576 l +80 544 l h </path> -<text matrix="1 0 0 1 -230.178 14.1775" transformations="translations" pos="380 530" stroke="seagreen" type="label" width="98.916" height="8.307" depth="2.32" valign="baseline" size="large">One skeleton graph</text> -<text matrix="1 0 0 1 -212.333 10.6762" transformations="translations" pos="282.952 524.893" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">0</text> -<text matrix="1 0 0 1 -210.178 14.1775" transformations="translations" pos="352.708 510.349" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">1</text> -<text matrix="1 0 0 1 -210.178 14.1775" transformations="translations" pos="310.693 578.759" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">2</text> -<text matrix="1 0 0 1 -210.178 14.1775" transformations="translations" pos="375.332 578.49" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">3</text> -<text matrix="1 0 0 1 -210.178 14.1775" transformations="translations" pos="272.179 660.635" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">4</text> -<text matrix="1 0 0 1 -209.478 4.0238" transformations="translations" pos="296.419 724.197" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">5</text> -<text matrix="1 0 0 1 -210.178 14.1775" transformations="translations" pos="375.332 689.453" stroke="black" type="label" width="4.981" height="6.42" depth="0" valign="baseline">6</text> -<path matrix="1 0 0 1 30.6497 14.0396" stroke="black" pen="heavier"> -60 710 m -40 660 l -</path> -<path matrix="1 0 0 1 30.3739 13.9018" stroke="black" pen="heavier"> -40 660 m -130 690 l -</path> -<path matrix="1 0 0 1 29.8225 14.1775" stroke="black" pen="heavier"> -130 690 m -60 710 l -</path> -<path matrix="1 0 0 1 29.8225 14.1775" stroke="black" pen="heavier"> -40 660 m -80 580 l -</path> -<path matrix="1 0 0 1 29.8225 14.1775" stroke="black" pen="heavier"> -80 580 m -130 580 l -130 580 l -</path> -<path matrix="1 0 0 1 29.8225 14.1775" stroke="black" pen="heavier"> -130 580 m -110 520 l -</path> -<path matrix="1 0 0 1 29.8225 14.1775" stroke="black" pen="heavier"> -110 520 m -50 530 l -50 530 l -50 530 l -</path> -<path matrix="1 0 0 1 29.8225 14.1775" stroke="black" pen="heavier"> -50 530 m -80 580 l -</path> -<path matrix="1 0 0 1 29.8225 14.1775" stroke="black" pen="heavier"> -130 580 m -130 690 l -</path> -<use matrix="1 0 0 1 -209.478 4.0238" name="mark/fdisk(sfx)" pos="300 720" size="normal" stroke="black" fill="white"/> -<use matrix="1 0 0 1 -210.178 14.1775" name="mark/fdisk(sfx)" pos="280 660" size="normal" stroke="black" fill="white"/> -<use matrix="1 0 0 1 -210.178 14.1775" name="mark/fdisk(sfx)" pos="370 690" size="normal" stroke="black" fill="white"/> -<use matrix="1 0 0 1 -210.178 14.1775" name="mark/fdisk(sfx)" pos="370 580" size="normal" stroke="black" fill="white"/> -<use matrix="1 0 0 1 -210.178 14.1775" name="mark/fdisk(sfx)" pos="290 530" size="normal" stroke="black" fill="white"/> -<path matrix="1 0 0 1 -40 -16" stroke="black" pen="heavier"> -150.038 609.9 m -179.929 549.727 l -</path> -<use matrix="1 0 0 1 -210.178 14.1775" name="mark/fdisk(sfx)" pos="320 580" size="normal" stroke="black" fill="white"/> -<use matrix="1 0 0 1 -210.178 14.1775" name="mark/fdisk(sfx)" pos="350 520" size="normal" stroke="black" fill="white"/> -<path stroke="black" pen="heavier"> -158.7 593.269 m -81.4925 544.805 l -</path> -<path matrix="1 0 0 1 -17.9662 -17.9662" stroke="gray"> -256.324 639.958 m -370.055 639.958 l +<use name="mark/fdisk(sfx)" pos="112 728" size="normal" stroke="black"/> +<path stroke="black"> +80 672 m +144 672 l +112 728 l +h </path> -<path matrix="1 0 0 1 -17.9662 -17.9662" stroke="gray"> -56.8567 0 0 56.8567 313.217 639.756 e +<use name="mark/fdisk(sfx)" pos="112 728" size="normal" stroke="black" fill="white"/> +<path stroke="black"> +48 576 m +48 640 l +32 608 l +h </path> -<use matrix="1 0 0 1 52.1387 -98.0941" name="mark/fdisk(sfx)" pos="300 720" size="normal" stroke="gray" fill="white"/> -<use matrix="1 0 0 1 -61.4926 -98.0942" name="mark/fdisk(sfx)" pos="300 720" size="normal" stroke="gray" fill="white"/> -<text matrix="1 0 0 1 -26.6167 -33.2708" transformations="translations" pos="295.735 657.944" stroke="gray" type="label" width="63.374" height="6.926" depth="1.93" valign="baseline">Rips threshold</text> +<use name="mark/fdisk(sfx)" pos="80 672" size="normal" stroke="black" fill="white"/> +<use name="mark/fdisk(sfx)" pos="144 672" size="normal" stroke="black" fill="white"/> +<use name="mark/fdisk(sfx)" pos="200 640" size="normal" stroke="black" fill="white"/> +<use name="mark/fdisk(sfx)" pos="144 608" size="normal" stroke="black" fill="white"/> +<use name="mark/fdisk(sfx)" pos="112 576" size="normal" stroke="black" fill="white"/> +<use name="mark/fdisk(sfx)" pos="80 544" size="normal" stroke="black" fill="white"/> +<use name="mark/fdisk(sfx)" pos="48 576" size="normal" stroke="black" fill="white"/> +<use name="mark/fdisk(sfx)" pos="48 640" size="normal" stroke="black" fill="white"/> +<use name="mark/fdisk(sfx)" pos="48 672" size="normal" stroke="black" fill="white"/> +<use name="mark/fdisk(sfx)" pos="32 608" size="normal" stroke="black" fill="white"/> +<text matrix="1 0 0 1 -334.178 94.1775" transformations="translations" pos="352.708 510.349" stroke="black" type="label" width="9.963" height="6.42" depth="0" valign="baseline">10</text> +<use name="mark/fdisk(sfx)" pos="204 576" size="normal" stroke="darkgray" fill="white"/> +<use name="mark/fdisk(sfx)" pos="236 576" size="normal" stroke="darkgray" fill="white"/> </page> </ipe> diff --git a/src/Cech_complex/doc/cech_one_skeleton.png b/src/Cech_complex/doc/cech_one_skeleton.png Binary files differindex ffa9c329..807e0936 100644 --- a/src/Cech_complex/doc/cech_one_skeleton.png +++ b/src/Cech_complex/doc/cech_one_skeleton.png |