From f1bc7baea1cefbb4a866d85a7d309cbcb5aefc64 Mon Sep 17 00:00:00 2001 From: Pratik Gupta <66073063+inomag@users.noreply.github.com> Date: Sun, 13 Mar 2022 12:04:22 +0530 Subject: [PATCH 01/15] Create CODE_OF_CONDUCT.rst --- CODE_OF_CONDUCT.rst | 152 ++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 152 insertions(+) create mode 100644 CODE_OF_CONDUCT.rst diff --git a/CODE_OF_CONDUCT.rst b/CODE_OF_CONDUCT.rst new file mode 100644 index 000000000..0822de9a3 --- /dev/null +++ b/CODE_OF_CONDUCT.rst @@ -0,0 +1,152 @@ +.. _code_of_conduct: + +Code of Conduct +=============== + + +Introduction +------------ + +This code of conduct applies to all spaces managed by the NetworkX project, +including all public and private mailing lists, issue trackers, wikis, and +any other communication channel used by our community. + +This code of conduct should be honored by everyone who participates in +the NetworkX community formally or informally, or claims any affiliation with the +project, in any project-related activities and especially when representing the +project, in any role. + +This code is not exhaustive or complete. It serves to distill our common +understanding of a collaborative, shared environment and goals. Please try to +follow this code in spirit as much as in letter, to create a friendly and +productive environment that enriches the surrounding community. + + +Specific Guidelines +------------------- + +We strive to: + +1. Be open. We invite anyone to participate in our community. We prefer to use + public methods of communication for project-related messages, unless + discussing something sensitive. This applies to messages for help or + project-related support, too; not only is a public support request much more + likely to result in an answer to a question, it also ensures that any + inadvertent mistakes in answering are more easily detected and corrected. + +2. Be empathetic, welcoming, friendly, and patient. We work together to resolve + conflict, and assume good intentions. We may all experience some frustration + from time to time, but we do not allow frustration to turn into a personal + attack. A community where people feel uncomfortable or threatened is not a + productive one. + +3. Be collaborative. Our work will be used by other people, and in turn we will + depend on the work of others. When we make something for the benefit of the + project, we are willing to explain to others how it works, so that they can + build on the work to make it even better. Any decision we make will affect + users and colleagues, and we take those consequences seriously when making + decisions. + +4. Be inquisitive. Nobody knows everything! Asking questions early avoids many + problems later, so we encourage questions, although we may direct them to + the appropriate forum. We will try hard to be responsive and helpful. + +5. Be careful in the words that we choose. We are careful and respectful in + our communication and we take responsibility for our own speech. Be kind to + others. Do not insult or put down other participants. We will not accept + harassment or other exclusionary behaviour, such as: + + - Violent threats or language directed against another person. + - Sexist, racist, or otherwise discriminatory jokes and language. + - Posting sexually explicit or violent material. + - Posting (or threatening to post) other people's personally identifying information ("doxing"). + - Sharing private content, such as emails sent privately or non-publicly, + or unlogged forums such as IRC channel history, without the sender's consent. + - Personal insults, especially those using racist or sexist terms. + - Unwelcome sexual attention. + - Excessive profanity. Please avoid swearwords; people differ greatly in their sensitivity to swearing. + - Repeated harassment of others. In general, if someone asks you to stop, then stop. + - Advocating for, or encouraging, any of the above behaviour. + + +Diversity Statement +------------------- + +The NetworkX project welcomes and encourages participation by everyone. We are +committed to being a community that everyone enjoys being part of. Although +we may not always be able to accommodate each individual's preferences, we try +our best to treat everyone kindly. + +No matter how you identify yourself or how others perceive you: we welcome you. +Though no list can hope to be comprehensive, we explicitly honour diversity in: +age, culture, ethnicity, genotype, gender identity or expression, language, +national origin, neurotype, phenotype, political beliefs, profession, race, +religion, sexual orientation, socioeconomic status, subculture and technical +ability. + +Though we welcome people fluent in all languages, NetworkX development is +conducted in English. + +Standards for behaviour in the NetworkX community are detailed in the Code of +Conduct above. Participants in our community should uphold these standards +in all their interactions and help others to do so as well (see next section). + + +Reporting Guidelines +-------------------- + +We know that it is painfully common for internet communication to start at or +devolve into obvious and flagrant abuse. We also recognize that sometimes +people may have a bad day, or be unaware of some of the guidelines in this Code +of Conduct. Please keep this in mind when deciding on how to respond to a +breach of this Code. + +For clearly intentional breaches, report those to the NetworkX Steering Council +(see below). For possibly unintentional breaches, you may reply to the person +and point out this code of conduct (either in public or in private, whatever is +most appropriate). If you would prefer not to do that, please feel free to +report to the NetworkX Steering Council directly, or ask the Council for +advice, in confidence. + +You can report issues to the +`NetworkX Steering Council `__, +at networkx-conduct@groups.io. + +If your report involves any members of the Council, or if they feel they have +a conflict of interest in handling it, then they will recuse themselves from +considering your report. Alternatively, if for any reason you feel +uncomfortable making a report to the Council, then you can also contact: + +- Senior `NumFOCUS staff `__: conduct@numfocus.org. + + +Incident reporting resolution & Code of Conduct enforcement +----------------------------------------------------------- + +We will investigate and respond to all complaints. The NetworkX Steering Council +will protect the identity of the reporter, and treat the content of +complaints as confidential (unless the reporter agrees otherwise). + +In case of severe and obvious breaches, e.g., personal threat or violent, sexist +or racist language, we will immediately disconnect the originator from NetworkX +communication channels. + +In cases not involving clear severe and obvious breaches of this code of +conduct, the process for acting on any received code of conduct violation +report will be: + +1. acknowledge report is received +2. reasonable discussion/feedback +3. mediation (if feedback didn't help, and only if both reporter and reportee agree to this) +4. enforcement via transparent decision by the NetworkX Steering Council + +The Council will respond to any report as soon as possible, and at most +within 72 hours. + + +Endnotes +-------- + +This document is adapted from: + +- `SciPy Code of Conduct `_ From 6f05d00e4fdf2570c5beb42b851a761f6155f293 Mon Sep 17 00:00:00 2001 From: Inomag Date: Thu, 14 Apr 2022 01:07:26 +0530 Subject: [PATCH 02/15] Added Delaunay notebook --- .../data/singapore_train_stations.csv | 158 ++++++++++ .../delaunay/images/delaunay_introduction.png | Bin 0 -> 221757 bytes .../geospatial/delaunay/images/edge_flip.png | Bin 0 -> 19907 bytes .../delaunay/images/incremental.png | Bin 0 -> 44944 bytes content/geospatial/delaunay/index.md | 276 ++++++++++++++++++ content/geospatial/index.md | 11 + requirements.txt | 4 +- site/index.md | 1 + 8 files changed, 449 insertions(+), 1 deletion(-) create mode 100644 content/geospatial/delaunay/data/singapore_train_stations.csv create mode 100644 content/geospatial/delaunay/images/delaunay_introduction.png create mode 100644 content/geospatial/delaunay/images/edge_flip.png create mode 100644 content/geospatial/delaunay/images/incremental.png create mode 100644 content/geospatial/delaunay/index.md create mode 100644 content/geospatial/index.md diff --git a/content/geospatial/delaunay/data/singapore_train_stations.csv b/content/geospatial/delaunay/data/singapore_train_stations.csv new file mode 100644 index 000000000..8f6a3fa18 --- /dev/null +++ b/content/geospatial/delaunay/data/singapore_train_stations.csv @@ -0,0 +1,158 @@ +station_name,type,lat,lng +Jurong East,MRT,1.333207,103.742308 +Bukit Batok,MRT,1.349069,103.749596 +Bukit Gombak,MRT,1.359043,103.751863 +Choa Chu Kang,MRT,1.385417,103.744316 +Yew Tee,MRT,1.397383,103.747523 +Kranji,MRT,1.425302,103.762049 +Marsiling,MRT,1.432579,103.77415 +Woodlands,MRT,1.436984,103.786406 +Admiralty,MRT,1.436984,103.786406 +Sembawang,MRT,1.449133,103.82006 +Yishun,MRT,1.429666,103.835044 +Khatib,MRT,1.417423,103.832995 +Yio Chu Kang,MRT,1.381765,103.844923 +Ang Mo Kio,MRT,1.370025,103.849588 +Bishan,MRT,1.35092,103.848206 +Braddell,MRT,1.34055,103.847098 +Toa Payoh,MRT,1.332405,103.847436 +Novena,MRT,1.320089,103.843405 +Newton,MRT,1.31383,103.838021 +Orchard,MRT,1.304041,103.831792 +Somerset,MRT,1.300508,103.838428 +Dhoby Ghaut,MRT,1.299169,103.845799 +City Hall,MRT,1.293119,103.852089 +Raffles Place,MRT,1.284001,103.85155 +Marina Bay,MRT,1.276481,103.854598 +Marina South Pier,MRT,1.271422,103.863581 +Tuas Link,MRT,1.340371,103.636866 +Tuas West Road,MRT,1.330075,103.639636 +Tuas Crescent,MRT,1.321091,103.649075 +Gul Circle,MRT,1.319809,103.66083 +Joo Koon,MRT,1.327826,103.678318 +Pioneer,MRT,1.337645,103.69742 +Boon Lay,MRT,1.33862,103.705817 +Lakeside,MRT,1.344264,103.720797 +Chinese Garden,MRT,1.342436,103.732582 +Clementi,MRT,1.314925,103.765341 +Dover,MRT,1.311414,103.778596 +Buona Vista,MRT,1.307337,103.790046 +Commonwealth,MRT,1.302439,103.798326 +Queenstown,MRT,1.294867,103.805902 +Redhill,MRT,1.289674,103.816787 +Tiong Bahru,MRT,1.286555,103.826956 +Outram Park,MRT,1.280319,103.839459 +Tanjong Pagar,MRT,1.276385,103.846771 +Bugis,MRT,1.300747,103.855873 +Lavender,MRT,1.307577,103.863155 +Kallang,MRT,1.311532,103.871372 +Aljunied,MRT,1.316474,103.882762 +Paya Lebar,MRT,1.318214,103.893133 +Eunos,MRT,1.319809,103.902888 +Kembangan,MRT,1.320998,103.913433 +Bedok,MRT,1.324043,103.930205 +Tanah Merah,MRT,1.327309,103.946479 +Simei,MRT,1.343237,103.953343 +Tampines,MRT,1.354467,103.943325 +Pasir Ris,MRT,1.373234,103.949343 +Expo,MRT,1.334479,103.961459 +Changi Airport,MRT,1.357622,103.988487 +HarbourFront,MRT,1.265453,103.820514 +Chinatown,MRT,1.284566,103.843626 +Clarke Quay,MRT,1.288949,103.847521 +Little India,MRT,1.306691,103.849396 +Farrer Park,MRT,1.312679,103.854872 +Boon Keng,MRT,1.320091,103.861655 +Potong Pasir,MRT,1.331316,103.868779 +Woodleigh,MRT,1.339202,103.870727 +Serangoon,MRT,1.349862,103.873635 +Kovan,MRT,1.360207,103.885163 +Hougang,MRT,1.371406,103.892533 +Buangkok,MRT,1.382991,103.893347 +Sengkang,MRT,1.391682,103.895475 +Punggol,MRT,1.405191,103.902367 +Bras Basah,MRT,1.296978,103.850715 +Esplanade,MRT,1.293995,103.855396 +Promenade,MRT,1.294063,103.860156 +Nicoll Highway,MRT,1.300292,103.863449 +Stadium,MRT,1.302847,103.875417 +Mountbatten,MRT,1.306106,103.883175 +Dakota,MRT,1.308474,103.888825 +MacPherson,MRT,1.326769,103.889901 +Tai Seng,MRT,1.33594,103.887706 +Bartley,MRT,1.342923,103.87966 +Lorong Chuan,MRT,1.35153,103.864957 +Marymount,MRT,1.349089,103.839116 +Caldecott,MRT,1.337649,103.839627 +Botanic Gardens,MRT,1.322387,103.814905 +Farrer Road,MRT,1.317606,103.807711 +Holland Village,MRT,1.311189,103.796119 +one-north,MRT,1.299854,103.787584 +Kent Ridge,MRT,1.293629,103.784441 +Haw Par Villa,MRT,1.283149,103.781991 +Pasir Panjang,MRT,1.276111,103.791893 +Labrador Park,MRT,1.27218,103.802557 +Telok Blangah,MRT,1.270769,103.809878 +Bayfront,MRT,1.281371,103.858998 +Bukit Panjang,MRT,1.37834,103.762452 +Cashew,MRT,1.369997,103.764569 +Hillview,MRT,1.363185,103.767371 +Beauty World,MRT,1.341607,103.775682 +King Albert Park,MRT,1.335721,103.783203 +Sixth Avenue,MRT,1.331221,103.79718 +Tan Kah Kee,MRT,1.325826,103.807959 +Stevens,MRT,1.320012,103.825964 +Rochor,MRT,1.303601,103.852581 +Downtown,MRT,1.27949,103.852802 +Telok Ayer,MRT,1.282285,103.848584 +Fort Canning,MRT,1.291631,103.844621 +Bencoolen,MRT,1.298477,103.849984 +Jalan Besar,MRT,1.305551,103.855443 +Bendemeer,MRT,1.313674,103.863098 +Geylang Bahru,MRT,1.321479,103.871457 +Mattar,MRT,1.326878,103.883304 +Ubi,MRT,1.330008,103.898911 +Kaki Bukit,MRT,1.335076,103.909057 +Bedok North,MRT,1.335268,103.918054 +Bedok Reservoir,MRT,1.336595,103.93307 +Tampines West,MRT,1.345583,103.938244 +Tampines East,MRT,1.35631,103.955471 +Upper Changi,MRT,1.342218,103.961505 +South View,LRT,1.380299,103.745286 +Keat Hong,LRT,1.378604,103.749058 +Teck Whye,LRT,1.376738,103.753665 +Phoenix,LRT,1.378798,103.758021 +Senja,LRT,1.382852,103.762312 +Jelapang,LRT,1.386703,103.764547 +Segar,LRT,1.387713,103.769599 +Fajar,LRT,1.384502,103.770862 +Bangkit,LRT,1.380281,103.772576 +Pending,LRT,1.376223,103.771277 +Petir,LRT,1.377828,103.76655 +Compassvale,LRT,1.394615,103.900443 +Rumbia,LRT,1.391553,103.905947 +Bakau,LRT,1.38804,103.905412 +Kangkar,LRT,1.383957,103.90216 +Ranggung,LRT,1.384116,103.897386 +Cheng Lim,LRT,1.396332,103.89379 +Farmway,LRT,1.397178,103.889168 +Kupang,LRT,1.398271,103.881283 +Thanggam,LRT,1.397378,103.87561 +Fernvale,LRT,1.392033,103.876256 +Layar,LRT,1.392141,103.880022 +Tongkang,LRT,1.389519,103.885829 +Renjong,LRT,1.386827,103.890541 +Cove,LRT,1.399534,103.905792 +Meridian,LRT,1.397002,103.908884 +Coral Edge,LRT,1.39392,103.912633 +Riviera,LRT,1.39454,103.916056 +Kadaloor,LRT,1.399633,103.916536 +Oasis,LRT,1.402304,103.912736 +Damai,LRT,1.405293,103.908606 +Sam Kee,LRT,1.409808,103.90492 +Teck Lee,LRT,1.412783,103.906565 +Punggol Point,LRT,1.416932,103.90668 +Samudera,LRT,1.415955,103.902185 +Nibong,LRT,1.411865,103.900321 +Sumang,LRT,1.408501,103.898605 +Soo Teck,LRT,1.405436,103.897287 diff --git a/content/geospatial/delaunay/images/delaunay_introduction.png b/content/geospatial/delaunay/images/delaunay_introduction.png new file 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ckM7>GZDHx)eP}uQjRpK@Jl0idP + A Delaunay triangulation in the plane with circumcircles shown +

Fig.1. A Delaunay triangulation in the plane with circumcircles shown
+ + +Delaunay triangulation for a set P of points in the plane is a triangulation DT(P) such that no point in P is inside the circumcircle of any triangle in DT(P). Delaunay triangulations maximize the minimum angle of all the angles of the triangles in the triangulation; they tend to avoid skinny triangles. The triangulation was invented by Boris Delaunay in 1934. + +## Properties of Denaulay Triangulation + +- Empty Circle Property of Triangles: the circumcircle of $\Delta pqr$ does not contain any other site of $P$. +- Empty Circle Property of Edges: A pair $(p_i, p_j)$ is an edge of DT if and only if there exists an empty circle passing through $p_i, p_j$. +- Closest Pair Property: Given a point set $P$, if $p_i, p_j$ are the two closest pair of points, then $(p_i, p_j)$ is an edge of DT. +- Minimum Spanning Tree: Another nice property of DT is that the minimum spanning tree of the sites is a subgraph of DT. +- Maximizing the Minimum Angle: In the plane, the Delaunay triangulation maximizes the minimum angle. Compared to any other triangulation of the points, the smallest angle in the Delaunay triangulation is at least as large as the smallest angle in any other. However, the Delaunay triangulation does not necessarily minimize the maximum angle. +- A circle circumscribing any Delaunay triangle does not contain any other input points in its interior. +- In the plane, each vertex has on average six surrounding triangles. + +## Visual Delaunay definition: Flipping + +
+
+ Edge Flipping property of Delaunay Triangulation +
Fig.2. Initial triangulation does not meet the Delaunay condition (the circumcircles contain more than 3 points).
Flipping the common edge produces a Delaunay triangulation for the four points.
+
+ +From the above properties an important feature arises: Looking at two triangles **ABD** and **BCD** with the common edge BD (see figures), if the sum of the angles $\alpha$ and $\gamma$ is less than or equal to $180^{\circ}$, the triangles meet the Delaunay condition. + +This is an important property because it allows the use of a flipping technique. If two triangles do not meet the Delaunay condition, switching the common edge BD for the common edge AC produces two triangles that do meet the Delaunay condition. + + +## Algorithms + +In two dimensions, one way to detect if point D lies in the circumcircle of A, B, C is to evaluate the determinant: + +$$ +\begin{bmatrix} +A_x & A_y & A_x^2 + A_y^2 & 1 \\ +B_x & B_y & B_x^2 + B_y^2 & 1 \\ +C_x & C_y & C_x^2 + C_y^2 & 1 \\ +D_x & D_y & D_x^2 + D_y^2 & 1 +\end{bmatrix} += +\begin{bmatrix} +A_x - D_x & A_y - D_y & (A_x^2 - D_x^2) + (A_y^2 - D_y^2) \\ +B_x - D_x & B_y - D_y & (B_x^2 - D_x^2) + (B_y^2 - D_y^2) \\ +C_x - D_x & C_y - D_y & (C_x^2 - D_x^2) + (C_y^2 - D_y^2) +\end{bmatrix} +> 0 +$$ + +Assuming A, B and C to lie counter-clockwise, this is positive if and only if D lies in the circumcircle. + +### Flip Algorithms + +As mentioned above, if a triangle is non-Delaunay, we can flip one of its edges. This leads to a straightforward algorithm: construct any triangulation of the points, and then flip edges until no triangle is non-Delaunay. Unfortunately, this can take $O(n^2)$ edge flips, and does not extend to three dimensions or higher. + +### Incremental + +The most straightforward way of efficiently computing the Delaunay triangulation is to repeatedly add one vertex at a time, retriangulating the affected parts of the graph. When a vertex $p$ is added (Fig.3.a), we split in three the triangle that contains $p$, then we apply the flip algorithm (Fig.3.b). Done naively, this will take $O(n)$ time: we search through all the triangles to find the one that contains $p$, then we potentially flip away every triangle. Then the overall runtime is $O(n^2)$. +
+
+ Edge Flipping property of Delaunay Triangulation +
Fig.3. Incremental Approach in Delaunay Point insertion
+
+ + +### Divide and Conquer + +In this algorithm, one recursively draws a line to split the vertices into two sets. The Delaunay triangulation is computed for each set, and then the two sets are merged along the splitting line. Using some clever tricks, the merge operation can be done in time $O(n)$, so the total running time is $O(nlogn)$. + +## Applications + +Connecting the centers of the circumcircles in Delaunay triangulation forms the Voronoi diagram. Voronoi diagram and the triangulations are useful in various geometrical applications. + +- A point location data structure can be built on top of the Voronoi diagram in order to answer nearest neighbor queries. For example, when one wants to find the nearest hospital. +- One can also find the largest empty circle amongst a set of points, and in an enclosing polygon. For example, to build a new supermarket as far as possible from all the existing ones. +- Useful in polymer physics. It can be used to represent free volume of the polymer. +- In climatology, Voronoi diagrams are used to calculate the rainfall of an area, based on a series of point measurements. In this usage, they are generally referred to as Thiessen polygons. +- Used to study the growth patterns of forests and forest canopies, and may also be helpful in developing predictive models for forest fires. + +## Delaunay Triangulation implementation + +Delaunay triangles alongwith the Voronoi diagram can be implemented in python using [PySAL](https://pysal.org/). It provides a rich suite of spatial analysis algorithms. + +The `voronoi_frames` method can be used to form the required operation. The following examples will show us how to build delaunay graph (with Voronoi diagrams) from a set of points. + +For basic understanding, we will use a set of random points to elaborate the usage of the function and its various parameters. + +- Necessary libraries are imported + +```{code-cell} ipython3 +from libpysal import weights, examples +from libpysal.cg.voronoi import voronoi_frames,voronoi +from shapely.geometry import Point +import matplotlib.pyplot as plt +import networkx as nx +import numpy as np +``` + +- Declaring the points to be plotted in delaunay graph + +```{code-cell} ipython3 +points = [(10.2, 5.1), (4.7, 2.2), (5.3, 5.7), (2.7, 5.3),(10.3,6.4),(4.5,7),(20,10),(0,2)] +regions, vertices = voronoi(points) +``` + +- Printing the regions and points of the triangulations + +```{code-cell} ipython3 +regions +``` + +```{code-cell} ipython3 +vertices +``` + +### Visualizing the Points + +The `voronoi_frames` takes in four parameters: + +- **points** (array): The originator points +- **radius** (float): The distance to ‘points at infinity’ used in building voronoi cells. Default is None. +- **clip** (string): An overloaded option about how to clip the voronoi cells. Default is 'extent'. +- **tolerance** (float): The percent of map width to use to buffer the extent of the map (default: .01, or 1%). + +Next, plotting the aformentioned points in a delaunay graph + +```{code-cell} ipython3 +region_df, point_df = voronoi_frames(points) +fig, ax = plt.subplots() +ax.set_title("Basic example of voronoi_frames",fontsize=12) +region_df.plot(ax=ax, color='blue',edgecolor='black', alpha=0.3) +point_df.plot(ax=ax, color='red'); +``` + +- Plotting the graph for a radius of 5.0. Here, the radius refers to the distance to ‘points at infinity’ used in building voronoi cells. The default value of radius is `None`. + +```{code-cell} ipython3 +fig, ax = plt.subplots(nrows=1,ncols=2,figsize=(10,6)) + +region_df, point_df = voronoi_frames(points,clip='none',radius=0.0) +ax[0].set_title('Voronoi Diagram with radius value of 0.0', fontsize=12) +region_df.plot(ax=ax[0], color='blue',edgecolor='black', alpha=0.3) +point_df.plot(ax=ax[0], color='red') + +region_df, point_df = voronoi_frames(points,clip='none',radius=100.0) +ax[1].set_title('Voronoi Diagram with radius value of 100.0', fontsize=12) +region_df.plot(ax=ax[1], color='blue',edgecolor='black', alpha=0.3) +point_df.plot(ax=ax[1], color='red'); +``` + +Finally, generating graph for different clip options.The clip options available are - +- `'none'` / `None`: No clip is applied +- `'bbox'` / `'extent'` / `'bounding box'`: Clip the voronoi cells to the bounding box of the input points +- `'chull'` / `'convex hull'`: Clip the voronoi cells to the convex hull of the input points +- `'ashape'` / `'ahull'`: Clip the voronoi cells to the tightest hull that contains all points + +```{code-cell} ipython3 +fig, ax = plt.subplots(nrows=2,ncols=2,figsize=(12,9)) + +region_df, point_df = voronoi_frames(points,clip='none') +ax[0,0].set_title('Voronoi Diagram with no clipping', fontsize=12) +region_df.plot(ax=ax[0,0], color='blue',edgecolor='black', alpha=0.3) +point_df.plot(ax=ax[0,0], color='red') + +region_df, point_df = voronoi_frames(points,clip='bbox') +ax[0,1].set_title('Voronoi Diagram with Bounding Box clipping', fontsize=12) +region_df.plot(ax=ax[0,1], color='blue',edgecolor='black', alpha=0.3) +point_df.plot(ax=ax[0,1], color='red') + +region_df, point_df = voronoi_frames(points,100.0,clip='chull') +ax[1,0].set_title('Voronoi Diagram with Convex Hull clipping', fontsize=12) +region_df.plot(ax=ax[1,0], color='blue',edgecolor='black', alpha=0.3) +point_df.plot(ax=ax[1,0], color='red') + +region_df, point_df = voronoi_frames(points,100.0,clip='ahull') +ax[1,1].set_title('Voronoi Diagram with tightest hull clipping', fontsize=12) +region_df.plot(ax=ax[1,1], color='blue',edgecolor='black', alpha=0.3) +point_df.plot(ax=ax[1,1], color='red'); +``` + +### Voronoi Frames with Real World Dataset + +This example shows how to build a delaunay graph (plus its dual, the set of Voronoi polygons) from a set of points. For this, we will use the dataset of train stations in Singapore. The methods shown here can also work directly with polygonal data using their centroids as representative points. + +- First, including the necessary libraries + +```{code-cell} ipython3 +from libpysal import weights, examples +from libpysal.cg import voronoi_frames +from contextily import add_basemap +import matplotlib.pyplot as plt +import networkx as nx +import pandas as pd +import numpy as np +``` + +- Reading the dataset from a CSV file using Pandas. The dataset contains the information about each train stations in Singapore alongwith its latitude and longitudes. Next, the coordinates are converted into float data type from string + +```{code-cell} ipython3 +data = pd.read_csv("data/singapore_train_stations.csv") + +data.lng = list(map(float, data.lng)) +data.lat = list(map(float,data.lat)) +``` + +- In order for networkx to plot the nodes of our graph correctly, we need to construct the array of coordinates for each point in our dataset. To get this as a numpy array, we extract the x and y coordinates from the geometry column. + +```{code-cell} ipython3 +coordinates = np.column_stack((data.lng, data.lat)) +``` + +- While we could simply present the Delaunay graph directly, it is useful to visualize the Delaunay graph alongside the Voronoi diagram. This is because the two are intrinsically linked: the adjacency graph of the Voronoi diagram is the Delaunay graph for the set of generator points! Put simply, this means we can build the Voronoi diagram (relying on scipy.spatial for the underlying computations), and then convert these polygons quickly into the Delaunay graph. Be careful, though; our algorithm, by default, will clip the voronoi diagram to the bounding box of the point pattern. This is controlled by the "clip" argument. + +```{code-cell} ipython3 +cells, generators = voronoi_frames(coordinates,clip="chull") +``` + +- With the voronoi polygons, we can construct the adjacency graph between them using "Rook" contiguity. This represents voronoi cells as being adjacent if they share an edge/face. This is an analogue to the "von Neuman" neighborhood, or the 4 cardinal neighbors in a regular grid. The name comes from the directions a Rook piece can move on a chessboard. + +```{code-cell} ipython3 +delaunay = weights.Rook.from_dataframe(cells) +``` + +- Once the graph is built, we can convert the graphs to networkx objects using the relevant method. + +```{code-cell} ipython3 +delaunay_graph = delaunay.to_networkx() +``` + +- To plot with networkx, we need to merge the nodes back to their positions in order to plot in networkx + +```{code-cell} ipython3 +positions = dict(zip(delaunay_graph.nodes, coordinates)) +``` + +- Now, we can plot with a nice basemap using Contextily + +```{code-cell} ipython3 +figure,ax = plt.subplots(figsize=(15, 9)) +cells.plot(ax=ax,facecolor="lightblue", alpha=0.50, edgecolor="cornsilk", linewidth=2) +add_basemap(ax,crs='EPSG:4326') +ax.axis("off") +nx.draw( + delaunay_graph, + positions, + ax=ax, + node_size=2, + node_color="k", + edge_color="k", + alpha=0.8, +) +plt.show() +``` + +## References + +- [Delaunay Triangulation](http://wiki.gis.com/wiki/index.php/Delaunay_triangulation) +- [libpysal.cg.voronoi_frames](https://pysal.org/libpysal/generated/libpysal.cg.voronoi_frames.html#libpysal.cg.voronoi_frames) +- [Incremental approach](https://www.cs.umd.edu/class/spring2020/cmsc754/Lects/lect13-delaun-alg.pdf) diff --git a/content/geospatial/index.md b/content/geospatial/index.md new file mode 100644 index 000000000..d32e5edbf --- /dev/null +++ b/content/geospatial/index.md @@ -0,0 +1,11 @@ +# Geospatial Examples + +A closer look at techniques and libraries recommended by Networkx when working with geospatial data (including reading and writing shapefiles). + +```{toctree} +--- +maxdepth: 1 +--- +delaunay/index + +``` \ No newline at end of file diff --git a/requirements.txt b/requirements.txt index 6fa8a0337..953190079 100644 --- a/requirements.txt +++ b/requirements.txt @@ -6,7 +6,9 @@ numpy scipy matplotlib pandas -ipython!=8.7.0 +libpysal +contextily +geopandas # For testing and site generation nbval diff --git a/site/index.md b/site/index.md index 319059d54..8998d327d 100644 --- a/site/index.md +++ b/site/index.md @@ -38,5 +38,6 @@ maxdepth: 1 content/algorithms/index content/generators/index content/exploratory_notebooks/facebook_notebook +content/geospatial/index ``` From 140193ea56352d675c3a3e2d4b5b277204498a83 Mon Sep 17 00:00:00 2001 From: Pratik Gupta <66073063+inomag@users.noreply.github.com> Date: Thu, 14 Apr 2022 03:06:20 +0530 Subject: [PATCH 03/15] Update index.md --- content/geospatial/index.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/content/geospatial/index.md b/content/geospatial/index.md index d32e5edbf..6fbd75e2b 100644 --- a/content/geospatial/index.md +++ b/content/geospatial/index.md @@ -1,4 +1,4 @@ -# Geospatial Examples +# Geospatial Information System A closer look at techniques and libraries recommended by Networkx when working with geospatial data (including reading and writing shapefiles). @@ -8,4 +8,4 @@ maxdepth: 1 --- delaunay/index -``` \ No newline at end of file +``` From 0bb5bbd38281ac285de6a023b8de48340c29d91c Mon Sep 17 00:00:00 2001 From: Pratik Gupta <66073063+inomag@users.noreply.github.com> Date: Thu, 14 Apr 2022 03:07:11 +0530 Subject: [PATCH 04/15] Update index.md --- content/geospatial/delaunay/index.md | 25 ++++++++----------------- 1 file changed, 8 insertions(+), 17 deletions(-) diff --git a/content/geospatial/delaunay/index.md b/content/geospatial/delaunay/index.md index 87e1206ab..6415e9423 100644 --- a/content/geospatial/delaunay/index.md +++ b/content/geospatial/delaunay/index.md @@ -13,14 +13,10 @@ kernelspec: # Delaunay Graph from Geographic Points - -
- A Delaunay triangulation in the plane with circumcircles shown -
Fig.1. A Delaunay triangulation in the plane with circumcircles shown
-
- Delaunay triangulation for a set P of points in the plane is a triangulation DT(P) such that no point in P is inside the circumcircle of any triangle in DT(P). Delaunay triangulations maximize the minimum angle of all the angles of the triangles in the triangulation; they tend to avoid skinny triangles. The triangulation was invented by Boris Delaunay in 1934. +![delaunay_triangulation](images/delaunay_introduction.png "A Delaunay triangulation in the plane with circumcircles shown") + ## Properties of Denaulay Triangulation - Empty Circle Property of Triangles: the circumcircle of $\Delta pqr$ does not contain any other site of $P$. @@ -33,11 +29,9 @@ Delaunay triangulation for a set P of points in the plane is a triangulation DT( ## Visual Delaunay definition: Flipping -
-
- Edge Flipping property of Delaunay Triangulation -
Fig.2. Initial triangulation does not meet the Delaunay condition (the circumcircles contain more than 3 points).
Flipping the common edge produces a Delaunay triangulation for the four points.
-
+ + +![edge_flip](images/edge_flip.png "Edge flipping property of Delaunay Triangulation") From the above properties an important feature arises: Looking at two triangles **ABD** and **BCD** with the common edge BD (see figures), if the sum of the angles $\alpha$ and $\gamma$ is less than or equal to $180^{\circ}$, the triangles meet the Delaunay condition. @@ -72,12 +66,9 @@ As mentioned above, if a triangle is non-Delaunay, we can flip one of its edges. ### Incremental -The most straightforward way of efficiently computing the Delaunay triangulation is to repeatedly add one vertex at a time, retriangulating the affected parts of the graph. When a vertex $p$ is added (Fig.3.a), we split in three the triangle that contains $p$, then we apply the flip algorithm (Fig.3.b). Done naively, this will take $O(n)$ time: we search through all the triangles to find the one that contains $p$, then we potentially flip away every triangle. Then the overall runtime is $O(n^2)$. -
-
- Edge Flipping property of Delaunay Triangulation -
Fig.3. Incremental Approach in Delaunay Point insertion
-
+The most straightforward way of efficiently computing the Delaunay triangulation is to repeatedly add one vertex at a time, retriangulating the affected parts of the graph. When a vertex $p$ is added (Fig.a), we split in three the triangle that contains $p$, then we apply the flip algorithm (Fig.b). Done naively, this will take $O(n)$ time: we search through all the triangles to find the one that contains $p$, then we potentially flip away every triangle. Then the overall runtime is $O(n^2)$. + +![incremental](images/incremental.png "Incremental Approach in generating Delaunay Triangles") ### Divide and Conquer From baa973a9cedded5605941c917dfc266952eb9705 Mon Sep 17 00:00:00 2001 From: Pratik Gupta <66073063+inomag@users.noreply.github.com> Date: Thu, 14 Apr 2022 10:09:06 +0530 Subject: [PATCH 05/15] Included shapely --- requirements.txt | 1 + 1 file changed, 1 insertion(+) diff --git a/requirements.txt b/requirements.txt index 953190079..dd1d3d21d 100644 --- a/requirements.txt +++ b/requirements.txt @@ -9,6 +9,7 @@ pandas libpysal contextily geopandas +shapely # For testing and site generation nbval From 3669b22834cfc4e41d043195c1407175a278ee88 Mon Sep 17 00:00:00 2001 From: Pratik Gupta <66073063+inomag@users.noreply.github.com> Date: Thu, 14 Apr 2022 10:48:00 +0530 Subject: [PATCH 06/15] Update index.md --- content/geospatial/delaunay/index.md | 7 +------ 1 file changed, 1 insertion(+), 6 deletions(-) diff --git a/content/geospatial/delaunay/index.md b/content/geospatial/delaunay/index.md index 6415e9423..0b0a3b7de 100644 --- a/content/geospatial/delaunay/index.md +++ b/content/geospatial/delaunay/index.md @@ -178,12 +178,7 @@ point_df.plot(ax=ax[0,1], color='red') region_df, point_df = voronoi_frames(points,100.0,clip='chull') ax[1,0].set_title('Voronoi Diagram with Convex Hull clipping', fontsize=12) region_df.plot(ax=ax[1,0], color='blue',edgecolor='black', alpha=0.3) -point_df.plot(ax=ax[1,0], color='red') - -region_df, point_df = voronoi_frames(points,100.0,clip='ahull') -ax[1,1].set_title('Voronoi Diagram with tightest hull clipping', fontsize=12) -region_df.plot(ax=ax[1,1], color='blue',edgecolor='black', alpha=0.3) -point_df.plot(ax=ax[1,1], color='red'); +point_df.plot(ax=ax[1,0], color='red'); ``` ### Voronoi Frames with Real World Dataset From 52e94f1d0fad6c0ddcbbcc193dd80fc9b226b4c8 Mon Sep 17 00:00:00 2001 From: Pratik Gupta <66073063+inomag@users.noreply.github.com> Date: Thu, 14 Apr 2022 20:29:28 +0530 Subject: [PATCH 07/15] Refactor code --- content/geospatial/delaunay/index.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/content/geospatial/delaunay/index.md b/content/geospatial/delaunay/index.md index 0b0a3b7de..489fee8d6 100644 --- a/content/geospatial/delaunay/index.md +++ b/content/geospatial/delaunay/index.md @@ -133,7 +133,7 @@ The `voronoi_frames` takes in four parameters: Next, plotting the aformentioned points in a delaunay graph ```{code-cell} ipython3 -region_df, point_df = voronoi_frames(points) +region_df, point_df = voronoi_frames(points,clip='extent') fig, ax = plt.subplots() ax.set_title("Basic example of voronoi_frames",fontsize=12) region_df.plot(ax=ax, color='blue',edgecolor='black', alpha=0.3) @@ -170,7 +170,7 @@ ax[0,0].set_title('Voronoi Diagram with no clipping', fontsize=12) region_df.plot(ax=ax[0,0], color='blue',edgecolor='black', alpha=0.3) point_df.plot(ax=ax[0,0], color='red') -region_df, point_df = voronoi_frames(points,clip='bbox') +region_df, point_df = voronoi_frames(points,clip='extent') ax[0,1].set_title('Voronoi Diagram with Bounding Box clipping', fontsize=12) region_df.plot(ax=ax[0,1], color='blue',edgecolor='black', alpha=0.3) point_df.plot(ax=ax[0,1], color='red') @@ -215,7 +215,7 @@ coordinates = np.column_stack((data.lng, data.lat)) - While we could simply present the Delaunay graph directly, it is useful to visualize the Delaunay graph alongside the Voronoi diagram. This is because the two are intrinsically linked: the adjacency graph of the Voronoi diagram is the Delaunay graph for the set of generator points! Put simply, this means we can build the Voronoi diagram (relying on scipy.spatial for the underlying computations), and then convert these polygons quickly into the Delaunay graph. Be careful, though; our algorithm, by default, will clip the voronoi diagram to the bounding box of the point pattern. This is controlled by the "clip" argument. ```{code-cell} ipython3 -cells, generators = voronoi_frames(coordinates,clip="chull") +cells, generators = voronoi_frames(coordinates,clip='chull') ``` - With the voronoi polygons, we can construct the adjacency graph between them using "Rook" contiguity. This represents voronoi cells as being adjacent if they share an edge/face. This is an analogue to the "von Neuman" neighborhood, or the 4 cardinal neighbors in a regular grid. The name comes from the directions a Rook piece can move on a chessboard. From c77b186482bfba67f956fc5be2bb890fbb07b5b6 Mon Sep 17 00:00:00 2001 From: Pratik Gupta <66073063+inomag@users.noreply.github.com> Date: Thu, 14 Apr 2022 20:42:55 +0530 Subject: [PATCH 08/15] Delete CODE_OF_CONDUCT.rst --- CODE_OF_CONDUCT.rst | 152 -------------------------------------------- 1 file changed, 152 deletions(-) delete mode 100644 CODE_OF_CONDUCT.rst diff --git a/CODE_OF_CONDUCT.rst b/CODE_OF_CONDUCT.rst deleted file mode 100644 index 0822de9a3..000000000 --- a/CODE_OF_CONDUCT.rst +++ /dev/null @@ -1,152 +0,0 @@ -.. _code_of_conduct: - -Code of Conduct -=============== - - -Introduction ------------- - -This code of conduct applies to all spaces managed by the NetworkX project, -including all public and private mailing lists, issue trackers, wikis, and -any other communication channel used by our community. - -This code of conduct should be honored by everyone who participates in -the NetworkX community formally or informally, or claims any affiliation with the -project, in any project-related activities and especially when representing the -project, in any role. - -This code is not exhaustive or complete. 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Participants in our community should uphold these standards -in all their interactions and help others to do so as well (see next section). - - -Reporting Guidelines --------------------- - -We know that it is painfully common for internet communication to start at or -devolve into obvious and flagrant abuse. We also recognize that sometimes -people may have a bad day, or be unaware of some of the guidelines in this Code -of Conduct. Please keep this in mind when deciding on how to respond to a -breach of this Code. - -For clearly intentional breaches, report those to the NetworkX Steering Council -(see below). For possibly unintentional breaches, you may reply to the person -and point out this code of conduct (either in public or in private, whatever is -most appropriate). If you would prefer not to do that, please feel free to -report to the NetworkX Steering Council directly, or ask the Council for -advice, in confidence. - -You can report issues to the -`NetworkX Steering Council `__, -at networkx-conduct@groups.io. - -If your report involves any members of the Council, or if they feel they have -a conflict of interest in handling it, then they will recuse themselves from -considering your report. Alternatively, if for any reason you feel -uncomfortable making a report to the Council, then you can also contact: - -- Senior `NumFOCUS staff `__: conduct@numfocus.org. - - -Incident reporting resolution & Code of Conduct enforcement ------------------------------------------------------------ - -We will investigate and respond to all complaints. The NetworkX Steering Council -will protect the identity of the reporter, and treat the content of -complaints as confidential (unless the reporter agrees otherwise). - -In case of severe and obvious breaches, e.g., personal threat or violent, sexist -or racist language, we will immediately disconnect the originator from NetworkX -communication channels. - -In cases not involving clear severe and obvious breaches of this code of -conduct, the process for acting on any received code of conduct violation -report will be: - -1. acknowledge report is received -2. reasonable discussion/feedback -3. mediation (if feedback didn't help, and only if both reporter and reportee agree to this) -4. enforcement via transparent decision by the NetworkX Steering Council - -The Council will respond to any report as soon as possible, and at most -within 72 hours. - - -Endnotes --------- - -This document is adapted from: - -- `SciPy Code of Conduct `_ From 3b0a709f1d36acca26d234b2c3814870b44e36d4 Mon Sep 17 00:00:00 2001 From: Pratik Gupta <66073063+inomag@users.noreply.github.com> Date: Thu, 14 Apr 2022 20:43:24 +0530 Subject: [PATCH 09/15] Include rtree --- requirements.txt | 1 + 1 file changed, 1 insertion(+) diff --git a/requirements.txt b/requirements.txt index dd1d3d21d..9301de9bd 100644 --- a/requirements.txt +++ b/requirements.txt @@ -10,6 +10,7 @@ libpysal contextily geopandas shapely +rtree # For testing and site generation nbval From 3b39d40eab90c1d1c69f148ebbe42978bea60b3c Mon Sep 17 00:00:00 2001 From: Pratik Gupta <66073063+inomag@users.noreply.github.com> Date: Fri, 15 Apr 2022 10:30:06 +0530 Subject: [PATCH 10/15] Include ahull --- content/geospatial/delaunay/index.md | 5 +++++ 1 file changed, 5 insertions(+) diff --git a/content/geospatial/delaunay/index.md b/content/geospatial/delaunay/index.md index 489fee8d6..d25ebc408 100644 --- a/content/geospatial/delaunay/index.md +++ b/content/geospatial/delaunay/index.md @@ -179,6 +179,11 @@ region_df, point_df = voronoi_frames(points,100.0,clip='chull') ax[1,0].set_title('Voronoi Diagram with Convex Hull clipping', fontsize=12) region_df.plot(ax=ax[1,0], color='blue',edgecolor='black', alpha=0.3) point_df.plot(ax=ax[1,0], color='red'); + +region_df, point_df = voronoi_frames(points,100.0,clip='ahull') +ax[1,1].set_title('Voronoi Diagram with tightest hull clipping', fontsize=12) +region_df.plot(ax=ax[1,1], color='blue',edgecolor='black', alpha=0.3) +point_df.plot(ax=ax[1,1], color='red'); ``` ### Voronoi Frames with Real World Dataset From b378d78437aae883cd214ee15ac375fc2eb0d0b2 Mon Sep 17 00:00:00 2001 From: Dan Schult Date: Thu, 31 Aug 2023 20:13:29 -0400 Subject: [PATCH 11/15] tweak requirements file --- requirements.txt | 11 ++++++----- 1 file changed, 6 insertions(+), 5 deletions(-) diff --git a/requirements.txt b/requirements.txt index 9301de9bd..b68a132cd 100644 --- a/requirements.txt +++ b/requirements.txt @@ -6,11 +6,7 @@ numpy scipy matplotlib pandas -libpysal -contextily -geopandas -shapely -rtree +ipython!=8.7.0 # For testing and site generation nbval @@ -24,3 +20,8 @@ pyupgrade # Notebook requirements pygraphviz +libpysal +contextily +geopandas +shapely +rtree From 26d3a02ec086f26f98f96854d16fd1d20bcae341 Mon Sep 17 00:00:00 2001 From: Dan Schult Date: Thu, 31 Aug 2023 21:02:20 -0400 Subject: [PATCH 12/15] move geospatial directory into algorithms --- .../data/singapore_train_stations.csv | 0 .../geospatial/delaunay/delaunay.md} | 32 +++++++++--------- .../delaunay/images/delaunay_introduction.png | Bin .../geospatial/delaunay/images/edge_flip.png | Bin .../delaunay/images/incremental.png | Bin content/{ => algorithms}/geospatial/index.md | 0 6 files changed, 16 insertions(+), 16 deletions(-) rename content/{ => algorithms}/geospatial/delaunay/data/singapore_train_stations.csv (100%) rename content/{geospatial/delaunay/index.md => algorithms/geospatial/delaunay/delaunay.md} (97%) rename content/{ => algorithms}/geospatial/delaunay/images/delaunay_introduction.png (100%) rename content/{ => algorithms}/geospatial/delaunay/images/edge_flip.png (100%) rename content/{ => algorithms}/geospatial/delaunay/images/incremental.png (100%) rename content/{ => algorithms}/geospatial/index.md (100%) diff --git a/content/geospatial/delaunay/data/singapore_train_stations.csv b/content/algorithms/geospatial/delaunay/data/singapore_train_stations.csv similarity index 100% rename from content/geospatial/delaunay/data/singapore_train_stations.csv rename to content/algorithms/geospatial/delaunay/data/singapore_train_stations.csv diff --git a/content/geospatial/delaunay/index.md b/content/algorithms/geospatial/delaunay/delaunay.md similarity index 97% rename from content/geospatial/delaunay/index.md rename to content/algorithms/geospatial/delaunay/delaunay.md index d25ebc408..3ddffbf4b 100644 --- a/content/geospatial/delaunay/index.md +++ b/content/algorithms/geospatial/delaunay/delaunay.md @@ -4,7 +4,7 @@ jupytext: extension: .md format_name: myst format_version: 0.13 - jupytext_version: 1.13.8 + jupytext_version: 1.15.0 kernelspec: display_name: Python 3 (ipykernel) language: python @@ -95,7 +95,7 @@ For basic understanding, we will use a set of random points to elaborate the usa - Necessary libraries are imported -```{code-cell} ipython3 +```{code-cell} from libpysal import weights, examples from libpysal.cg.voronoi import voronoi_frames,voronoi from shapely.geometry import Point @@ -106,18 +106,18 @@ import numpy as np - Declaring the points to be plotted in delaunay graph -```{code-cell} ipython3 +```{code-cell} points = [(10.2, 5.1), (4.7, 2.2), (5.3, 5.7), (2.7, 5.3),(10.3,6.4),(4.5,7),(20,10),(0,2)] regions, vertices = voronoi(points) ``` - Printing the regions and points of the triangulations -```{code-cell} ipython3 +```{code-cell} regions ``` -```{code-cell} ipython3 +```{code-cell} vertices ``` @@ -132,7 +132,7 @@ The `voronoi_frames` takes in four parameters: Next, plotting the aformentioned points in a delaunay graph -```{code-cell} ipython3 +```{code-cell} region_df, point_df = voronoi_frames(points,clip='extent') fig, ax = plt.subplots() ax.set_title("Basic example of voronoi_frames",fontsize=12) @@ -142,7 +142,7 @@ point_df.plot(ax=ax, color='red'); - Plotting the graph for a radius of 5.0. Here, the radius refers to the distance to ‘points at infinity’ used in building voronoi cells. The default value of radius is `None`. -```{code-cell} ipython3 +```{code-cell} fig, ax = plt.subplots(nrows=1,ncols=2,figsize=(10,6)) region_df, point_df = voronoi_frames(points,clip='none',radius=0.0) @@ -162,7 +162,7 @@ Finally, generating graph for different clip options.The clip options available - `'chull'` / `'convex hull'`: Clip the voronoi cells to the convex hull of the input points - `'ashape'` / `'ahull'`: Clip the voronoi cells to the tightest hull that contains all points -```{code-cell} ipython3 +```{code-cell} fig, ax = plt.subplots(nrows=2,ncols=2,figsize=(12,9)) region_df, point_df = voronoi_frames(points,clip='none') @@ -192,7 +192,7 @@ This example shows how to build a delaunay graph (plus its dual, the set of Voro - First, including the necessary libraries -```{code-cell} ipython3 +```{code-cell} from libpysal import weights, examples from libpysal.cg import voronoi_frames from contextily import add_basemap @@ -204,7 +204,7 @@ import numpy as np - Reading the dataset from a CSV file using Pandas. The dataset contains the information about each train stations in Singapore alongwith its latitude and longitudes. Next, the coordinates are converted into float data type from string -```{code-cell} ipython3 +```{code-cell} data = pd.read_csv("data/singapore_train_stations.csv") data.lng = list(map(float, data.lng)) @@ -213,37 +213,37 @@ data.lat = list(map(float,data.lat)) - In order for networkx to plot the nodes of our graph correctly, we need to construct the array of coordinates for each point in our dataset. To get this as a numpy array, we extract the x and y coordinates from the geometry column. -```{code-cell} ipython3 +```{code-cell} coordinates = np.column_stack((data.lng, data.lat)) ``` - While we could simply present the Delaunay graph directly, it is useful to visualize the Delaunay graph alongside the Voronoi diagram. This is because the two are intrinsically linked: the adjacency graph of the Voronoi diagram is the Delaunay graph for the set of generator points! Put simply, this means we can build the Voronoi diagram (relying on scipy.spatial for the underlying computations), and then convert these polygons quickly into the Delaunay graph. Be careful, though; our algorithm, by default, will clip the voronoi diagram to the bounding box of the point pattern. This is controlled by the "clip" argument. -```{code-cell} ipython3 +```{code-cell} cells, generators = voronoi_frames(coordinates,clip='chull') ``` - With the voronoi polygons, we can construct the adjacency graph between them using "Rook" contiguity. This represents voronoi cells as being adjacent if they share an edge/face. This is an analogue to the "von Neuman" neighborhood, or the 4 cardinal neighbors in a regular grid. The name comes from the directions a Rook piece can move on a chessboard. -```{code-cell} ipython3 +```{code-cell} delaunay = weights.Rook.from_dataframe(cells) ``` - Once the graph is built, we can convert the graphs to networkx objects using the relevant method. -```{code-cell} ipython3 +```{code-cell} delaunay_graph = delaunay.to_networkx() ``` - To plot with networkx, we need to merge the nodes back to their positions in order to plot in networkx -```{code-cell} ipython3 +```{code-cell} positions = dict(zip(delaunay_graph.nodes, coordinates)) ``` - Now, we can plot with a nice basemap using Contextily -```{code-cell} ipython3 +```{code-cell} figure,ax = plt.subplots(figsize=(15, 9)) cells.plot(ax=ax,facecolor="lightblue", alpha=0.50, edgecolor="cornsilk", linewidth=2) add_basemap(ax,crs='EPSG:4326') diff --git a/content/geospatial/delaunay/images/delaunay_introduction.png b/content/algorithms/geospatial/delaunay/images/delaunay_introduction.png similarity index 100% rename from content/geospatial/delaunay/images/delaunay_introduction.png rename to content/algorithms/geospatial/delaunay/images/delaunay_introduction.png diff --git a/content/geospatial/delaunay/images/edge_flip.png b/content/algorithms/geospatial/delaunay/images/edge_flip.png similarity index 100% rename from content/geospatial/delaunay/images/edge_flip.png rename to content/algorithms/geospatial/delaunay/images/edge_flip.png diff --git a/content/geospatial/delaunay/images/incremental.png b/content/algorithms/geospatial/delaunay/images/incremental.png similarity index 100% rename from content/geospatial/delaunay/images/incremental.png rename to content/algorithms/geospatial/delaunay/images/incremental.png diff --git a/content/geospatial/index.md b/content/algorithms/geospatial/index.md similarity index 100% rename from content/geospatial/index.md rename to content/algorithms/geospatial/index.md From 23ece5629f5915006a3fd01daf71a79c4d8bca33 Mon Sep 17 00:00:00 2001 From: Dan Schult Date: Thu, 31 Aug 2023 21:06:04 -0400 Subject: [PATCH 13/15] rename index -> delaunay --- content/algorithms/geospatial/index.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/content/algorithms/geospatial/index.md b/content/algorithms/geospatial/index.md index 6fbd75e2b..005decd74 100644 --- a/content/algorithms/geospatial/index.md +++ b/content/algorithms/geospatial/index.md @@ -6,6 +6,6 @@ A closer look at techniques and libraries recommended by Networkx when working w --- maxdepth: 1 --- -delaunay/index +delaunay/delaunay ``` From d947c1f6873b57e2157a4f1545e81ea02e1a3750 Mon Sep 17 00:00:00 2001 From: Dan Schult Date: Thu, 31 Aug 2023 21:34:11 -0400 Subject: [PATCH 14/15] apply nbqa-black --- .../geospatial/delaunay/delaunay.md | 91 ++++++++++--------- 1 file changed, 50 insertions(+), 41 deletions(-) diff --git a/content/algorithms/geospatial/delaunay/delaunay.md b/content/algorithms/geospatial/delaunay/delaunay.md index 3ddffbf4b..10266165b 100644 --- a/content/algorithms/geospatial/delaunay/delaunay.md +++ b/content/algorithms/geospatial/delaunay/delaunay.md @@ -97,7 +97,7 @@ For basic understanding, we will use a set of random points to elaborate the usa ```{code-cell} from libpysal import weights, examples -from libpysal.cg.voronoi import voronoi_frames,voronoi +from libpysal.cg.voronoi import voronoi_frames, voronoi from shapely.geometry import Point import matplotlib.pyplot as plt import networkx as nx @@ -107,7 +107,16 @@ import numpy as np - Declaring the points to be plotted in delaunay graph ```{code-cell} -points = [(10.2, 5.1), (4.7, 2.2), (5.3, 5.7), (2.7, 5.3),(10.3,6.4),(4.5,7),(20,10),(0,2)] +points = [ + (10.2, 5.1), + (4.7, 2.2), + (5.3, 5.7), + (2.7, 5.3), + (10.3, 6.4), + (4.5, 7), + (20, 10), + (0, 2), +] regions, vertices = voronoi(points) ``` @@ -133,27 +142,27 @@ The `voronoi_frames` takes in four parameters: Next, plotting the aformentioned points in a delaunay graph ```{code-cell} -region_df, point_df = voronoi_frames(points,clip='extent') +region_df, point_df = voronoi_frames(points, clip="extent") fig, ax = plt.subplots() -ax.set_title("Basic example of voronoi_frames",fontsize=12) -region_df.plot(ax=ax, color='blue',edgecolor='black', alpha=0.3) -point_df.plot(ax=ax, color='red'); +ax.set_title("Basic example of voronoi_frames", fontsize=12) +region_df.plot(ax=ax, color="blue", edgecolor="black", alpha=0.3) +point_df.plot(ax=ax, color="red"); ``` - Plotting the graph for a radius of 5.0. Here, the radius refers to the distance to ‘points at infinity’ used in building voronoi cells. The default value of radius is `None`. ```{code-cell} -fig, ax = plt.subplots(nrows=1,ncols=2,figsize=(10,6)) +fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(10, 6)) -region_df, point_df = voronoi_frames(points,clip='none',radius=0.0) -ax[0].set_title('Voronoi Diagram with radius value of 0.0', fontsize=12) -region_df.plot(ax=ax[0], color='blue',edgecolor='black', alpha=0.3) -point_df.plot(ax=ax[0], color='red') +region_df, point_df = voronoi_frames(points, clip="none", radius=0.0) +ax[0].set_title("Voronoi Diagram with radius value of 0.0", fontsize=12) +region_df.plot(ax=ax[0], color="blue", edgecolor="black", alpha=0.3) +point_df.plot(ax=ax[0], color="red") -region_df, point_df = voronoi_frames(points,clip='none',radius=100.0) -ax[1].set_title('Voronoi Diagram with radius value of 100.0', fontsize=12) -region_df.plot(ax=ax[1], color='blue',edgecolor='black', alpha=0.3) -point_df.plot(ax=ax[1], color='red'); +region_df, point_df = voronoi_frames(points, clip="none", radius=100.0) +ax[1].set_title("Voronoi Diagram with radius value of 100.0", fontsize=12) +region_df.plot(ax=ax[1], color="blue", edgecolor="black", alpha=0.3) +point_df.plot(ax=ax[1], color="red"); ``` Finally, generating graph for different clip options.The clip options available are - @@ -163,27 +172,27 @@ Finally, generating graph for different clip options.The clip options available - `'ashape'` / `'ahull'`: Clip the voronoi cells to the tightest hull that contains all points ```{code-cell} -fig, ax = plt.subplots(nrows=2,ncols=2,figsize=(12,9)) - -region_df, point_df = voronoi_frames(points,clip='none') -ax[0,0].set_title('Voronoi Diagram with no clipping', fontsize=12) -region_df.plot(ax=ax[0,0], color='blue',edgecolor='black', alpha=0.3) -point_df.plot(ax=ax[0,0], color='red') - -region_df, point_df = voronoi_frames(points,clip='extent') -ax[0,1].set_title('Voronoi Diagram with Bounding Box clipping', fontsize=12) -region_df.plot(ax=ax[0,1], color='blue',edgecolor='black', alpha=0.3) -point_df.plot(ax=ax[0,1], color='red') - -region_df, point_df = voronoi_frames(points,100.0,clip='chull') -ax[1,0].set_title('Voronoi Diagram with Convex Hull clipping', fontsize=12) -region_df.plot(ax=ax[1,0], color='blue',edgecolor='black', alpha=0.3) -point_df.plot(ax=ax[1,0], color='red'); - -region_df, point_df = voronoi_frames(points,100.0,clip='ahull') -ax[1,1].set_title('Voronoi Diagram with tightest hull clipping', fontsize=12) -region_df.plot(ax=ax[1,1], color='blue',edgecolor='black', alpha=0.3) -point_df.plot(ax=ax[1,1], color='red'); +fig, ax = plt.subplots(nrows=2, ncols=2, figsize=(12, 9)) + +region_df, point_df = voronoi_frames(points, clip="none") +ax[0, 0].set_title("Voronoi Diagram with no clipping", fontsize=12) +region_df.plot(ax=ax[0, 0], color="blue", edgecolor="black", alpha=0.3) +point_df.plot(ax=ax[0, 0], color="red") + +region_df, point_df = voronoi_frames(points, clip="extent") +ax[0, 1].set_title("Voronoi Diagram with Bounding Box clipping", fontsize=12) +region_df.plot(ax=ax[0, 1], color="blue", edgecolor="black", alpha=0.3) +point_df.plot(ax=ax[0, 1], color="red") + +region_df, point_df = voronoi_frames(points, 100.0, clip="chull") +ax[1, 0].set_title("Voronoi Diagram with Convex Hull clipping", fontsize=12) +region_df.plot(ax=ax[1, 0], color="blue", edgecolor="black", alpha=0.3) +point_df.plot(ax=ax[1, 0], color="red") + +region_df, point_df = voronoi_frames(points, 100.0, clip="ahull") +ax[1, 1].set_title("Voronoi Diagram with tightest hull clipping", fontsize=12) +region_df.plot(ax=ax[1, 1], color="blue", edgecolor="black", alpha=0.3) +point_df.plot(ax=ax[1, 1], color="red"); ``` ### Voronoi Frames with Real World Dataset @@ -208,7 +217,7 @@ import numpy as np data = pd.read_csv("data/singapore_train_stations.csv") data.lng = list(map(float, data.lng)) -data.lat = list(map(float,data.lat)) +data.lat = list(map(float, data.lat)) ``` - In order for networkx to plot the nodes of our graph correctly, we need to construct the array of coordinates for each point in our dataset. To get this as a numpy array, we extract the x and y coordinates from the geometry column. @@ -220,7 +229,7 @@ coordinates = np.column_stack((data.lng, data.lat)) - While we could simply present the Delaunay graph directly, it is useful to visualize the Delaunay graph alongside the Voronoi diagram. This is because the two are intrinsically linked: the adjacency graph of the Voronoi diagram is the Delaunay graph for the set of generator points! Put simply, this means we can build the Voronoi diagram (relying on scipy.spatial for the underlying computations), and then convert these polygons quickly into the Delaunay graph. Be careful, though; our algorithm, by default, will clip the voronoi diagram to the bounding box of the point pattern. This is controlled by the "clip" argument. ```{code-cell} -cells, generators = voronoi_frames(coordinates,clip='chull') +cells, generators = voronoi_frames(coordinates, clip="chull") ``` - With the voronoi polygons, we can construct the adjacency graph between them using "Rook" contiguity. This represents voronoi cells as being adjacent if they share an edge/face. This is an analogue to the "von Neuman" neighborhood, or the 4 cardinal neighbors in a regular grid. The name comes from the directions a Rook piece can move on a chessboard. @@ -244,9 +253,9 @@ positions = dict(zip(delaunay_graph.nodes, coordinates)) - Now, we can plot with a nice basemap using Contextily ```{code-cell} -figure,ax = plt.subplots(figsize=(15, 9)) -cells.plot(ax=ax,facecolor="lightblue", alpha=0.50, edgecolor="cornsilk", linewidth=2) -add_basemap(ax,crs='EPSG:4326') +figure, ax = plt.subplots(figsize=(15, 9)) +cells.plot(ax=ax, facecolor="lightblue", alpha=0.50, edgecolor="cornsilk", linewidth=2) +add_basemap(ax, crs="EPSG:4326") ax.axis("off") nx.draw( delaunay_graph, From e244ab75702645f672d398c7f2dff7113ff54367 Mon Sep 17 00:00:00 2001 From: Dan Schult Date: Fri, 1 Sep 2023 10:39:04 -0400 Subject: [PATCH 15/15] update toctree --- site/index.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/site/index.md b/site/index.md index 8998d327d..1bad56b99 100644 --- a/site/index.md +++ b/site/index.md @@ -36,8 +36,8 @@ maxdepth: 1 --- content/algorithms/index +content/algorithms/geospatial/index content/generators/index content/exploratory_notebooks/facebook_notebook -content/geospatial/index ```