From e839e741020602bdb2464ea6aeeb2d0953135776 Mon Sep 17 00:00:00 2001 From: Peter Corke Date: Tue, 13 Oct 2026 08:54:09 +1000 Subject: [PATCH 1/6] docs: README shows the London route map A subsection after the Queensland example with the map of the road network and the routes there and back between Buckingham Palace and Tower Bridge, drawn by the london notebook, and a link to it. The figure is in docs/figs. Co-Authored-By: Claude Sonnet 5.5 --- README.md | 8 ++++++++ docs/figs/london_route.png | Bin 0 -> 258588 bytes 2 files changed, 8 insertions(+) create mode 100644 docs/figs/london_route.png diff --git a/README.md b/README.md index 5cd4794e..1c534546 100644 --- a/README.md +++ b/README.md @@ -71,6 +71,14 @@ g.plot(block=False) # plot it g.highlight_path(p) # overlay the path ``` +### A bigger example: routing through central London + +![route through central London](https://github.com/petercorke/pgraph-python/raw/main/docs/figs/london_route.png) + +A directed graph of the road network of central London, taken from [OpenStreetMap](https://www.openstreetmap.org/copyright), and the shortest drive between Buckingham Palace and Tower Bridge, there (solid) and back (dashed). The two routes differ in length, 5,515 m and 5,948 m, because of the one-way streets. The notebook [`examples/london.ipynb`](https://github.com/petercorke/pgraph-python/blob/main/examples/london.ipynb) builds the graph from the map data, keeps the part of it that can be driven around in, and plans with A*. + +Map data © OpenStreetMap contributors, available under the Open Database License. + ### Properties and methods of the graph Graphs belong to the class `UGraph` or `DGraph` for undirected or directed graphs respectively. 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z@APfDJCyO3UQw0gbjCcj=s*vsUbX&Fg#!k(>NoCl3HD6+4yf3^14}q zNVQ3Dq_f~AL(kcPYh;WO>ddV&rqb@x+6P=Y8xbd()Bbznf3SCQ6jK^vBGpNSEG z`L35$VdFQpB0DsBHMO(0Ad!dx_!I}lU3tb0ZgBXKe@Z~dXE@@G#m*!4D|zc@?AVH- zUc~~w>aCsz2{uS5zi(8SQVbE4eVDmC$$MpLyw@(LkZDj_{viR5(l?}HUe@kh!g8)$ zpKE*fG)o4CO0W-kyc%OfiO_8+mrqE)Ygzr!AS@11!BhQ?1&|E(waaj4co)6l27EQX z&$snQGyKG07GjWR9%S3|;a$nlLoWOI(+=qqg@HF(quYLtTG8o_0`KROmH=Ox@0rLN6M@RnHzXTEgE-%b{wzyy69QFK7VvLYq Octc6;YW81d_x}fpk$l|% literal 0 HcmV?d00001 From d2c0ebc6ad47a2cf90ccc3f60124548676e638ae Mon Sep 17 00:00:00 2001 From: Peter Corke Date: Tue, 13 Oct 2026 10:06:06 +1000 Subject: [PATCH 2/6] docs: fix the name of the package in the history paragraph of intro Co-Authored-By: Claude Sonnet 5.5 --- docs/source/intro.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/source/intro.rst b/docs/source/intro.rst index 4b9aec8e..71da1c45 100644 --- a/docs/source/intro.rst +++ b/docs/source/intro.rst @@ -300,5 +300,5 @@ Alternatively, we can make the decision at runtime by using the ``directed`` arg History -------- -``pgaph-python`` is based on ``PGraph.m`` which is part of the +``pgraph-python`` is based on ``PGraph.m`` which is part of the earlier `Spatial Math Toolbox for MATLAB `_. From a41747951898fef38846ccb11f0e6449491e7e8b Mon Sep 17 00:00:00 2001 From: Peter Corke Date: Tue, 13 Oct 2026 10:06:06 +1000 Subject: [PATCH 3/6] docs: README review, performance tables Installation; the Queensland example reads the same data file as the notebook it links to and gives the same path; component(c) takes a component number, and v.label is the component of a vertex; path_UCS, the geometry methods, metric, copy, export and validate are listed; vertex_class and edge_class in the subclassing section; headings that make an outline; the two benchmark tables, with the description of the runs in one paragraph above them. Co-Authored-By: Claude Sonnet 5.5 --- README.md | 136 +++++++++++++++++++++++++++++++++++++++++------------- 1 file changed, 105 insertions(+), 31 deletions(-) diff --git a/README.md b/README.md index 1c534546..45623208 100644 --- a/README.md +++ b/README.md @@ -44,42 +44,57 @@ distance metric (Euclidean, Manhattan, SE(2), or your own), the vertex nearest a point can be found, `A*` uses the metric as its heuristic, and the graph can be plotted, or exported with its layout preserved. -![road network](https://github.com/petercorke/pgraph-python/raw/main/examples/roads.png) +## Installation ``` -from pgraph import * +pip install pgraph-python +``` + +This needs Python 3.9 or later. The dependencies, NumPy, Matplotlib and Spatial Maths, are installed with it. + +## Examples + +### A small example: routing through towns in Queensland + +![road network](https://github.com/petercorke/pgraph-python/raw/main/examples/roads.png) + +```python +from pgraph import UGraph import json -# load places and routes -with open('places.json', 'r') as f: - places = json.loads(f.read()) -with open('routes.json', 'r') as f: - routes = json.loads(f.read()) +# load the places and routes +with open('queensland.json', 'r') as f: + data = json.load(f) # build the graph g = UGraph() - -for name, info in places.items(): - g.add_vertex(name=name, coord=info["utm"]) - -for route in routes: - g.add_edge(route[0], route[1], cost=route[2]) +for name, info in data['places'].items(): + g.add_vertex(name=name, coord=info['utm']) +for route in data['routes']: + g.add_edge(route['start'], route['end'], cost=route['distance']) # plan a path from Hughenden to Brisbane p, length, _ = g.path_Astar('Hughenden', 'Brisbane') -g.plot(block=False) # plot it +g.plot(block=False) # plot it g.highlight_path(p) # overlay the path ``` +The data file and the complete example are in the notebook [`examples/roads.ipynb`](https://github.com/petercorke/pgraph-python/blob/main/examples/roads.ipynb). + ### A bigger example: routing through central London ![route through central London](https://github.com/petercorke/pgraph-python/raw/main/docs/figs/london_route.png) -A directed graph of the road network of central London, taken from [OpenStreetMap](https://www.openstreetmap.org/copyright), and the shortest drive between Buckingham Palace and Tower Bridge, there (solid) and back (dashed). The two routes differ in length, 5,515 m and 5,948 m, because of the one-way streets. The notebook [`examples/london.ipynb`](https://github.com/petercorke/pgraph-python/blob/main/examples/london.ipynb) builds the graph from the map data, keeps the part of it that can be driven around in, and plans with A*. +A directed graph of the road network of central London, taken from [OpenStreetMap](https://www.openstreetmap.org/copyright), and the shortest drive between Buckingham Palace and Tower Bridge, there (solid) and back (dashed). The two routes differ in length, 5,515 m and 5,948 m, because of the one-way streets. The notebook [`examples/london.ipynb`](https://github.com/petercorke/pgraph-python/blob/main/examples/london.ipynb) builds the graph from the map data, keeps the part of it that can be driven around in, and plans with `A*`. -Map data © OpenStreetMap contributors, available under the Open Database License. +Map data © OpenStreetMap contributors, available under the [Open Database License](https://www.openstreetmap.org/copyright). + +## Using pgraph + +Full details are given in the [online documentation](https://petercorke.github.io/pgraph-python). ### Properties and methods of the graph + Graphs belong to the class `UGraph` or `DGraph` for undirected or directed graphs respectively. The graph is essentially a container for the vertices. - `g.add_vertex()` add a vertex @@ -92,23 +107,39 @@ Graphs belong to the class `UGraph` or `DGraph` for undirected or directed graph - `g.edges()` all edges in the graph - `g.plot()` plots the vertices and edges - `g.nc` the number of graph components, 1 if fully connected -- `g.component(v)` the component that vertex `v` belongs to +- `g.component(c)` the vertices in component number `c`, numbered from 0 - `g.samecomponent(v1, v2)` predicate for vertices belonging to the same component *** -- `g.path_BFS()` breadth-first search -- `g.path_Astar()` A* search +- `g.path_BFS()` breadth-first search, the path with the fewest edges +- `g.path_UCS()` uniform-cost search, the cheapest path +- `g.path_Astar()` A* search, the cheapest path using a heuristic + + *** +- `g.closest(point)` the vertex nearest to a point +- `g.near(point, radius)` the vertices within a distance of a point +- `g.within(box)` the vertices inside a box +- `g.subgraph(vertices)` the part of the graph that those vertices induce, as a new graph +- `g.coordinates()` the vertex coordinates as a matrix, a column per vertex +- `g.build_kdtree()` an optional spatial index (needs scipy) that makes `closest` and `near` faster on a large graph +- `g.metric` the distance metric: `"L2"` (the default), `"L1"`, `"SE2"`, `SE2Metric(weight)` that weights the angle of a pose, or a function of your own *** - `g.adjacency()` adjacency matrix - `g.laplacian()` Laplacian matrix - `g.incidence()` incidence matrix + *** +- `g.copy()` a deep copy; a graph can also be pickled +- `g.export()` write the graph as GraphViz DOT, Mermaid, GraphML, ELK, or an image (which needs GraphViz) +- `g.validate()` check that the graph's records agree with each other + ### Properties and methods of a vertex Vertices are instances of the class `Vertex`, for both undirected and directed graphs. - `v.coord` the coordinate vector for embedded graph (optional) - `v.name` the name of the vertex (optional) +- `v.label` the number of the component that the vertex belongs to - `v.adjacent()` is a list of the adjacent vertices (`neighbours()` and `neighbors()` are the same) Vertices can be named and referenced by name. @@ -121,12 +152,12 @@ Each edge references a pair of vertices, the graph lists all of its edges in `g. - `e.next(v)` vertex on edge `e` that is not `v` - `e.v1`, `e.v2` the two vertices that define the edge `e` -## Modifying a graph +### Modifying a graph - `g.remove_vertex(v)` or `v.remove()` remove vertex `v` - `g.remove_edge(e)` or `e.remove()` remove edge `e` -## Subclassing pgraph classes +### Subclassing `pgraph` classes Consider a user class `Foo` that we would like to connect using a graph _overlay_, i.e. instances of `Foo` become vertices in a graph. @@ -134,12 +165,16 @@ instances of `Foo` become vertices in a graph. - Have it subclass `Vertex` - Then place instances of `Foo` into the graph using `add_vertex` and create edges as required -``` +```python +from pgraph import UGraph, Vertex + class Foo(Vertex): - # foo stuff goes here - -f1 = Foo(...) -f2 = Foo(...) + # foo stuff goes here + def say_hi(self): + print(f"hi from {self.name}") + +f1 = Foo(name="f1") +f2 = Foo(name="f2") g = UGraph() # create a new undirected graph g.add_vertex(f1) @@ -150,14 +185,53 @@ for f in f1.adjacent(): f.say_hi() # say hi to the neighbours ``` +Or tell the graph which classes to make, with `UGraph(vertex_class=Foo, edge_class=Bar)`, and `g.add_vertex()` and `g.add_edge()` create instances of them, so they never need to be constructed by hand. + +## Performance + +Timings of the key operations on random geometric graphs, each vertex joined to its 4 nearest neighbours, of 100, 1,000 and 10,000 vertices, measured with [`examples/benchmark.py`](https://github.com/petercorke/pgraph-python/blob/main/examples/benchmark.py) on an Apple M4 with Python 3.12 and NumPy 2.5. The path times are the median of 10 random start and goal pairs. The last column is the exponent *b* in time ∝ N*b* between the smallest and the largest graph for the quantity shown, so 0 is constant, 1 is linear and 2 is quadratic. The adjacency, Laplacian and incidence matrices are dense, so they are only formed up to 1,000 vertices. + +### Undirected graphs + +| Operation | per | N=100 | N=1,000 | N=10,000 | growth exponent | +| :----------------------------------- | :---------- | -----: | ------: | -------: | --------------: | +| add a vertex | µs / vertex | 2.41 | 2.45 | 2.35 | 0.0 | +| add an edge (cost from the metric) | µs / edge | 1.69 | 1.76 | 1.77 | 0.0 | +| copy the graph | ms | 0.847 | 8.69 | 142 | 1.1 | +| pickle and unpickle the graph | ms | 0.488 | 4.99 | 109 | 1.2 | +| number of components, after a change | ms | 0.0824 | 0.83 | 10.6 | 1.1 | +| number of components, unchanged | µs | 0.083 | 0.083 | 0.083 | 0.0 | +| remove a vertex | µs | 6.29 | 12.5 | 55.8 | 0.5 | +| closest vertex to a point | µs / query | 71.2 | 724 | 6,994 | 1.0 | +| adjacency matrix | ms | 0.107 | 1.7 | – | 1.2 | +| Laplacian matrix | ms | 0.12 | 3.69 | – | 1.5 | +| incidence matrix | ms | 0.0558 | 1.63 | – | 1.5 | +| path, breadth-first | ms / query | 0.0375 | 0.319 | 4.31 | 1.0 | +| path, uniform cost | ms / query | 0.0841 | 0.82 | 9.24 | 1.0 | +| path, A* | ms / query | 0.0517 | 0.301 | 2.42 | 0.8 | + +### Directed graphs + +| Operation | per | N=100 | N=1,000 | N=10,000 | growth exponent | +| :----------------------------------- | :---------- | -----: | ------: | -------: | --------------: | +| add a vertex | µs / vertex | 2.36 | 2.48 | 2.4 | 0.0 | +| add an edge (cost from the metric) | µs / edge | 1.66 | 1.72 | 1.83 | 0.0 | +| copy the graph | ms | 1.12 | 12 | 200 | 1.1 | +| pickle and unpickle the graph | ms | 0.583 | 6.44 | 151 | 1.2 | +| number of components, after a change | ms | 0.124 | 1.26 | 17 | 1.1 | +| number of components, unchanged | µs | 0.083 | 0.083 | 0.083 | 0.0 | +| remove a vertex | µs | 8.42 | 16.6 | 69.2 | 0.5 | +| closest vertex to a point | µs / query | 70.6 | 692 | 6,909 | 1.0 | +| adjacency matrix | ms | 0.0822 | 1.24 | – | 1.2 | +| Laplacian matrix | ms | 0.0964 | 2.67 | – | 1.4 | +| incidence matrix | ms | 0.0889 | 2.34 | – | 1.4 | +| path, breadth-first | ms / query | 0.0232 | 0.403 | 3.09 | 1.1 | +| path, uniform cost | ms / query | 0.055 | 0.931 | 6.94 | 1.1 | +| path, A* | ms / query | 0.0479 | 0.745 | 3.67 | 0.9 | + ## MATLAB version This is a re-engineered version of [PGraph.m](https://github.com/petercorke/spatialmath-matlab/blob/main/PGraph.m) which ships as part of the [Spatial Math Toolbox for MATLAB](https://github.com/petercorke/spatialmath-matlab). This class is used to support bundle adjustment, pose-graph SLAM and various planners such as PRM, RRT and Lattice. The Python version was designed from the start to work with directed and undirected graphs, whereas directed graphs were a late addition to the MATLAB version. Semantics are similar but not identical. In particular the use of subclassing rather than references to _user data_ is encouraged. - - - - - From 20d5a0bc0cfc164358f776f93a8cfcca91a1b185 Mon Sep 17 00:00:00 2001 From: Peter Corke Date: Tue, 13 Oct 2026 10:20:48 +1000 Subject: [PATCH 4/6] docs: the Queensland figure shows the shortest route, alt text for the figures The figure was drawn from places.json, whose coordinates are in metres while the road distances are in km, so the A* heuristic was far too large and the route it found, 1,759 km via Rockhampton, was not the shortest. The notebook and the snippet use queensland.json, in km: 1,659 km via Roma. The figure is drawn from that, with the axes in km. The README figures have a description as their alternative text. Co-Authored-By: Claude Sonnet 5.5 --- README.md | 4 ++-- examples/roads.png | Bin 200094 -> 218898 bytes 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/README.md b/README.md index 45623208..fa3a0784 100644 --- a/README.md +++ b/README.md @@ -56,7 +56,7 @@ This needs Python 3.9 or later. The dependencies, NumPy, Matplotlib and Spatial ### A small example: routing through towns in Queensland -![road network](https://github.com/petercorke/pgraph-python/raw/main/examples/roads.png) +![Map of 20 towns in Queensland as blue circles joined by roads, with the shortest route from Hughenden to Brisbane, 1,659 km via Barcaldine, Blackall, Charleville and Roma, highlighted in red](https://github.com/petercorke/pgraph-python/raw/main/examples/roads.png) ```python from pgraph import UGraph @@ -83,7 +83,7 @@ The data file and the complete example are in the notebook [`examples/roads.ipyn ### A bigger example: routing through central London -![route through central London](https://github.com/petercorke/pgraph-python/raw/main/docs/figs/london_route.png) +![Map of central London as a network of grey streets, with two routes between Buckingham Palace and Tower Bridge: a solid blue route of 5,515 m via Big Ben, and a dashed orange route of 5,948 m back through the north of the area, with five landmarks labelled](https://github.com/petercorke/pgraph-python/raw/main/docs/figs/london_route.png) A directed graph of the road network of central London, taken from [OpenStreetMap](https://www.openstreetmap.org/copyright), and the shortest drive between Buckingham Palace and Tower Bridge, there (solid) and back (dashed). The two routes differ in length, 5,515 m and 5,948 m, because of the one-way streets. 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From fde0e7d0c78641f376415b74f3056f8b00c2d1c3 Mon Sep 17 00:00:00 2001 From: Peter Corke Date: Tue, 13 Oct 2026 10:23:12 +1000 Subject: [PATCH 5/6] docs: README benchmark tables from current main Measured on main with the faster planners, the components union-find, and the vertex constructor that does not pay for the coordinate hook: a vertex is 1.5 us, the components after a change are 3.9 ms (undirected) and 5.9 ms (directed) at 10,000 vertices. Co-Authored-By: Claude Sonnet 5.5 --- README.md | 52 ++++++++++++++++++++++++++-------------------------- 1 file changed, 26 insertions(+), 26 deletions(-) diff --git a/README.md b/README.md index fa3a0784..447fe23d 100644 --- a/README.md +++ b/README.md @@ -195,39 +195,39 @@ Timings of the key operations on random geometric graphs, each vertex joined to | Operation | per | N=100 | N=1,000 | N=10,000 | growth exponent | | :----------------------------------- | :---------- | -----: | ------: | -------: | --------------: | -| add a vertex | µs / vertex | 2.41 | 2.45 | 2.35 | 0.0 | -| add an edge (cost from the metric) | µs / edge | 1.69 | 1.76 | 1.77 | 0.0 | -| copy the graph | ms | 0.847 | 8.69 | 142 | 1.1 | -| pickle and unpickle the graph | ms | 0.488 | 4.99 | 109 | 1.2 | -| number of components, after a change | ms | 0.0824 | 0.83 | 10.6 | 1.1 | +| add a vertex | µs / vertex | 1.52 | 1.65 | 1.59 | 0.0 | +| add an edge (cost from the metric) | µs / edge | 1.55 | 1.58 | 1.85 | 0.0 | +| copy the graph | ms | 0.823 | 8.17 | 151 | 1.1 | +| pickle and unpickle the graph | ms | 0.456 | 4.76 | 113 | 1.2 | +| number of components, after a change | ms | 0.0292 | 0.319 | 3.86 | 1.1 | | number of components, unchanged | µs | 0.083 | 0.083 | 0.083 | 0.0 | -| remove a vertex | µs | 6.29 | 12.5 | 55.8 | 0.5 | -| closest vertex to a point | µs / query | 71.2 | 724 | 6,994 | 1.0 | -| adjacency matrix | ms | 0.107 | 1.7 | – | 1.2 | -| Laplacian matrix | ms | 0.12 | 3.69 | – | 1.5 | -| incidence matrix | ms | 0.0558 | 1.63 | – | 1.5 | -| path, breadth-first | ms / query | 0.0375 | 0.319 | 4.31 | 1.0 | -| path, uniform cost | ms / query | 0.0841 | 0.82 | 9.24 | 1.0 | -| path, A* | ms / query | 0.0517 | 0.301 | 2.42 | 0.8 | +| remove a vertex | µs | 6.19 | 11.6 | 56.5 | 0.5 | +| closest vertex to a point | µs / query | 69.9 | 708 | 7,056 | 1.0 | +| adjacency matrix | ms | 0.107 | 1.46 | – | 1.1 | +| Laplacian matrix | ms | 0.121 | 2.76 | – | 1.4 | +| incidence matrix | ms | 0.0565 | 1.44 | – | 1.4 | +| path, breadth-first | ms / query | 0.038 | 0.317 | 5.4 | 1.1 | +| path, uniform cost | ms / query | 0.0822 | 0.806 | 11.7 | 1.1 | +| path, A* | ms / query | 0.0498 | 0.295 | 2.48 | 0.8 | ### Directed graphs | Operation | per | N=100 | N=1,000 | N=10,000 | growth exponent | | :----------------------------------- | :---------- | -----: | ------: | -------: | --------------: | -| add a vertex | µs / vertex | 2.36 | 2.48 | 2.4 | 0.0 | -| add an edge (cost from the metric) | µs / edge | 1.66 | 1.72 | 1.83 | 0.0 | -| copy the graph | ms | 1.12 | 12 | 200 | 1.1 | -| pickle and unpickle the graph | ms | 0.583 | 6.44 | 151 | 1.2 | -| number of components, after a change | ms | 0.124 | 1.26 | 17 | 1.1 | +| add a vertex | µs / vertex | 1.53 | 1.58 | 1.59 | 0.0 | +| add an edge (cost from the metric) | µs / edge | 1.56 | 1.64 | 1.84 | 0.0 | +| copy the graph | ms | 1.12 | 12.1 | 227 | 1.2 | +| pickle and unpickle the graph | ms | 0.573 | 6.58 | 151 | 1.2 | +| number of components, after a change | ms | 0.0405 | 0.485 | 5.87 | 1.1 | | number of components, unchanged | µs | 0.083 | 0.083 | 0.083 | 0.0 | -| remove a vertex | µs | 8.42 | 16.6 | 69.2 | 0.5 | -| closest vertex to a point | µs / query | 70.6 | 692 | 6,909 | 1.0 | -| adjacency matrix | ms | 0.0822 | 1.24 | – | 1.2 | -| Laplacian matrix | ms | 0.0964 | 2.67 | – | 1.4 | -| incidence matrix | ms | 0.0889 | 2.34 | – | 1.4 | -| path, breadth-first | ms / query | 0.0232 | 0.403 | 3.09 | 1.1 | -| path, uniform cost | ms / query | 0.055 | 0.931 | 6.94 | 1.1 | -| path, A* | ms / query | 0.0479 | 0.745 | 3.67 | 0.9 | +| remove a vertex | µs | 8.04 | 15.7 | 70 | 0.5 | +| closest vertex to a point | µs / query | 70.2 | 711 | 6,921 | 1.0 | +| adjacency matrix | ms | 0.0815 | 1.21 | – | 1.2 | +| Laplacian matrix | ms | 0.0928 | 2.64 | – | 1.5 | +| incidence matrix | ms | 0.0871 | 2.41 | – | 1.4 | +| path, breadth-first | ms / query | 0.0225 | 0.386 | 3.87 | 1.1 | +| path, uniform cost | ms / query | 0.0536 | 0.936 | 8.06 | 1.1 | +| path, A* | ms / query | 0.046 | 0.721 | 3.68 | 1.0 | ## MATLAB version From d5551703ff2eea8c8dcfe043d90c440b33959ba9 Mon Sep 17 00:00:00 2001 From: Peter Corke Date: Tue, 13 Oct 2026 10:24:05 +1000 Subject: [PATCH 6/6] docs: README, performance sentence and a History section Co-Authored-By: Claude Sonnet 5.5 --- README.md | 11 +++++------ 1 file changed, 5 insertions(+), 6 deletions(-) diff --git a/README.md b/README.md index 447fe23d..e9921cb2 100644 --- a/README.md +++ b/README.md @@ -36,7 +36,7 @@ This pure-Python package provides classes for directed and undirected graphs: vertices connected by edges, with edge costs and path planning. Self-loops and -parallel edges are permitted. +parallel edges are permitted. Performance is good enough to support bundle adjustment, pose-graph SLAM and path planning over thousands of vertices. Vertices can optionally be *embedded*: given a coordinate in a space of any dimension. Edge costs are then computed from the vertex positions using a @@ -85,7 +85,7 @@ The data file and the complete example are in the notebook [`examples/roads.ipyn ![Map of central London as a network of grey streets, with two routes between Buckingham Palace and Tower Bridge: a solid blue route of 5,515 m via Big Ben, and a dashed orange route of 5,948 m back through the north of the area, with five landmarks labelled](https://github.com/petercorke/pgraph-python/raw/main/docs/figs/london_route.png) -A directed graph of the road network of central London, taken from [OpenStreetMap](https://www.openstreetmap.org/copyright), and the shortest drive between Buckingham Palace and Tower Bridge, there (solid) and back (dashed). The two routes differ in length, 5,515 m and 5,948 m, because of the one-way streets. The notebook [`examples/london.ipynb`](https://github.com/petercorke/pgraph-python/blob/main/examples/london.ipynb) builds the graph from the map data, keeps the part of it that can be driven around in, and plans with `A*`. +A directed graph of the road network of central London, taken from [OpenStreetMap](https://www.openstreetmap.org/copyright), and the shortest drive between Buckingham Palace and Tower Bridge, there (solid) and back (dashed). The two routes differ in length, 5,515 m and 5,948 m, because of the one-way streets. The notebook [`examples/london.ipynb`](https://github.com/petercorke/pgraph-python/blob/main/examples/london.ipynb) builds the graph from the map data, keeps the part of it that can be driven around in, and plans with `A*`. This graph has over 4,000 vertices. Map data © OpenStreetMap contributors, available under the [Open Database License](https://www.openstreetmap.org/copyright). @@ -229,9 +229,8 @@ Timings of the key operations on random geometric graphs, each vertex joined to | path, uniform cost | ms / query | 0.0536 | 0.936 | 8.06 | 1.1 | | path, A* | ms / query | 0.046 | 0.721 | 3.68 | 1.0 | -## MATLAB version +## History -This is a re-engineered version of [PGraph.m](https://github.com/petercorke/spatialmath-matlab/blob/main/PGraph.m) which ships as part of the [Spatial Math Toolbox for MATLAB](https://github.com/petercorke/spatialmath-matlab). This class is used to support bundle adjustment, pose-graph SLAM and various planners such as PRM, RRT and Lattice. +This is a re-engineered version of [PGraph.m](https://github.com/petercorke/spatialmath-matlab/blob/main/PGraph.m) which ships as part of the [Spatial Math Toolbox for MATLAB](https://github.com/petercorke/spatialmath-matlab). That class was used to support bundle adjustment, pose-graph SLAM and various planners such as PRM, RRT and Lattice. -The Python version was designed from the start to work with directed and undirected graphs, whereas directed graphs were a late addition to the MATLAB version. Semantics are similar but not identical. In particular the use of subclassing rather than references to -_user data_ is encouraged. +The Python version was designed from the start to work with directed and undirected graphs, whereas directed graphs were a late addition to the MATLAB version. Semantics are similar but not identical. In particular the use of subclassing rather than references to _user data_ is encouraged.