Develop Reference

CadQuery: Selecting an edge by index (Filleting specific edges)

I come from the engineering CAD world and I'm creating some designs in CadQuery. What I want to do is this (pseudocode):
edges = part.edges()
edges[n].fillet(r)
Or ideally have the ability to do something like this (though I can't find any methods for edge properties). Pseudocode:
edges = part.edges()
for edge in edges:
if edge.length() > x:
edge.fillet(a)
else:
edge.fillet(b)
This would be very useful when a design contains non-orthogonal faces. I understand that I can select edges with selectors, but I find them unnecessarily complicated and work best with orthogonal faces. FreeCAD lets you treat edges as a list.
I believe there might be a method to select the closest edge to a point, but I can't seem to track it down.
If someone can provide guidance that would be great -- thank you!
Bonus question: Is there a way to return coordinates of geometry as a list or vector? e.g.:
origin = cq.workplane.center().val
>> [x,y,z]
(or something like the above)

Take a look at this code, i hope this will be helpful.
import cadquery as cq
plane1 = cq.Workplane()
block = plane1.rect(10,12).extrude(10)
edges = block.edges("|Z")
filleted_block = edges.all()[0].fillet(0.5)
show(filleted_block)

For the posterity. To select multiple edges eg. for chamfering you can use newObject() on Workplane. The argument is a list of edges (they have to be cq.occ_impl.shapes.Edge instances, NOT cq.Workplane instances).
import cadquery as cq
model = cq.Workplane().box(10, 10, 5)
edges = model.edges()
# edges.all() returns worplanes, we have to get underlying geometry
selected = list(map(lambda x: x.objects[0], edges.all()))
model_with_chamfer = model.newObject(selected).chamfer(1)
To get edge length you can do something like this:
edge = model.edges().all()[0] # This select one 'random' edge
length = edge.objects[0].Length()
edge.Length() doesn't work since edge is Workplane instance, not geometry instance.
To get edges of certain length you can just create dict with edge geometry and length and filter it using builtin python's filter(). Here is a snippet of my implementation for chamfering short edges on topmost face:
top_edges = model.edges(">Z and #Z")
def get_length(edge):
try:
return edge.vals()[0].Length()
except Exception:
return 0.0
# Inside edges are shorter - filter only those
edge_len_list = list(map(
lambda x: (x.objects[0], get_length(x)),
top_edges.all()))
avg = mean([a for _, a in edge_len_list])
selected = filter(lambda x: x[1] < avg, edge_len_list)
selected = [e for e, _ in selected]
vertical_edges = model.edges("|Z").all()
selected.extend(vertical_edges)
model = model.newObject(selected)
model = model.chamfer(chamfer_size)

Compute reachability of elements in a list of tuples

I have a list of tuples like this.
a = [(1,2),(1,3),(1,4),(2,5),(6,5),(7,8)]
In this list 1 relates to 2 and then 2 relates to 5 and 5 relates to 6 therefore 1 relates to 6. Similarly I need to find the relations between other elements in tuples. I need a function that takes the input values and outputs as follows:
input = (1,6) #output = True
input = (5,3) #output = True
input = (2,8) #output = False
I do not have knowledge of itertools or map functions. Can they be used to solve these types of problems?
And for the sake of curiosity and interest where can I find these types of questions to solve and where are these types of problems encountered in real life situations?

This can be easily done by considering the tuples as edges in a graph. The question is then reduced to checking if there is a path between the two nodes.
There exists lots of nice libraries for this, see e.g. networkx
import networkx as nx
a = [(1,2),(1,3),(1,4),(2,5),(6,5),(7,8)]
G = nx.Graph(a)
nx.has_path(G, 1, 6) # True
nx.has_path(G, 5, 3) # True
nx.has_path(G, 2, 8) # False

This answer here nicely states your problem as a graph problem, where every time you need to run your algorithm you need to check for the existence of a path between your input vertices. The time complexity for every query then depends on the size, order, diameter, degree of the underlying graph.
However, if you intend to run this algorithm many times with the same array a, it may be worth doing some preprocessing on the input graph to find the connected components (Wikipedia : connected components) first. In that case you can get constant time for every query. Here is the code I suggest :
# NOTE : tested using python 3.6.1
# WARNING : no input sanitization
a = [(1,2),(1,3),(1,4),(2,5),(6,5),(7,8)]
n = 8 # order of the underlying graph
# prepare graph as lists of neighbors for every vertex, i.e. adjacency lists (extra unused vertex '0', just to match the value range of the problem)
graph = [[] for i in range(n+1)]
for edge in a:
graph[edge[0]].append(edge[1])
graph[edge[1]].append(edge[0])
print( "graph : " + str(graph) )
# list of unprocessed vertices : contains all of them at the beginning
unprocessed_vertices = {i for i in range(1,n+1)}
# subroutine to discover the connected component of a vertex
def build_component():
component = [] # current connected component
curr_vertices = {unprocessed_vertices.pop()} # locally unprocessed vertices, initialize with one of the globally unprocessed vertices
while len(curr_vertices) > 0:
curr_vertex = curr_vertices.pop() # vertex to be processed
# add unprocessed neighbours of current vertex to the set of vertices to process
for neighbour in graph[curr_vertex]:
if neighbour in unprocessed_vertices:
curr_vertices.add(neighbour)
unprocessed_vertices.remove(neighbour)
component.append(curr_vertex)
return component
# main algorithm : graph traversal on multiple connected components
components = []
while len(unprocessed_vertices) > 0:
components.append( build_component() )
print( "components : " + str(components) )
# assign a number to each component
component_numbers = [None] * (n+1)
curr_number = 1
for comp in components:
for vertex in comp:
component_numbers[vertex] = curr_number
curr_number += 1
print( "component_numbers : " + str(component_numbers) )
# main functionality
def is_connected( pair ):
return component_numbers[pair[0]] == component_numbers[pair[1]]
# run main functionnality on inputs : every call is executed in constant time now, regardless of the size of the graph
print( is_connected( (1,6) ) )
print( is_connected( (5,3) ) )
print( is_connected( (2,8) ) )
I don't really know about the most likely situations where this problem could be encountered, but I suppose it can have application is some clustering tasks, or maybe if you want to know if it is possible to go from one place to another. If the edges of the graph represent dependencies between modules, this problem would tell you if two parts depend on each other, so maybe some potential applications in compiling or the managment of large projects. The underlying problem is a "Connected component" problem which is among the problems we know polynomial algorithms for.
It is generally very useful to model these kind of problems with graphs as these objects have a very simple structure, and most of the time we can reduce the original problem to a well known problem on graphs.

Filling a closed curve in PyX (python) failing

I am clearly misunderstanding how closed curves and filling a closed curve works in PyX. I'm building a closed curve from four parts, but the filling fails depending on how I define one of the four curves. Below is a minimal working/failing example and the output. Why does the first definition of upArc work but the second one does not?
from pyx import *
c = canvas.canvas()
cL = canvas.canvas()
cR = canvas.canvas()
upArc = path.path(path.arc(0,3,1,180,0))
right = path.line(1,3,1,0)
downArc = path.path(path.arcn(0,0,1,0,180))
left = path.line(-1,0,-1,3)
p = upArc+right+downArc<<left
cR.fill(p,[color.rgb.blue])
cR.stroke(p)
upArc = path.path(path.arc(0,0,1,180,0)).transformed(trafo.translate(0,3))
right = path.line(1,3,1,0)
downArc = path.path(path.arcn(0,0,1,0,180))
left = path.line(-1,0,-1,3)
p = upArc+right+downArc<<left
cL.fill(p,[color.rgb.blue])
cL.stroke(p)
c.insert(cL,[trafo.translate(-2,0)])
c.insert(cR,[trafo.translate( 2,0)])
c.writePDFfile("minfail")
A picture of the results.

PyX uses the postscript path model, which can contain several subpaths within a path. (Think of using a path element moveto within a path.) When filling such paths, things like you observe happen. Note that the arc contains an implicit moveto at the beginning, which for filling is taken like a lineto, but not for stroking. This is why it makes a difference to use the add operator + and the join operator <<. Switching to join resolves your problem.
(You can use
print(p.normpath().normsubpaths)
to see, that you have several normsubpaths when adding the paths, even though the arclen does not alter, as the moveto commands from one normsubpath to the next are not part of the arc length.)

Using astropy.fits and numpy to apply coincidence corrections to SWIFT fits image

This question may be a little specialist, but hopefully someone might be able to help. I normally use IDL, but for developing a pipeline I'm looking to use python to improve running times.
My fits file handling setup is as follows:
import numpy as numpy
from astropy.io import fits
#Directory: /Users/UCL_Astronomy/Documents/UCL/PHASG199/M33_UVOT_sum/UVOTIMSUM/M33_sum_epoch1_um2_norm.img
with fits.open('...') as ima_norm_um2:
#Open UVOTIMSUM file once and close it after extracting the relevant values:
ima_norm_um2_hdr = ima_norm_um2[0].header
ima_norm_um2_data = ima_norm_um2[0].data
#Individual dimensions for number of x pixels and number of y pixels:
nxpix_um2_ext1 = ima_norm_um2_hdr['NAXIS1']
nypix_um2_ext1 = ima_norm_um2_hdr['NAXIS2']
#Compute the size of the images (you can also do this manually rather than calling these keywords from the header):
#Call the header and data from the UVOTIMSUM file with the relevant keyword extensions:
corrfact_um2_ext1 = numpy.zeros((ima_norm_um2_hdr['NAXIS2'], ima_norm_um2_hdr['NAXIS1']))
coincorr_um2_ext1 = numpy.zeros((ima_norm_um2_hdr['NAXIS2'], ima_norm_um2_hdr['NAXIS1']))
#Check that the dimensions are all the same:
print(corrfact_um2_ext1.shape)
print(coincorr_um2_ext1.shape)
print(ima_norm_um2_data.shape)
# Make a new image file to save the correction factors:
hdu_corrfact = fits.PrimaryHDU(corrfact_um2_ext1, header=ima_norm_um2_hdr)
fits.HDUList([hdu_corrfact]).writeto('.../M33_sum_epoch1_um2_corrfact.img')
# Make a new image file to save the corrected image to:
hdu_coincorr = fits.PrimaryHDU(coincorr_um2_ext1, header=ima_norm_um2_hdr)
fits.HDUList([hdu_coincorr]).writeto('.../M33_sum_epoch1_um2_coincorr.img')
I'm looking to then apply the following corrections:
# Define the variables from Poole et al. (2008) "Photometric calibration of the Swift ultraviolet/optical telescope":
alpha = 0.9842000
ft = 0.0110329
a1 = 0.0658568
a2 = -0.0907142
a3 = 0.0285951
a4 = 0.0308063
for i in range(nxpix_um2_ext1 - 1): #do begin
for j in range(nypix_um2_ext1 - 1): #do begin
if (numpy.less_equal(i, 4) | numpy.greater_equal(i, nxpix_um2_ext1-4) | numpy.less_equal(j, 4) | numpy.greater_equal(j, nxpix_um2_ext1-4)): #then begin
#UVM2
corrfact_um2_ext1[i,j] == 0
coincorr_um2_ext1[i,j] == 0
else:
xpixmin = i-4
xpixmax = i+4
ypixmin = j-4
ypixmax = j+4
#UVM2
ima_UVM2sum = total(ima_norm_um2[xpixmin:xpixmax,ypixmin:ypixmax])
xvec_UVM2 = ft*ima_UVM2sum
fxvec_UVM2 = 1 + (a1*xvec_UVM2) + (a2*xvec_UVM2*xvec_UVM2) + (a3*xvec_UVM2*xvec_UVM2*xvec_UVM2) + (a4*xvec_UVM2*xvec_UVM2*xvec_UVM2*xvec_UVM2)
Ctheory_UVM2 = - alog(1-(alpha*ima_UVM2sum*ft))/(alpha*ft)
corrfact_um2_ext1[i,j] = Ctheory_UVM2*(fxvec_UVM2/ima_UVM2sum)
coincorr_um2_ext1[i,j] = corrfact_um2_ext1[i,j]*ima_sk_um2[i,j]
The above snippet is where it is messing up, as I have a mixture of IDL syntax and python syntax. I'm just not sure how to convert certain aspects of IDL to python. For example, the ima_UVM2sum = total(ima_norm_um2[xpixmin:xpixmax,ypixmin:ypixmax]) I'm not quite sure how to handle.
I'm also missing the part where it will update the correction factor and coincidence correction image files, I would say. If anyone could have the patience to go over it with a fine tooth comb and suggest the neccessary changes I need that would be excellent.
The original normalised image can be downloaded here: Replace ... in above code with this file

One very important thing about numpy is that it does every mathematical or comparison function on an element-basis. So you probably don't need to loop through the arrays.
So maybe start where you convolve your image with a sum-filter. This can be done for 2D images by astropy.convolution.convolve or scipy.ndimage.filters.uniform_filter
I'm not sure what you want but I think you want a 9x9 sum-filter that would be realized by
from scipy.ndimage.filters import uniform_filter
ima_UVM2sum = uniform_filter(ima_norm_um2_data, size=9)
since you want to discard any pixel that are at the borders (4 pixel) you can simply slice them away:
ima_UVM2sum_valid = ima_UVM2sum[4:-4,4:-4]
This ignores the first and last 4 rows and the first and last 4 columns (last is realized by making the stop value negative)
now you want to calculate the corrections:
xvec_UVM2 = ft*ima_UVM2sum_valid
fxvec_UVM2 = 1 + (a1*xvec_UVM2) + (a2*xvec_UVM2**2) + (a3*xvec_UVM2**3) + (a4*xvec_UVM2**4)
Ctheory_UVM2 = - np.alog(1-(alpha*ima_UVM2sum_valid*ft))/(alpha*ft)
these are all arrays so you still do not need to loop.
But then you want to fill your two images. Be careful because the correction is smaller (we inored the first and last rows/columns) so you have to take the same region in the correction images:
corrfact_um2_ext1[4:-4,4:-4] = Ctheory_UVM2*(fxvec_UVM2/ima_UVM2sum_valid)
coincorr_um2_ext1[4:-4,4:-4] = corrfact_um2_ext1[4:-4,4:-4] *ima_sk_um2
still no loop just using numpys mathematical functions. This means it is much faster (MUCH FASTER!) and does the same.
Maybe I have forgotten some slicing and that would yield a Not broadcastable error if so please report back.
Just a note about your loop: Python's first axis is the second axis in FITS and the second axis is the first FITS axis. So if you need to loop over the axis bear that in mind so you don't end up with IndexErrors or unexpected results.

Count number of points in multipolygon shapefile using Python

I have a polygon shapefile of the U.S. made up of individual states as their attribute values. In addition, I have arrays storing latitude and longitude values of point events that I am also interested in. Essentially, I would like to 'spatial join' the points and polygons (or perform a check to see which polygon [i.e., state] each point is in), then sum the number of points in each state to find out which state has the most number of 'events'.
I believe the pseudocode would be something like:
Read in US.shp
Read in lat/lon points of events
Loop through each state in the shapefile and find number of points in each state
print 'Here is a list of the number of points in each state: '
Any libraries or syntax would be greatly appreciated.
Based on what I can tell, the OGR library is what I need, but I am having trouble with the syntax:
dsPolygons = ogr.Open('US.shp')
polygonsLayer = dsPolygons.GetLayer()
#Iterating all the polygons
polygonFeature = polygonsLayer.GetNextFeature()
k=0
while polygonFeature:
k = k + 1
print "processing " + polygonFeature.GetField("STATE") + "-" + str(k) + " of " + str(polygonsLayer.GetFeatureCount())
geometry = polygonFeature.GetGeometryRef()
#Read in some points?
geomcol = ogr.Geometry(ogr.wkbGeometryCollection)
point = ogr.Geometry(ogr.wkbPoint)
point.AddPoint(-122.33,47.09)
point.AddPoint(-110.11,33.33)
#geomcol.AddGeometry(point)
print point.ExportToWkt()
print point
numCounts=0.0
while pointFeature:
if pointFeature.GetGeometryRef().Within(geometry):
numCounts = numCounts + 1
pointFeature = pointsLayer.GetNextFeature()
polygonFeature = polygonsLayer.GetNextFeature()
#Loop through to see how many events in each state

I like the question. I doubt I can give you the best answer, and definitely can't help with OGR, but FWIW I'll tell you what I'm doing right now.
I use GeoPandas, a geospatial extension of pandas. I recommend it — it's high-level and does a lot, giving you everything in Shapely and fiona for free. It is in active development by twitter/#kajord and others.
Here's a version of my working code. It assumes you have everything in shapefiles, but it's easy to generate a geopandas.GeoDataFrame from a list.
import geopandas as gpd
# Read the data.
polygons = gpd.GeoDataFrame.from_file('polygons.shp')
points = gpd.GeoDataFrame.from_file('points.shp')
# Make a copy because I'm going to drop points as I
# assign them to polys, to speed up subsequent search.
pts = points.copy()
# We're going to keep a list of how many points we find.
pts_in_polys = []
# Loop over polygons with index i.
for i, poly in polygons.iterrows():
# Keep a list of points in this poly
pts_in_this_poly = []
# Now loop over all points with index j.
for j, pt in pts.iterrows():
if poly.geometry.contains(pt.geometry):
# Then it's a hit! Add it to the list,
# and drop it so we have less hunting.
pts_in_this_poly.append(pt.geometry)
pts = pts.drop([j])
# We could do all sorts, like grab a property of the
# points, but let's just append the number of them.
pts_in_polys.append(len(pts_in_this_poly))
# Add the number of points for each poly to the dataframe.
polygons['number of points'] = gpd.GeoSeries(pts_in_polys)
The developer tells me that spatial joins are 'new in the dev version', so if you feel like poking around in there, I'd love to hear how that goes! The main problem with my code is that it's slow.

import geopandas as gpd
# Read the data.
polygons = gpd.GeoDataFrame.from_file('polygons.shp')
points = gpd.GeoDataFrame.from_file('points.shp')
# Spatial Joins
pointsInPolygon = gpd.sjoin(points, polygons, how="inner", op='intersects')
# Add a field with 1 as a constant value
pointsInPolygon['const']=1
# Group according to the column by which you want to aggregate data
pointsInPolygon.groupby(['statename']).sum()
**The column ['const'] will give you the count number of points in your multipolygons.**
#If you want to see others columns as well, just type something like this :
pointsInPolygon = pointsInPolygon.groupby('statename').agg({'columnA':'first', 'columnB':'first', 'const':'sum'}).reset_index()
[1]: https://geopandas.org/docs/user_guide/mergingdata.html#spatial-joins
[2]: https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.groupby.html