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Rotate/Scale Polylines Based on Field in Attribute Table

MorganHarris

Does anyone know a way or have a script that allows you to rotate and/or scale a polyline based on a field in the attribute table. I know you can do this with the editor, but I have about 1200 different lines that need to be rotated and scaled and all to different angles and sizes (based on the angle) that will be defined by a field in the attribute table. I am working with 3D polylines and have an advanced license for ArcGIS 10.2.2.

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DanPatterson_Retired

Morgan... remember it is a demo script, demonstrating the principles, I will try to get something functional once I am done marking term projects. Be safe... Dan

MorganHarris

Dan Patterson‌, thank you for that script, but unfortunately I have been in the field for a little while and haven't been able to look at this and about to take about a month of leave. When I get back from leave I will play around with your method you posted here. Thanks for posting the demo and I will be sure to take a look!

DanPatterson_Retired

This is what I am thinking... it currently is a demonstration so if Xander, or anyone else wants to make it work with your shapefiles, then the principles might be useful.

For the demo, all it does is take a line, takes the first and last points and ignores the rest(ish). performs a translation to the origin, a rotation by a certain angle, and scales the x axis by a factor of 2x. The only real input parameters needed are provided in the documentation and you can see alternates after the if __name__ section of the script.
I can't get back to this for a day or 2, but this may keep you or others busy until you get your rotation data. bear in mind, this can be greatly expanded, but I wanted to demonstrate what an affine transformation was. I was as verbose as possible and didn't bury the code in one-liners since I teach and I hate unwrapping those for students so they can understand.

So have fun and give me some feedback via here or if it is more verbose...email etc.

Dan

'''
affine_line.py
Author: Dan.Patterson@carleton.ca
Purpose: a one-off script to rotate a line about its center
         ... aka ... a 2 point polyline
Requires:
  import numpy as np  either in the script or in 'rotate'
Namespace:
  line    2 point line
  angle   rotation angle in degrees
  x=2,y=1 scaling in the x and/or y directions
  XY_c, XY_t, XY_r, XY_s
     namespace representing center, translated, rotated, scaled pnts
'''
import numpy as np
np.set_printoptions(precision=2,threshold=20,edgeitems=3,suppress=True,linewidth=60)  # set default print options
def array_check(pnts):
  '''check to see if the pnts are expressed as an array'''
  bool = type(line).__module__ == np.__name__
  if not bool: #not an array
    pnts = np.array(pnts,dtype='float64')
  return pnts
def angle(pnts):
  '''angle between first and last points in array format'''
  pnts = array_check(pnts)
  dx,dy = pnts[0] - pnts[-1]
  deg = np.rad2deg(np.arctan2(dx,dy))
  return deg
def center(pnts):
  '''average x, y coordinate for points'''
  pnts = array_check(pnts)
  XY_c = np.mean(pnts,axis=0)
  return XY_c
def distance(pnts):
  '''returns the length/distance between the first and last points'''
  pnts = array_check(pnts)
  dx,dy = pnts[0] - pnts[-1]
  return np.hypot(dx,dy)
def translate(pnts, XY_c=None):
  '''translate a point(s)'''
  if XY_c == None:
    XY_c = center(pnts)
  XY_t = pnts - XY_c
  return XY_t
def rotate(pnts,angle):
  '''rotate points about the origin, given an angle in degrees,
    (-ve counterclockwise, +ve for clockwise'''
  angle = np.deg2rad(angle)
  s = np.sin(angle)
  c = np.cos(angle)
  aff_matrix = np.array([[c, -s],[s, c]])
  XY_r = np.dot(pnts, aff_matrix)
  return XY_r
def scale(pnts, x=1, y=1):
  '''returns the points scaled by x and y for the x and y direction'''
  XY_s = np.multiply(pnts, [x,y]) 
  return XY_s
 
if __name__ == '__main__':
  '''read the header...a verbose demonstration follows'''
  line = [[0.0,0.0],[1.0,1.0]]  # line as a sequence of points
  angle = -45.0                 # angle to rotate in degrees
  x = 2.0; y = 1                # scaling in x and y directions
  XY_c = center(line)           # center(line)
  XY_t = translate(line, XY_c)  # translate(line, center(line))
  XY_r = rotate(XY_t,angle)     # rotate(translate(line, center(line)), angle)
  XY_s = scale(XY_r,x=2, y=1)   # scale(rotate(translate(line, center(line)), angle), x=2, y=1)
  print '\n','-'*60
  print __doc__
  print('Input line (pnts):\n {}'.format(line))
  print('Center point:\n {}'.format(XY_c))
  print('Translate to center:\n {}'.format(XY_t))
  print('Rotate about center:\n {}'.format(XY_r))
  print('Scaled with x=2,y=1:\n {}'.format(XY_s))
  print('Rotate back:\n {}'.format( rotate(XY_s,-angle) ))
  print('Translate back:\n {}'.format( translate(rotate(XY_s,-angle),-XY_c) ))
  print '\n','-'*60

MorganHarris

Yea, I think it would be best if it rotated around the center point. I wish I had the rotation angles and scale changes that will need to happen to show you too, but unfortunately that is out of my hands! Thanks for taking such an interest in this question!

DanPatterson_Retired

Ahhh Ok, that does clarify the problem...I will revisit in light of the new information. The only question that remains is do you want the rotation to occur about the center point? the start point or the end point? One of the points needs to be fixed during the rotation process....think about it

MorganHarris

I just replied above to Xander Bakker‌ with some information that is relevant to your concerns. So you see in the attribute table that there is a span ID that covers that whole section. Those are the 'sections' that I am trying to rotate (the whole section represented by 1 span ID). The multiple points in there are because I had to densify the lines by 10 meters for another process. I have provided here a new dataset that has not been densified if you want to play around with it. But yes, I do realize they won'te be connected anymore and that is ok for what I am trying to do. Refer to my reply to Xander for a picture of my end goal.

Thanks!

All_transimission.zip

DanPatterson_Retired

Sorry I forgot to include an image for the first feature

DanPatterson_Retired

The data are indeed segments many points for some bizarre reason since they appear to form straight line segments.

I calculated angle relative to the x-axis using

Python interpreter

expression box:

polyline_angle(!Shape!)

''' input shape field: returns angle relative to x-axis using the first and last point
polyline_angle(!Shape!)    #enter into the expression box'''
import math
def polyline_angle(shape):
  radian = math.atan2((shape.lastPoint.Y - shape.firstPoint.Y),(shape.lastPoint.X - shape.firstPoint.X))
  degrees = math.degrees(radian)
  return degrees

I calculated the number of points using

Python

Expression:

count_pnts(!Shape!)

''' input shape field, return number of points in a feature
count_pnts(!Shape!)    #enter into the expression box'''
def count_pnts(shape):
  counter = 0
  num_parts = shape.partCount
  num_pnts = 0
  while counter < num_parts:
    part = shape.getPart(counter)
    pnt = part.next()
    while pnt:
      num_pnts += 1
      pnt = part.next()
      if not pnt:
        pnt = part.next()
    counter += 1
  return num_pnts

For example your feature FID 1, Span 000 consists of 13 points ( use the FeatureVerticesToPoints tool ) so this file for some reason has densified points along each segment. No clue how it was generated, but my guess is that the angles that I calculated apply to each of your little tiny segments and under no circumstances should you explode them. You can generalize the data within each segment ... you could try the Simplify Line tool to get rid of those excessive fiddly-bits. So in short...I would find out how those lines were generated and why before you get too far on the rotation stuff. If you want to rotate all the shapes by some amount then that is simple...if features have to be rotated by different amounts, then you do realize that they will in all likelihood not be connected any more.

Have fun

XanderBakker

Visually there are few lines, but each line consist of many features. I guess that is what you were referring to with "section". Angle is not provided yet... in what unit are the angles provided? Degrees? Are the angles geographic or arithmetic?

What would be the field to hold the "scale" value?

I'm still a little confused, if the sections (features) that make up a line are applied different scaling and rotation, the polyline (combination of the sections) will not make much sense (I think). What is the purpose of this process?

MorganHarris

Xander Bakker and Dan Patterson‌ I attached my "Power_Line_Spans" so that you can take a look. Right now, this is what I have, but it only represents 2d lines because my 3D data is not here yet. The attribute table for the 3D data will be the same though with each "section" of polyline containing a separate "span_ID". Thanks for taking a look! I also don't have the angle field in this data yet because I'm waiting on another part of my team to complete that task.

power_line_spans.zip

XanderBakker

Cool! A sabbatical and being coached by William Huber‌. I'm getting a little jealous here.

XanderBakker

If the feature has attributes about the rotation and translation, I suppose it doesn't really matter if it is a multipart or not, since the affine transformation will be applied to the entire feature. Right?

But yeah, it would be nice to post a small part of you data or create some comparable dummy data so we can have a look at it.

DanPatterson_Retired

Can you post a section of your attribute table. You say "every section of your polyline" suggests to me that your polyline consists of parts which are separated out and that each "section" is part of a bigger one. A polyline is usually represented by one record in the table and you would not see its sections unless the part was exploded into its individual parts...essentially making many polylines from the original and they may be "sections" in the sense that they originated from the parent polyline...but now they are all grown up and have move out on their own...

MorganHarris

This got over my head pretty quick! It does seem to me, Dan Patterson, looking through the spatial adjustments help it seems that method will change each section of my polyline the same. What I need to be able to do is iterate through basically each line (every section of line in my polyline has its own "span ID" in the attribute table) in my attribute table and rotate each "span ID" by a field labelled "angle" in my attribute table. I feel like this should be a pretty simple script just to rotate and then call in a field in the attribute table to be the value for rotation, but I haven't used code in about 2 years now and have only ever used it minimally.

Xander Bakker‌, I looked at that code you sent and am trying to decipher it. There are a lot of terms in there that I have never used so I'm not sure yet if that will work for me. In the mean time, maybe the way I re-worded the problem here will help spark up a simple solution! Thanks for helping!

DanPatterson_Retired

Xander Bakker‌ I got the impression that the various parameters were set within a table so that translation, rotation and/or scale could be applied to individual features and not the whole featureclass itself. If the affine were to be applied to the whole feature class, then yes, spatial adjustment would be easy.

On a side note, affine (translation to...rotation about...and scaling along the axis... of the origin) is what I used to determine the base parameters for a minimum area bounding ellipse (MABR) for feature data (ie point clusters, polylines and/or points). An affine transformation of an ellipse to the origin will yield a circle, hence, if the transformed feature isn't a pure circle, then you can solve for the ellipse parameters there using 3,4 or 5 point solutions to the ellipse...then reverse the transform and the resultant ellipse. A long story, but something William Huber‌ was coaching me on during my last sabbatical when I was working on my 'containers' toolbox and studying algorithms, programming and computational geometry.

XanderBakker

Hi Dan Patterson‌, doesn't the Spatial Adjustment tools transform the entire featureclass (all features) the same way? The help (ArcGIS Help (10.2, 10.2.1, and 10.2.2) ) may assist in programming the formula to apply for each polygon based on the attributes for that specific polygon. I just wonder when using rotation, will you rotate the feature around the center? And with 3D data things get a little more interesting...

Maybe this resource helps you:

geometry/transformations.py at hydro-devel · ros/geometry · GitHub

MorganHarris

I will look in to that and see if I can figure it out. Thanks for the tip!

DanPatterson_Retired

You want to use the Spatial Adjustment tools using an 'Affine' transformation. search the help using that keyword and it will link you to the concepts and the tools but there is no field based option so you will have to roll out your own using the Polyline class in arcpy

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