Create a line perpendicular to an existing line in ArcGIS

Question

For an existing set of line features, I would like to generate a perpendicular line, of say 1km, at the midpoint of each existing line feature in ArcGIS.

I imagine that The methodology would be to:

1. create a tangent line at the midpoint of each existing line feature
2. calculate the angle of the tangent line
3. based on the angle of the tangent line, calculate the location of the endpoint of the new line
4. create the new line with the calculated endpoint of the new line and the existing midpoint of the old line

Let's assume that we are in a UTM projection and can use coordinates to calculate distance and direction.

How would I do this with ArcGIS tools or with ArcPy?

Answer 1

Based on @Felix's answer, here's an approach that uses built-in methods on geometry objects. Supported on 10.3+.

from math import atan2, pi

# epsilon
e = 1e-10

def tangentLine(line, dist):
    '''creates a tangent line of length dist at line midpoint
    line - arcpy.Polyline() object
    dist - distance in meters
    '''

    midpoint = line.positionAlongLine(0.5, True)

    # get points immediately before and after midpoint
    before = line.positionAlongLine(0.5-e, True)
    after = line.positionAlongLine(0.5+e, True)

    dX = after.firstPoint.X - before.firstPoint.X
    dY = after.firstPoint.Y - before.firstPoint.Y

    # angle of the midpoint segment
    angle = atan2(dX, dY) * 180 / pi
    newpoint = midpoint.pointFromAngleAndDistance(angle + 90, dist)

    return arcpy.Polyline(arcpy.Array((midpoint.firstPoint, newpoint.firstPoint)))

You could use cursors to read the line geometries and write them to a new feature class. Or, for a "great" 1 liner:

arcpy.CopyFeatures_management([tangentLine(line, 1000)
    for line in arcpy.CopyFeatures_management("myFC", arcpy.Geometry())],
    "in_memory/tangentLines")

The +90 will place the tangent line on the right side of the input line (based on digitized direction).

Answer 2

• Create midpoints, using one of multiple possible techniques.
• Buffer them by small number, e.g. 0.5 m
• Clip originals by buffer, output - SHAPEFILE

Use this field calculator expression on field Shape:

def RotateExtend(plyP,sLength):
 l=plyP.length
 ptX=plyP.positionAlongLine (l/2).firstPoint
 ptX0=plyP.firstPoint
 ptX1=plyP.lastPoint
 dX=float(ptX1.X)-float(ptX0.X)
 dY=float(ptX1.Y)-float(ptX0.Y)
 lenV=math.sqrt(dX*dX+dY*dY)
 sX=-dY*sLength/lenV;sY=dX*sLength/lenV
 leftP=arcpy.Point(ptX.X+sX,ptX.Y+sY)
 rightP=arcpy.Point(ptX.X-sX, ptX.Y-sY)
 array = arcpy.Array([leftP,rightP])
 section=arcpy.Polyline(array)
 return section

-------------------------------

RotateExtend( !Shape!, 1000)

UPDATE:

Ooops! it creates perpendicular, not tangent. Can be easily modified