QGIS calculate radius of an arc to attributes

Question

I have QGIS 2.18.16 installed. My problem is, how to calculate radius of an arc / curve feature (line)? The lines are originated from .dgn file, which I read with FME and wrote to PostGis DB. I have created primary keys etc, and the table is fully editable. I calculated lengths for the arcs successfully, but cant figure out how to calculate radius for these curves. This ( https://www.mathopenref.com/arcradius.html ) might give some idea on the math side, though I can't figure out how to use it in QGIS calculator. So I need to calculate the "R" for all the lines i have in the DB.

Bellow is an example. My data has Arcs / Curves on different table than "normal" polylines.

Answer 1

Lightly tested formulas follow, so proceed with caution. But following along with an example here: https://www.mathopenref.com/arcradius.html

If your circular arcs have a vertex at the middle point along the arc (which I am saying is x1, y1 in the figure), you could use it along with the start and end points to calculate the chord length "W" and the height "h" to get the radius "R" using the following formula:

and saying

W =

sqrt(
     ( $x_at(-1) - $x_at(0) )^2 +
     ( $y_at(-1) - $y_at(0) )^2
    )

and

H =

sqrt(
    ( $x_at(1) - ( $x_at(-1) + $x_at(0) )/2 )^2
    + ( $y_at(1) - ( $y_at(-1) + $y_at(0) )/2 )^2
)

in your Expression Dialog of the Field Calculator you'd have this long equation for the radius calculation:

R =

sqrt( 
    ( $x_at(1) - ($x_at(-1) + $x_at(0) )/2 )^2 
    + ( $y_at(1) - ($y_at(-1) + $y_at(0))/2 )^2
     ) /2
+
(   ( $x_at(-1) - $x_at(0) )^2 )  + 
    ( $y_at(-1) - $y_at(0) )^2 )  )
/ ( 8 * sqrt(
            ( ($x_at(1) - ($x_at(-1) + $x_at(0) )/2 )^2
            + ( $y_at(1) - ($y_at(-1) + $y_at(0) )/2 )^2
             )
   )

Answer 2

What about extracting the radius while extracting the data with FME? There you have the ArcPropertyExtractor transformer, which should give you the radius values in attributes ready to set in your PostGIS DB

Answer 3

I wrote an octave/matlab script that calculates the radius of a polygon consisting of 5 or more vertices/points. Just put your polyline(s) in a shp-file and my script will add the radius as an attribute in the dbf-file. You need octave to run it.

You can find it here: Find radius of curve?

Answer 4

I was able to get the radius of all lines in the attributes table by adding a custom function.

from qgis.core import *
from qgis.gui import *

@qgsfunction(args='auto', group='Custom', referenced_columns=[])
def radius_function(startpoint, midpoint, endpoint, feature, parent):
    """
    Calculate the radius of an arc line, using the inbuilt circleCenterRadius
    function and evaluations of the line end points and mid point.
    <h2>Example usage:</h2>
    <ul>
      <li>radius_function( start_point($geometry), $geometry, end_point($geometry) )</li>
    </ul>
  
    
    """
    
    # # https://gis.stackexchange.com/questions/58079/finding-middle-point-midpoint-of-line-in-qgis
    
    startpoint_ = QgsPoint(startpoint.asPoint().x(), startpoint.asPoint().y()) # start of the line
    half_length = midpoint.length() # half length to the middle of the line
    midpoint_i = midpoint.interpolate(half_length /2) # calculate the middle of the line
    midpoint_ = QgsPoint(midpoint_i.asPoint().x(), midpoint_i.asPoint().y()) # Convert to Point
    endpoint_ = QgsPoint(endpoint.asPoint().x(), endpoint.asPoint().y()) # end point of the line
    
    # circleCenterRadius returns tuple (radius, center x coordinate, center y coordinate)
    radius_, center_x, center_y = QgsGeometryUtils.circleCenterRadius(startpoint_, midpoint_, endpoint_)     
    
    return float(radius_)