Splitting polygon at points using ArcPy with ArcMap

Question

I am trying to divide irregularly shaped polygons at specific points. I don't have any fields that inform the angle at which the polygons should be divided.

I am using Create Thiessen Polygons which generally wants to build a polygon around a point, such that it is centered, rather than with the point at the edge.

Is there a way to force the polygons to be shifted such that they are along the points? Is there a different tool I should use? I have sketches below of input, current output, and desired output. (And the next step is to intersect the base polygon with the output Thiessen polygons; that is the final answer, but I have left it out here because it is a simple step.)

This is related to ArcGIS force Thiessen polygons to be larger or alternative tool?, but this is a new/separate question because of the shifting vs. centering issue.

import arcpy
    
#mypoly = filepath to my polygon SHP
#mypts = filepath to my points SHP
#myoutput = filepath to save Thiessen polgons output

arcpy.env.extent = mypoly
arcpy.CreateThiessenPolygons_analysis(mypts, myoutput)

Answer 1

Hard to understand what you want, this is how I see it (similar to @Michael Stimson. Create polygon outlines, and generate near table. Add 2 more columns (highlighted in a picture below):

Calculate coordinates of point 'opposite' to nearest with big enough distance. This is how I computed OPP_X:

!FROM_X!-500*math.cos(math.radians( !NEAR_ANGLE! ) )

Construct lines from above table (XY to line) using near and opposite pairs and IN_FID as line ID.

Result might surprise you:

Answer 2

I ended up making a polyline out of the points, splitting the polyline at each point, and getting the midpoint of each split polyline. Then I did the Thiessen polygons on the midpoints.

import arcpy

arcpy.PointsToLine_management(SHP_IN_PTS, templine1)
arcpy.SplitLine_management(templine1, templine2)
arcpy.AddGeometryAttributes_management(templine2, "LINE_START_MID_END")
arcpy.MakeXYEventLayer_management(templine2, "MID_X", "MID_Y", "pts_layer",
                                  arcpy.SpatialReference(4326))
arcpy.FeatureClassToFeatureClass_conversion("pts_layer", outpath, 'temp_midpoints.shp')

arcpy.env.extent = SHP_IN_POLY
arcpy.CreateThiessenPolygons_analysis(midpoints, thiesspoly)

arcpy.Intersect_analysis([SHP_IN_POLY, thiesspoly], SHP_OUT_POLY_FINAL)