Can you taper a buffer?

HeatherAlexander

I am looking at creating a tapered buffer for a drain off a field that meets up with the drain that runs alongside the road.  the buffer would be used to negotiate with the farmer to create a grassed runway(drain) to minimize erosion of his field.  Any help, advice or suggestions is greatly appreciated.

The Pink lines represent the stream delineation that I've run in the area.  What I want to do is create a tapered buffer from a point on the pink line(NW-SE) (ex. 15m) from the ditch (E-W pink).  We would like to use the teal line(road allowance) to determine how much land creating this buffer the farmer will 'lose' from production.

DarrenWiens2

I assume the link in Dan's link is more polished than this, but it caught my interest, and here's the Python code I came up with. Basically, it creates vertex-dependent buffers and trapezoids between the buffers. Math for calculating tangent lines to buffers from here:

>>> lines = 'a_line' # line feature class
... sr = arcpy.Describe(lines).spatialReference # spatial reference
... new_polys = []
... new_scratch_polys = []
... new_lines = []
... buffers = []
... max_buff = 50 # buffer at line start
... min_buff = 10 # buffer at line end
... with arcpy.da.SearchCursor(lines,'SHAPE@',spatial_reference=sr) as cursor: # loop through lines
...    for row in cursor:
...        prev_buff = None
...        for part in row[0]:
...            for pnt in part:
...                cur_rad = ((max_buff-min_buff) * (1-row[0].measureOnLine(pnt,True))) + min_buff # calc current proportional buffer size
...                cur_buff = arcpy.PointGeometry(pnt,sr).buffer(cur_rad) # create buffer geometry
...                new_poly_array = arcpy.Array()
...                if prev_buff: # if at least second vertex
...                    cur_poly = cur_poly.union(cur_buff) # add buffer to cumulative geometry
...                    c1 = prev_pnt # math starts here. See: Tangent lines to circles
...                    c2 = pnt
...                    r1 = prev_rad
...                    r2 = cur_rad
...                    dx = c2.X - c1.X
...                    dy = c2.Y - c1.Y
...                    dr = r2 - r1
...                    d = math.sqrt(math.pow(dx,2)+math.pow(dy,2))
...                    X = dx/d
...                    Y = dy/d
...                    R = dr/d
...                    ks = [1,-1]
...                    for k in ks:
...                        a = (R*X)-((k*Y)*math.sqrt(1-math.pow(R,2)))
...                        b = -((R*Y)+((k*X)*math.sqrt(1-math.pow(R,2))))
...                        c = r1 - (a*c1.X) + (b*c1.Y)
...                        tan_x1 = c2.X-10000
...                        tan_x2 = c2.X+10000
...                        tan_y1 = -((((-a)*(tan_x1))-c)/(b))
...                        tan_y2 = -((((-a)*(tan_x2))-c)/(b))
...                        new_line = arcpy.Polyline(arcpy.Array([[arcpy.Point(tan_x1,tan_y1),arcpy.Point(tan_x2,tan_y2)]]),sr) # create line
...                        new_lines.append(new_line)
...                        if k > 0:
...                            new_poly_array.add(new_line.intersect(prev_buff,1).centroid) # find intersections
...                            new_poly_array.add(new_line.intersect(cur_buff,1).centroid) # find intersections
...                        else:
...                            new_poly_array.add(new_line.intersect(cur_buff,1).centroid) # find intersections
...                            new_poly_array.add(new_line.intersect(prev_buff,1).centroid) # find intersections
...                    new_rect = arcpy.Polygon(new_poly_array,sr) # make polygon from intersections
...                    new_scratch_polys.append(new_rect) # add rectangle to scratch geometry
...                    cur_poly = cur_poly.union(new_rect) # add rectangle to cumulative geometry
...                else:
...                    cur_poly = cur_buff # add buffer to cumulative geometry
...                prev_rad = cur_rad #remember values     
...                prev_pnt = pnt
...                prev_buff = cur_buff
...                buffers.append(prev_buff)
...            new_polys.append(cur_poly) # add cumulative geometry to list
... arcpy.CopyFeatures_management(buffers,r'in_memory\buffers') # write outputs
... arcpy.CopyFeatures_management(new_scratch_polys,r'in_memory\scratch_polys')
... arcpy.CopyFeatures_management(new_lines,r'in_memory\lines')
... arcpy.CopyFeatures_management(new_polys,r'in_memory\polys')