CircleFromTanCrvsAndCenterCrv

# 14.12.2019 DSP
# create a circle through first two tangent crvs, and the third one on which the circle center lies on
# example shown at: https://discourse.mcneel.com/t/wish-add-circle-tangent-tangent-center-along-curve/93634

import rhinoscriptsyntax as rs
import Rhino.Geometry as rg
import Rhino


def CircleFromTwoTanCrvsAndCentCrv(crv1, crv2, crv3):
    
    # circCentPt
    crv3_t_distance_sortTuple_LL = []
    crv3.Domain = rg.Interval(0,100000)
    for i in xrange(100001):
        
        ptOnCrv3 = crv3.PointAt(i)
        
        succ, t1 = crv1.ClosestPoint(ptOnCrv3)
        ptOnCrv1closestTo_ptOnCrv3 = crv1.PointAt(t1)
        distFromPtOnCrv3_toCrv1 = ptOnCrv1closestTo_ptOnCrv3.DistanceTo(ptOnCrv3)
        
        succ2, t2 = crv2.ClosestPoint(ptOnCrv3)
        ptOnCrv2closestTo_ptOnCrv3 = crv2.PointAt(t2)
        distFromPtOnCrv3_toCrv2 = ptOnCrv2closestTo_ptOnCrv3.DistanceTo(ptOnCrv3)
        
        divisor = max(distFromPtOnCrv3_toCrv1, distFromPtOnCrv3_toCrv2) / min(distFromPtOnCrv3_toCrv1, distFromPtOnCrv3_toCrv2)
        crv3_t_distance_sortTuple_LL.append( [divisor, i] )
        
    crv3_t_distance_sortTuple_LL.sort()
    
    final_crv3_t = crv3_t_distance_sortTuple_LL[0][1]
    circCenPt = crv3.PointAt(final_crv3_t)
    
    
    # radius
    succ3, t3 = crv1.ClosestPoint(circCenPt, 0)
    circCenPt_closestPtOnCrv1 = crv1.PointAt(t3)
    radius = circCenPt.DistanceTo(circCenPt_closestPtOnCrv1)
    
    
    # circPln
    succ4, t4 = crv2.ClosestPoint(circCenPt, 0)
    circCenPt_closestPtOnCrv2 = crv2.PointAt(t4)
    
    
    planeFitResult, circPln = rg.Plane.FitPlaneToPoints([circCenPt, circCenPt_closestPtOnCrv1, circCenPt_closestPtOnCrv2])
    
    if planeFitResult == rg.PlaneFitResult.Success:
        circPln.Origin = circCenPt
        circ = rg.Circle(circPln, radius)
        
        circ_id = Rhino.RhinoDoc.ActiveDoc.Objects.AddCircle(circ)
    else:
        print "something went wrong. Make sure that all three crvs do not overlap each other"
        return




ids = rs.GetObjects("select the first and the second curve the circle will touch. Then select the curve on which the circle radius will be located on.", 4)

if (len(ids) != 3):
    print "Three crvs are needed to be selected in order to create the circle"
else:
    crv1 = rs.coercegeometry(ids[0])
    crv2 = rs.coercegeometry(ids[1])
    crv3 = rs.coercegeometry(ids[2])
    
    circ_id = CircleFromTwoTanCrvsAndCentCrv(crv1, crv2, crv3)