Extend line to specific point

Question

I have a line layer which is cut at the level of the point layer,

I want it to be connected at the nearest point while saving the forme ( just adding the missing part the that line without moving it) as showing in the next picture

My idea is to calculate the distance between each extremity of the line with the points and take the nearest point then draw a line between them..But the drowing come out bizzarly.

I was wondering ,Is there a simple way of doing this or maybe could anyone help me with the following code?

from qgis.core import *
from qgis.gui import *
import processing
layer = iface.activeLayer()
feat1=layer.selectedFeatures()

for lyrr4 in QgsMapLayerRegistry.instance().mapLayers().values():
  if lyrr4.name().startswith( 'Boitier_B1'):
     ch = lyrr4
     pr= ch.dataProvider()
chs= ch.getFeatures()
for f in feat1:
 min1=10000.55
 min2=10000.55
 attrs = f.attributes()

 idc = f["ID"]
 x1=f["x1"]
 y1=f["y1"]
 x2=f["x2"]
 y2=f["y2"] 
 print "id_cab"
 print idc
 print "x1"
 print x1
 print "y1"
 print x1
 print"x2"
 print x2
 print "y2"
 print y2
 if  "%.2f" % x1 != "%.4f" %xc and "%.2f" %x2 != "%.4f" %xc:
     point1 = QgsPoint(x1,y1)
     point2 = QgsPoint(x2,y2)
     for ch in chs:
         id = ch["ID"]
         xc= ch["xcoord"]
         yc= ch["ycoord"]
         print "id_ch"
         print id
         print "xc"
         print xc
         print "yc"
         print yc
         pointc = QgsPoint(xc,yc)
         geom = f.geometry()
         distance = QgsDistanceArea()
         m1 = distance.measureLine(pointc, point1)
         m2 = distance.measureLine(pointc, point2)
         print "m1"
         print m1
         print "m2"
         print m2
         fet = QgsFeature()
         if m1<min1:
             min1=m1
             pts=pointc
         if m2<min2:
             min2=m2
             idmin2=id
             pts1=pointc
         print "min1"
         print min1
         print "min2"
         print min2
     if min1<5:
         fet.setGeometry(QgsGeometry.fromPolyline([pts, point1]))
         fet.setAttributes(attrs)
         outFeat = QgsFeature()
         pr = layer.dataProvider()
         outGeom  = fet.geometry()
         outGeom = outGeom.combine(geom)
         outFeat.setGeometry(outGeom)
         outFeat.setAttributes(attrs)
         layer.addFeatures(([outFeat]))
         layer.deleteFeature(f.id())

     if min2<5:
         fet.setGeometry(QgsGeometry.fromPolyline([pts, point2]))
         fet.setAttributes(attrs)
         outFeat = QgsFeature()
         pr = layer.dataProvider()
         outGeom  = fet.geometry()
         outGeom = outGeom.combine(geom)
         outFeat.setGeometry(outGeom)
         outFeat.setAttributes(attrs)
         layer.addFeatures(([outFeat]))
         layer.deleteFeature(f.id())