QGIS - From a point along a line (centreline), find the longest line to the centreline, without crossing a polygon boundary

See my finalised code.

BinarySearch - Visibility

name1='Interpolated points' #QGIS Layer - the closer the spacing the greater the accuracy
name2='VergeExtents' #QGIS Layer - Extents to which the visibility should not cross

layer1 = QgsProject.instance().mapLayersByName(name1)[0]
layer2= QgsProject.instance().mapLayersByName(name2)[0]

#initialise variables
pi=0 #first initial observation point
pn=((layer1.featureCount())) #end initial observation point
 
for feature in layer2.getFeatures():
    geom3=feature.geometry()

#create the longest line vector layer
v_layer = QgsVectorLayer('LineString?crs=epsg:27700', 'HMVLines', 'memory')
pr1 = v_layer.dataProvider()

#For loop finding the longest line for every points at a given interval
for x in range(1,pn,50):
    pi=x 
    l=pi+1 #low point
    h=pn # high point


#While loop to binary search the longest line from a given start point from the for loop
while l < h: 
    #initialise start of line
    for feature in layer1.getFeatures([pi]):
        geom1=feature.geometry()
    
    #iteration on the midpoint of the point set
    mid = l + (h - l) // 2; 
    
    #initialise end of line
    for feature in layer1.getFeatures([mid]):
        geom2=feature.geometry()
   
    #create line between pi and mid
    line=QgsFeature()
    line.setGeometry(QgsGeometry.fromPolylineXY([geom1.asPoint(), geom2.asPoint()]))
              
    #1ST CHECK - if difference between h and l is less 1 then stop while loop(i.e. minimum spacing between points)
    if (h-l)<=1: 
        break
    
    #2ND CHECK - if the visibility line and the boundary intersect, set high point to middle
    elif geom3.intersects(line.geometry())==1:
        h=mid
       
    #3RD CHECK - if the visibility line and the boundary do not intersect, set low point to middle
    elif geom3.intersects(line.geometry())==0: 
        l=mid
    
#Once binary search has complete, l will be the longest line that does not intersects the boundary - get this geometry.
for feature in layer1.getFeatures([l]):
    geom4=(feature.geometry())
        
#create the longest line from pi to l
visibility = QgsFeature()
visibility.setGeometry(QgsGeometry.fromPolylineXY([geom1.asPoint(), geom4.asPoint()]))
pr1.addFeatures([visibility])

QgsProject.instance().addMapLayers([v_layer])
iface.zoomToActiveLayer()

Your proposed procedure would work if you are willing to accept an approximation, since there is no guarantee that your one of your radial bearing lines is the true longest line. It's also horribly inefficient.

A slightly better procedure would be:

1. For each observation point P_i, draw the line to P_{i + 1}, P_i+2 until the line crosses the boundary. Let's say the last point where the line remains inside the polygon is P _{i + n}
2. The longest line will intersect the centerline between points i+n and i+n+1. Now use binary search to create new points along the centerline, drawing a line from P_i until you reach the precision you desire.