Drawing perpendicular lines in PyQGIS?

I have a situation like this:

What I need to do is to connect each point to every line that is at most, let's say 200 m, away from the point. In other words, I need to draw a perpendicular line from each point to every line that is in the buffer.

Is there a way to do this in PyQGIS?

Answer

It is a problem of analytical geometry and the solution was given by Paul Bourke in 1998 (Minimum Distance betweena Point and a Line). The shortest distance from a point to a line or line segment is the perpendicular from this point to the line segment. Several versions of his algorithm have been proposed in various languages ​​including Python as in Measuring distance from a point to a line segment in Python. but there are many others (like Nearest neighbor between a point layer and a line layer with Shapely)

# basic example with PyQGIS
# the end points of the line
line_start = QgsPoint(50,50)
line_end = QgsPoint(100,150)
# the line
line = QgsGeometry.fromPolyline([line_start,line_end])

# the point
point = QgsPoint(30,120)

def intersect_point_to_line(point, line_start, line_end):
     ''' Calc minimum distance from a point and a line segment and intersection'''
      # sqrDist of the line (PyQGIS function = magnitude (length) of a line **2)
      magnitude2 = line_start.sqrDist(line_end) 
      # minimum distance
      u = ((point.x() - line_start.x()) * (line_end.x() - line_start.x()) + (point.y() - line_start.y()) * (line_end.y() - line_start.y()))/(magnitude2)

      # intersection point on the line
      ix = line_start.x() + u * (line_end.x() - line_start.x())
      iy = line_start.y() + u * (line_end.y() - line_start.y())
      return QgsPoint(ix,iy)

line = QgsGeometry.fromPolyline([point,intersect_point_to_line(point, line_start, line_end)])

and the result is

Adapting the solution to your problem is easy,just loop through all line segments, extracting the segments end points and apply the function.