Question

I am trying to plot large amounts of points using some library. The points are ordered by time and their values can be considered unpredictable.

My problem at the moment is that the sheer number of points makes the library take too long to render. Many of the points are redundant (that is – they are “on” the same line as defined by a function y = ax + b). Is there a way to detect and remove redundant points in order to speed rendering ?

Thank you for your time.

Answer 1

The following is a variation on the Ramer-Douglas-Peucker algorithm for 1.5d graphs:

1. Compute the line equation between first and last point
2. Check all other points to find what is the most distant from the line
3. If the worst point is below the tolerance you want then output a single segment
4. Otherwise call recursively considering two sub-arrays, using the worst point as splitter

In python this could be

def simplify(pts, eps):
    if len(pts) < 3:
        return pts
    x0, y0 = pts[0]
    x1, y1 = pts[-1]
    m = float(y1 - y0) / float(x1 - x0)
    q = y0 - m*x0
    worst_err = -1
    worst_index = -1
    for i in xrange(1, len(pts) - 1):
        x, y = pts[i]
        err = abs(m*x + q - y)
        if err > worst_err:
            worst_err = err
            worst_index = i
    if worst_err < eps:
        return [(x0, y0), (x1, y1)]
    else:
        first = simplify(pts[:worst_index+1], eps)
        second = simplify(pts[worst_index:], eps)
        return first + second[1:]

print simplify([(0,0), (10,10), (20,20), (30,30), (50,0)], 0.1)

The output is [(0, 0), (30, 30), (50, 0)].

About python syntax for arrays that may be non obvious:

• x[a:b] is the part of array from index a up to index b (excluded)
• x[n:] is the array made using elements of x from index n to the end
• x[:n] is the array made using first n elements of x
• a+b when a and b are arrays means concatenation
• x[-1] is the last element of an array

An example of the results of running this implementation on a graph with 100,000 points with increasing values of eps can be seen here.