Question

Greetings,

I am trying to bin an array of points (x, y) into an array of boxes [(x0, y0), (x1, y0), (x0, y1), (x1, y1)] (tuples are the corner points)

So far I have the following routine:

def isInside(self, point, x0, x1, y0, y1):
    pr1 = getProduct(point, (x0, y0), (x1, y0))
    if pr1 >= 0:
        pr2 = getProduct(point, (x1, y0), (x1, y1))
        if pr2 >= 0:
            pr3 = getProduct(point, (x1, y1), (x0, y1))
            if pr3 >= 0:
                pr4 = getProduct(point, (x0, y1), (x0, y0))
                if pr4 >= 0:
                    return True
    return False

def getProduct(origin, pointA, pointB):
    product = (pointA[0] - origin[0])*(pointB[1] - origin[1]) - (pointB[0] - origin[0])*(pointA[1] - origin[1])
    return product

Is there any better way then point-by-point lookup? Maybe some not-obvious numpy routine?

Thank you!

Answer 1

Are these boxes axis aligned? i.e. are the edges parallel to the coordinate axes? If so this can be done quite efficiently with vectorized comparisons on NumPy arrays.

def in_box(X, B):
    """
    Takes an Nx2 NumPy array of points and a 4x2 NumPy array of corners that 
    form an axis aligned box.
    """
    xmin = B[:,0].min(); xmax = B[:,0].max()
    ymin = X[:,1].min(); ymax = X[:,1].max()
    return X[X[:,0] > xmin & X[:,0] < xmax & X[:,1] > ymin & X[:,1] < ymax]

amending to >= and <= if you prefer them to be inclusive.

If you need it for an arbitrary quadrilateral, matplotlib actually has a routine matplotlib.nxutils.points_inside_poly that you could use (if you have it installed) or else copy it (it’s BSD-licensed). See this page for a discussion of the algorithms used and other algorithms for inside-a-polygon tests.