CODEWITHSUNDEEP
pythonmatplotlib
P Ved
P Ved

Reputation: 139

Finding Cross Product to find points above/below a line in MatplotLib

I am trying to draw a line in MatPlotLib , and find all points above or below the line depending on the slope.

After reading this post, and reading about Cross Product, I believe this is the best approach for me to check the points.

I am unsure what would be the most optimal way to implement this in python.

v1 = {x2-x1, y2-y1}   # Vector 1
v2 = {x2-xA, y2-yA}   # Vector 2
xp = v1.x*v2.y - v1.y*v2.x  # Cross product

Has anyone tried implementing something similar ?

Is there some other way for me to find if points on the plot are above or below a line in MatPlotLib ?

Upvotes: 4

Views: 6478

Answers (2)

onefineday
onefineday

Reputation: 1

A dirty way - use the method for left/right with cross product (How to tell whether a point is to the right or left side of a line), then evaluate the slope of the line. If slope is negative, then any point left of the line is above the line, and if slope is positive any point left of the line is below the line. If the point is to the right, these are reversed. (Obviously the answer depends on the orientation of the y-axis, for my example up is negative and down is positive.) This method requires programming the special cases for vertical and horizontal lines. For horizontal lines, the cross product method will give you the point's position above the line. For vertical lines, there is no real answer, but we point to isLeftOfLine instead.

C++ code:

bool Point::isLeftOfLine(Line cmp)
{
    return ((cmp.p2.x - cmp.p1.x) * (y - cmp.p1.y) > (cmp.p2.y - cmp.p1.y) * (x - cmp.p1.x));
}

bool Point::isTopOfLine(Line cmp)
{
    if(cmp.p1.x == cmp.p2.x || cmp.p1.y == cmp.p2.y)
    {
        return isLeftOfLine(cmp);
    }
return isLeftOfLine(cmp) == cmp.slope() < 0;
}

double Line::slope()
{
    return (p2.y - p1.y) / (p2.x - p1.x);
}

Upvotes: 0

ImportanceOfBeingErnest
ImportanceOfBeingErnest

Reputation: 339695

As seen e.g. in this question the cross product can indeed be used to determine whether a point lies above or below a line which is defined by two points.

So let a and b be two points defining a line, and p a (set of) point(s) for which we want to know the relative position to the line. Then if

numpy.cross(p-a, b-a) < 0

is True the point(s) lie above the line.

To be accurate here, "above" means that looking from point a towards point b, the point p lies to the left of the line.

This can be used to colorize points in a scatter plot differently depending on whether they're above or below the line, as seem below:

import numpy as np
import matplotlib.pyplot as plt

isabove = lambda p, a,b: np.cross(p-a, b-a) < 0

a = np.array([1,1])
b = np.array([4,3])

p1 = np.array([2,4])
p2 = np.array([3,1])

p = np.array([p1,p2])


fig, (ax,ax2) = plt.subplots(ncols=2, sharex=True, sharey=True)

ax.plot([a[0],b[0]],[a[1],b[1]], marker="o", color="k")
ax.scatter(p[:,0],p[:,1], c=isabove(p,a,b), cmap="bwr", vmin=0, vmax=1)

p = np.random.rand(10,2)*5

ax2.plot([a[0],b[0]],[a[1],b[1]], marker="o", color="k")
ax2.scatter(p[:,0],p[:,1], c=isabove(p,a,b), cmap="bwr", vmin=0, vmax=1)


ax.set_xlim(0,6)
ax.set_ylim(0,6)
plt.show()

enter image description here

Upvotes: 10

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