Using Matplotlib and Numpy, is there a way to find all line intersections for Linear Equations?

Question

I am using the following code to plot the intersection points on a graph, then visually inspecting the intersection points to go back to code and shade the feasibility region.

Is there a better way to find the feasible region than simply plotting the lines and reading the intersection points off the graph?

# Filling a polygon locating the corner points
# Then let Matplotlib fill within these points
x= [0.0, 0.0, 6.67,5.0]
y= [0.0, 4.0, .67, 0.0]
fill(x,y)
show()

Full code example:

x= arange(-3,10.1,0.1)
y= arange(-3,10.1,0.1)
y1= 0.4*x-2.0
y2= 4.0-0.5*x

xlim(-3,10)
ylim(-3,10)
hlines(0,-3,10,color='k')
vlines(0,-3,10,color='k')
grid(True)

xlabel('x-axis')
ylabel('y-axis')
title ('Shaded Area Shows the Feasible Region')

plot(x,y1,color='b')
plot(x,y2,color='r')
legend(['2x-5y=10','x+2y=8'])

x= [0.0, 0.0, 6.67,5.0]
y= [0.0, 4.0, .67, 0.0]
fill(x,y)
show()

elyase · Accepted Answer · 2015-01-26 02:55:40Z

1

If you just want to draw the feasibility region you can do:

x= arange(-3,10.1,0.1)
y= arange(-3,10.1,0.1)
y1= 0.4*x-2.0
y2= 4.0-0.5*x

xlim(-3,10)
ylim(-3,10)
hlines(0,-3,10,color='k')
vlines(0,-3,10,color='k')
grid(True)

xlabel('x-axis')
ylabel('y-axis')
title ('Shaded Area Shows the Feasible Region')

plot(x,y1,color='b')
plot(x,y2,color='r')
legend(['2x-5y=10','x+2y=8'])

bottom = np.maximum(y1, 0)
fill_between(x, bottom, y2, where=(x>0) & (y2>y1))

enter image description here

answered Jan 26, 2015 at 2:55

elyase

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4 Comments

Boerseun Over a year ago

Thank you Alyase, but I need to know the plot points. I found some indications that perhaps something like explained here link but I don't know how to make it work with my code.

elyase Over a year ago

The intersection point is easy, just calculate y1-y2 and look where it crosses 0.

bmc Over a year ago

Could you please explain this snippet in a little bit more detail: bottom = np.maximum(y1, 0)?

elyase Over a year ago

@bmc, that returns an array with the positive values from y1, and zeros where y1 is negative.

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