How do I tell if a point is in or on a boundary set by equations

I have a power curve, horizontal line, vertical line, and a linear line. The four of these enclose a region on a plot. I am looking to see if a user-inputted point is within or on the boundary. If anyone could guide me into the right direction, I would appreciate it.

Answer 1

[Star Strider]

The inpolygon (link) function could be helpful.

[Andrew Padilla]

Hi Strider,

thank you for the help. I looked at this function already but it seems to not work for some points. I am assuming this is because a part of what is bounding the region is a power curve which is not a straight line. inpolygon() takes the vertices of the boundaries and connects them with straight lines to determine the boundary. Are there any other approaches I could take?

[Star Strider]

Not that I am aware of.

[Andrew Padilla]

Strider,

I figured out a solution. It turns out, inpolygon() can be used to help out. Because the other equations are linear, in_polygon() will work for those boundaries. It fails where the shape is bounded by the power curve. Because of this, I have to check that the y value is greater than the x of the y value plugged in to the power curve equation. With that said, I created a conditional statement that checked if the y value was greater AND in or on is equal to one. If both of these are true, the point is in the shape. I will accept this as an answer because it did guide me to getting the answer.

[Star Strider]

Thank you.