Solving implicit equation of a plane

[kouma]

Hello,

Can someone tell me if what I am doing is correct. I am trying to solve this equation of 0 = n ( p - p0 ) where n, p, and p0 are points on the plane. Assume this is a 2D dimension (x,y). Is this the correct way of calculating this equation.

0 = nx (px - p0x) + ny (py + p0y)

Purpose: I am trying to find if point p resides on the positive or negative side of the plane.

Only help if you know the answer please.

Thanks

 

[mathman]

Hello,

Can someone tell me if what I am doing is correct. I am trying to solve this equation of 0 = n ( p - p0 ) where n, p, and p0 are points on the plane. Assume this is a 2D dimension (x,y). Is this the correct way of calculating this equation.

0 = nx (px - p0x) + ny (py + p0y)

Purpose: I am trying to find if point p resides on the positive or negative side of the plane.

Only help if you know the answer please.

Thanks

You do have a typo (should be py - p0y).

Your question is vague. What do you mean by positive or negative side of the plane? All your points are in the plane.

 

[kouma]

You are right about the typo, my bad. Thanks.

To clarify my question with an example, assume i have n and p0 given as n= (1,1) and p0=(2, 3). Now, say I have the following set of p {(1,3), (2,4), (1,5), (0,1), (2,3), (3,1)}. I would like to know where does each of the elements in the p set reside with respect to the plane. That is, it is on the positive side of the plane, zero, or negative? solving the equation should give me that answer.

Is this the correct way to solve this equation:

0 = nx (px - p0x) + ny (py - p0y)

Thanks

 

[mathman]

I still don't know what you mean by positive side or negative side? If n, p0, and all the p's are given, the dot product you wrote has a definite value in each case. To = 0, p-p0 is perpendicular to n-(0,0).

 

[CellCoree]

for reaching out for help on this problem. It looks like you are on the right track in solving this equation. To confirm, the equation you have written is correct for a 2D dimension (x,y). This equation represents the dot product of the normal vector (n) and the vector between the point p and the point p0.

To determine if point p is on the positive or negative side of the plane, you can plug in the coordinates of point p into the equation and solve for the result. If the result is greater than 0, then point p is on the positive side of the plane. If the result is less than 0, then point p is on the negative side of the plane.

I would also recommend checking your units and making sure they are consistent throughout the equation. Additionally, it may be helpful to visualize the plane and points in a graph to better understand the relationship between them.

I hope this helps and good luck with your problem!