Get Point intersection between vertical plane ('ZY') and 3d line

Hello ppl,

I have a set of lines defined by its first and last coordinates {(X1,Y1,Z1);(X2,Y2,Z2)} , and am trying to get the intersection points when crossing a set of YZ (lets call them vertical planes) with known 'X" values. Is there anyway excel would be able to intercept 3D lines and return the values? lines vs planes? planes vs planes? . Thanks

For questions like this, I believe that, if one understands the math/geometry of the problem, programming Excel to provide the solution should be relatively easy. Unfortunately, it has been a very long time since I've had to do this kind of math, so I'm too rusty to remember exactly how to obtain these solutions. But it does beg the question: do you understand the math well enough to provide a solution outside of Excel, so that you just need help figuring out how to get Excel to do it, or do you need the math lesson first, so you can understand how a solution is to be constructed?

It's too late for me to fully digest this problem tonight. A quick internet search for "equation of a line in 3 dimensions" yields several good looking tutorials, most mentioning vector equations and other concepts I recall dealing with back in the day, but I can't right off hand remember exactly how these concepts work. If you need a math lesson, I'd suggest you start with a similar search to begin to understand the math behind it.

Ultimately, gut feel suggests that one way or another this kind of problem will end up as a system of three equations in three unkowns, so it would also be useful to refresh our memory on techniques for solving systems of equations as well. If it comes down to Gaussian elimination, Excel does provide a built in MINVERSE() function for finding the inverse of a matrix.

in response to your previews comment, is not a math enquiry . I found a few functions offered by excel (e.g. INTERCEPT function) that works for 2d problems, however I was wondering if someone had something similar to use (macro script) in order to get values for point of interception created by a line vs plane. Am pretty sure most of the ppl in this chat knows the solution to that simple math/geometry problem, but thanks anyway for point it out. However my question still remains intact : "Is there anyway excel would be able to intercept 3D lines, line vs plane... and return the values/coordenate? "---> by using a function/macro pre-defined (sorry, but being an excel forum, i did not think it was necessary to express the last statement).


regards,

Originally Posted by mikerickson

Given a line defined by two points P1=(x1,y1,z1) and P2=(x2,y2,z2).
To find the point where that line intersects the YZ plane defined by x=x0, consider.

The formula of the line is P = P1 + t*(P2-P1)
=(x1,y1,z1) + t*(x2-x1, y2-y1, z2-z1)

If x1 + t*(x2-x1) = x0, then t = (x0-x1) / (x2-x1)

so y0 = y1 + [(x0-x1) / (x2-x1)] * (y2-y1)

similarly for the z coordinate.

Note: if 0 <= t <= 1 then the line segment P1P2 intersects the given plane

thomasaxn,
By applying the formula as mikerickson laid out, excel can perform the operation i believe you're asking for. I've created a spreadsheet where you can enter data into the boxes and the results will come up. There are XY, YZ, and XZ intercepts included. See the attached spreadsheet. Feel free to play around with it.
XYZ int.xlsx
-QEJohn

PS - i agree with you regarding MrShorty's post. get off your high horse buddy and see if you can actually help/answer a question...