# Retrieve a particular point coordinate from an edge

Hi there,
In Ruby, would you have a clue that could help me to retrieve the x and y coordinate of a point located on a particular z coordinate (for instance 30) along a line starting on (0,0,0) to (10,10,100) ?
Cheers !
Manu

For your specific case,

``````x = y = 10.0*(z/100.0)
``````
1 Like

Thanks, it"s so obvious!
What about a line starting from (0,0,0) to (20,45,100) ?
I should look back 30 years ago to my descriptive geometry â€śknowledgeâ€ť

Yeah, it does rot with age

The general equation of a line from P1 to P2 is

P = P1 + k(P2 - P1), 0.0 <= k <= 1.0

which broken down by component means

px = p1x + k(p2x - p1x)
py = p1y + k(p2y - p1y)
pz = p1z + k(p2z - p1z)

So, solve for k in any one of these equations and plug that into the other two.

In your second example, p1z = 0 and p2z - p1z = 100, so

k = pz/100.0 = 30.0/100.0 = 3.0/10.0

and

px = (3.0/10.0) * 20.0 = 6.0
py = (3.0/10.0) * 45.0 = 13.5

Note: Ruby does integer arithmetic if you donâ€™t make it clear that you want real numbers. Thatâ€™s why I put â€ś.0â€ť onto each value.

``````# Given an edge object
line = edge.line
# or from arbitrary points ...
# line = [Geom::Point3d.new(0,0,0), Geom::Point3d.new(20,45,100)]
plane = [Geom::Point3d.new(0, 0, 30.0), Z_AXIS]
point = Geom::intersect_line_plane(line,plane)
# Lastly test that point is non-nil for success.
``````
1 Like

Just to be 100% clear, what @DanRathbun showed uses methods from the SketchUp Ruby API, not simply Ruby. Depending on what else you are doing, his way might be more compatible with the rest of your code. Also, since the API methods are often wrappers around a compiled C routine, if this calculation is done in a loop for a lot of points, using the API might be faster.

Thatâ€™s clear ! Very helpfull

Great ! Thatâ€™s the function I was looking for
Thanks

Be mindful that using Geom::intersect_line_plane uses the infinite line defined by edge, and not just the line-segment bound by the vertices of edge. Thus the intersection point may lie outside the two points you specified in the original post if they are used to define the line, as in:

``````line = [Geom::Point3d.new(0,0,0), Geom::Point3d.new(10,10,100)]
``````

â€¦ we discussed testing whether a point was on an edge in this thread â€¦