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THE FEUTEX TOOLKIT

Line and Plane Intersection

Find the parameter and coordinates where a 3D parametric line crosses a plane.

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01 Your input
02 Your result
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FormulaT = (d-a*px-b*py-c*pz)/(a*ux+b*uy+c*uz); X = px+ux*(d-a*px-b*py-c*pz)/(a*ux+b*uy+c*uz); Y = py+uy*(d-a*px-b*py-c*pz)/(a*ux+b*uy+c*uz); Z = pz+uz*(d-a*px-b*py-c*pz)/(a*ux+b*uy+c*uz)
Sources and model references

Made for real tasks

  • Find the parameter and coordinates where a 3D parametric line crosses a plane.
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Worked example

Inputs

Line origin x
0 length
Line origin y
0 length
Line origin z
0 length
Direction x
1 number
Direction y
2 number
Direction z
3 number
Plane coefficient A
0 dimensionless
Plane coefficient B
0 dimensionless
Plane coefficient C
1 dimensionless
Plane right side D
6 length

Expected results

T
2 number
X
2 length
Y
4 length
Z
6 length

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter line origin x, line origin y, line origin z, direction x, direction y, direction z, plane coefficient a, plane coefficient b, plane coefficient c, plane right side d.
  2. Use the displayed units and confirm the model assumptions.
  3. Calculate and compare the outputs against your input scenario.

Try this example

{
  "px": 0,
  "py": 0,
  "pz": 0,
  "ux": 1,
  "uy": 2,
  "uz": 3,
  "a": 0,
  "b": 0,
  "c": 1,
  "d": 6
}

Accuracy and scope

Plane convention Ax+By+Cz=D; infinite line, not a bounded ray.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.