 # I have a need and need a strong mathematical foundation. Knowledge is limited, ask for help, thank you

As shown in the figure, A, B, and C are all known, and now the coordinates of D and E are required. Their Y-axis is equal to 0 The dotted lines are all parallel lines of solid lines, and their distances are known.

Can you add/subtract from both x and z axis the distance between the lines? If you only know the distances between a,d, and e then you can divide by math.sqrt(2)? This illustration may be clearer.

If I am understanding your image correctly and you know the position of A. Let’s call it a Vector3 `a`.
Then
`let D = new Vector3(a.x + 2, 0, a.z + 2)` and
`let E = new Vector3(a.x - 2, 0, a.z - 2)`

If that’s not the case, can you draw the X,Y and Z axis? Otherwise I will try for a PG Thank you for your answer, but it doesn’t seem to be the result I want. The angle between B, A and C is uncertain. Their position is not uncertain, but it can be determined that their Y-axis is zero. And their normal line is not consistent. There may also be different results. What I may need is a formula.

I think it’s just trigonometry, but I can’t visualize what you are after. Can you make a PG?

This playground that draws a 2D line of given width uses the mathematics you require https://www.babylonjs-playground.com/#FA2H7X#3 . When you want to draw just the dotted lines the data you need is in the two arrays `innerData` and `outerData` just delete the mesh building part, build lines instead and rename function https://www.babylonjs-playground.com/#FA2H7X#16.

The maths to find the inner and outer points is at 46 to 49 and then lines 71 - 78. Lines 80 to 90 deal with whether there are just two points or more than two points.