How to give a position an offset relative to its forward vector in local space?

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In my road creation tool, I want to create a road out of 2 points. In order to do that I need to create a box of vertexes where 4 points surround the 2 initial points. However, I am struggling to find out where to place those points when the road is at an angle. I have the feeling it might be something really easy but my brain is just not cathcing it.

The difference in the example is really small but I hope it makes clear what I am trying to achieve. if you need any initial information feel free to ask but I hope the illustration speaks for itself.

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Answer by Captain_Pineapple · Apr 08 at 01:04 PM

Yes that illustration is enough.

So if we assume you have a starting point and endpoint and an offset:

  Vector2 startpoint = new Vector2(x1, y1); 
  Vector2 endpoint = new Vector2(x2, y2); 
  float offset = 3;

Then you can calulate the following vectors:

   //connect the red dots, get the vector and shorten it to length 1:
   Vector2 direction_normalized = (endpoint - startpoint).normalized;
   // get the perpendicular vector: (normalization might not be needed here - not sure):
   Vector2 direction_perpendicular = Vector2.perpendicular(direction_normalized).normalized;

Then the 4 points you are searching for are:

   Vector2 P1 = startpoint + offset*(-direction_normalized  + direction_perpendicular);
   Vector2 P2 = startpoint + offset*(-direction_normalized  - direction_perpendicular);

   Vector2 P3 = endpoint + offset*(direction_normalized  - direction_perpendicular);
   Vector2 P4 = endpoint + offset*(direction_normalized  - direction_perpendicular);

This can ofc also be done in 3D space. Only thing to change in that regard is that 3D space does not contain a simple "perpendicular" function. There you'd have to learn to use the cross product. (`Vector3.cross(v1, v2)`)

Let me know if something was unclear.

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arjenvklaveren · Apr 08 at 01:25 PM 0

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That's such an elegant solution! I was just trying stuff like rotating the forward vector by 45 degrees and stuff but this makes way more sense. Thanks!

Captain_Pineapple arjenvklaveren · Apr 08 at 02:42 PM 0

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Doing this with rotations is also very much a possible solution! As this would be more complex and more taxing regarding performance the pure vector calculations are more favorable for a real application though.

How to give a position an offset relative to its forward vector in local space?

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