Random perpendicular vector3 after rotation

Question

I am generating random vectors3 (lets name it R), which would be perpendicular to given vector3 (lets name it A). If vector A is defined as:

 Vector3 A = new Vector3(0f,1f,0f);

I can easily get any random vector3 which would be perpendicular to A by:

 Vector3 R = new Vector3(Random.Range(-1f,1f), 0f, Random.Range(-1f,1f));

How I could create random vector R which would be perpendicular to any vector in 3d space?

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Answer 1

Best Answer

Answer by robertbu · Oct 14, 2014 at 04:05 PM

Given any two non-parallel vectors, you can generate the perpendicular by Vector3.Cross(). The direction of that vector will depend on the order you pass the two parameters in the Cross() call.

http://docs.unity3d.com/ScriptReference/Vector3.Cross.html

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Scribe · Oct 14, 2014 at 04:39 PM 0

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To add to this, if you only have 1 vector (i, j, k), then there are an infinite number of perpendicular vectors, all of which line on the plane of equation ix + jy + kz = 0, you can then solve that equation to find related x, y, z values for a random perpendicular vector, for example:

 Vector3 v = Vector3.zero;
 while(v == Vector3.zero){
     v = new Vector3(Random.Range(0.0f, 1.0f), Random.Range(0.0f, 1.0f), Random.Range(0.0f, 1.0f));
 }
 Vector3 vPerpendicular = Vector3.one;
 if(v.x != 0){
     vPerpendicular.x = -(v.y*vPerpendicular.y + v.z*vPerpendicular.z)/v.x;
 }else{
     vPerpendicular.x = Random.Range(0.0f, 1.0f);
 }
 if(v.y != 0){
     vPerpendicular.y = -(v.x*vPerpendicular.x + v.z*vPerpendicular.z)/v.y;
 }else{
     vPerpendicular.y = Random.Range(0.0f, 1.0f);
 }
 if(v.z != 0){
     vPerpendicular.z = -(v.y*vPerpendicular.y + v.x*vPerpendicular.x)/v.z;
 }else{
     vPerpendicular.z = Random.Range(0.0f, 1.0f);
 }
 Debug.Log(vPerpendicular);

vPerpendicular will be a random vector in the plane for which v was the normal

Hope that helps!

chanfort · Oct 15, 2014 at 12:40 PM 0

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Cross product with any other random vector seems to be working. Thanks.

Random perpendicular vector3 after rotation

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