math help with random points on a plane off of transform.forward

Unity Engine
1

Hello,
I could use some math help with the following:

Given transform.position (a point in space), transform.forward (a direction in space), and a maximum distance I want to calculate a random point that is on a plane that passes through transform.position and is perpendicular to transform.forward. The random point should be up to a maximum distance away.

I know how to use Random.value. What I am looking for is the equation that comes back with an xyz point as noted above.

I am attaching a picture that hopefully illustrates/illuminates what I am looking for.

Appreciate any math help!

1181419--45682--$AsteroidRegen.jpg
1181419--45682--$AsteroidRegen.jpg1024×1024 63.8 KB

2

Planes:

Amazing plane and line maths:
http://wiki.unity3d.com/index.php?title=3d_Math_functions
You probably need a combo of something like, get a random vector in the plane with project vector on plane, and then distanceWanted*vector

3

Interesting stuff but my math background is not strong. I was hoping to get help to derive the actual equation c# code I would use to perfrom this.

4

this should give you the general idea how at least i would approach this

http://answers.unity3d.com/questions/60252/placing-object-with-ray-cast.html
generally script attached to a invisible cube gravity off , cubes transforms locked from rotating … And fire the Ray when MouseOver() + Mouse Click. Then jump to some routine that does the random() Vector3 transforms around the invisible Cubes transform.position.

View the concept like it’s kinda like a drag Drop Manager

5

You could use the Vector3.Exclude method to exclude the plane normal from a Random.InUnitSphere, that should put all your randomized vectors on the plane.

Afterwards, you just multiply those vectors by whatever max size you want them to have.

Something like this:

randomVector = Vector3.Exclude(transform.forward, Random.InUnitSphere()) * maxSize;

Cheers