# Projecting vectors to transform an ellipsoid

So, I have some math under my belt, but I haven’t taken any courses that include vector math yet, so bear with me.

I have an ellipsoid class that generates ellipsoids in terms of `Vector3i`s, with an (x, y, z) center. Now what I want to do is be able to rotate that ellipsoid in “any” direction. My question is, would projecting the `Vector3i`s of the ellipsoid onto the `Vector2d`s of the Direction enum accomplish this task? I mean, of course it would, but more specifically:

• Is this accomplish-able through `Vector3i#project(Vector3i)`?
• Should I use the rounded, ceiled, or floored, directional or coordinate, Direction enum vectors?

Thanks for any replies

No, projecting the vector will distort the shape.

Projecting can be thought of having a vector, which is the original point/line and having a second vector, which is an infinite line/wall.

Projection is “shining a torch” perpendicular to the wall, causing a shadow of the original vector, and the result vector represents the shadow.

It’s a slightly bad analogy, because shadows in real life usually have a single light point and can distort the result, but I hope it’s good enough to help you understand how it’s not what you want to do.

click for full image.

Sorry for imgur, but I was having troubles uploading images to the forums.

This is odd, because I was also having trouble. Stuck at 100%?

I think the forum may upload to imgur anyway.

Anyways, thanks for “shedding some light” on the situation. I’ve been working on calculating angles and rotating a vector by that angle, and I think that’s how I need to accomplish this.

Yeah, as far as I know the most performant way to do that, would be to create a rotation matrix between an origin vector representing the original rotation, and a rotation vector showing where the new origin vector should be translated to.

I’m sorry I couldn’t provide an example of this, as I’m unsure about several specifics, what point is it rotated around, can you do the transformation with a single matrix even using world co-ordinates rather then local co-ordinates to the oval.