Add Projection about ppb-vector HOT 9 CLOSED

@astronouth7303 Is that supposed to be the projection of a on the surface normal to b?
'cause that wouldn't be it, I think.

Anyhow, yes, having a projection method seems reasonable to me.

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No, that would be the projection of a onto the vector b, not its normal, as per wikipedia.

Although maybe defining a version that operates on the normal make sense? Matches reflect then?

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@astronouth7303 Both make sense:

• if we think of projecting and reflecting on surfaces (which makes extra sense in higher dimensions), we definitely want a normal;
• if we think of projecting and reflecting on a line, defining it by a collinear vector also makes sense.

I guess we could have project_by (for the projection on a vector's normal) and project_unto (the vector's collinear line), and similarly reflect_by and reflect_unto (and deprecate reflect, as the name is ambiguous). The method names are just a placeholder proposal, I didn't think deeply about it and there might be better choices.

If that's something we agree on, I'd be happy to make it happen.

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Higher dimensions is something that's explicitly out of scope?

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@astronouth7303 This was a parenthesis specifically because of that; interpret that point as “it's an API which is sensible in 2D, and is the main thing you would want in 3D”.

I don't think it's out-of-scope to provide an API that's consistent with what happens in not-2D geometry (lowering cognitive load on users).

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@pathunstrom any perspective from the teaching/student side?

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I'm going to ask around, but first thoughts:

reflect is there because it's an algorithm I used regularly for physics based games (like Arkanoid clones). I've never needed reflect across a line. So my thought on that is Vector.reflect should be the physics based version, and something like Vector.reflect_across for the across a line version. (Also I'd prefer reflect_onto over reflect_unto but neither of those feel accurate to me.)

EDIT: Thinking about this further, is there that much of a difference between these two? Add a keyword argument to handle the offset that defaults to the null vector and the mechnics of both are the same? (Correct me if I'm wrong, please.)

I need to dig more into projection, another thing I've never needed so need to understand better before I can comment.

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I realized we might need it because @\eevee was discussing some physics they were doing and one of the steps involved projecting the momentum onto the ground. (They were dealing with momentum going over a hill causing the character to catch some air.)

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That's a good enough reason to add some kind of projection method, so good even if I don't grok it yet.

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