Missing impl: Mul for Affine * Vec2

[waywardmonkeys]

@crockeo pointed out that there's no impl Mul for Affine and Vec2.

[raphlinus]

Yeah, this is on purpose. The mathematical meaning is ambiguous. Is it the same as Point, or does only the matrix apply and not the translation?

[waywardmonkeys]

The code they had (using their own multiply):

pub fn arrow(from: Point, to: Point) -> [Line; 3] {
    let backwards_direction = (from.to_vec2() - to.to_vec2()).normalize();

    let clockwise_arm =
        to + (Mat2::rotate(ARROW_ARM_ANGLE) * backwards_direction * ARROW_ARM_LENGTH);
    let anticlockwise_arm =
        to + (Mat2::rotate(-ARROW_ARM_ANGLE) * backwards_direction * ARROW_ARM_LENGTH);

    [
        Line::new(from, to),
        Line::new(to, clockwise_arm),
        Line::new(to, anticlockwise_arm),
    ]
}

[raphlinus]

I think the principled way to do this is to_point() on backwards_direction.

[crockeo]

Your explanation of why one wouldn't implement Mul between Affine and Vec2 makes sense, thanks! This was more or less my gut feeling, but I took linear algebra years ago so I wasn't confident anymore 😅.

To me the "nicest" implementation would be to use Affine directly to express the transform:

• Translate to by backwards_direction * ARROW_ARM_LENGTH to make a point p.
• Rotate p about to by +/- ARROW_ARM_ANGLE to create the ends of the arrow arms.

I didn't figure out the math at the time, but I was planning on giving it another go whenever I get around to that TODO.

[raphlinus]

I think I'll close this, as there isn't consensus it should be part of the API, and it seems like there's another way to get the same effect. Thanks for the input!