"Bald Eagle" <cre### [at] netscapenet> wrote:

> r0 = P.x * D.z - P.z * D.x;
> and that is only multiplied by the y unit basis vector,
> so since there are no other dimensional units, this directly evaluates to the
> length of the perpendicular y vector, and we don't have to do the expensive
> square root of the sum of the squares.
>
> a is the squared length of the [NORMALIZED and PROJECTED] direction vector
> which, if non-zero, the vector cross product length gets divided by,
> which should be the shortest, perpendicular length.

So what happens is that the "perp dot product" is essentially taking one vector,
rotating it counterclockwise by 90 degrees, and then taking the dot product,
which projects one vector onto the other.
This gives its projected length along the other vector.

And that's supposed to give the perpendicular, shortest distance between the
origin and the ray.

Diagrammatically, it's all looking good, but for some strange reason, the
perpendicular distance seems to be shorter than it should be, with the error
increasing the farther away the ray is.

- BW

If anyone has any ideas what the source of this error is, I'm all ears.

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