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Re: [FT][computer] Has anyone considered...

From: Tony Francis <tony.francis@k...>
Date: Mon, 11 Sep 2000 13:00:24 +0100
Subject: Re: [FT][computer] Has anyone considered...
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"Bell, Brian K" wrote:

> My math skills must be lacking or I misunderstood your post
>
> How does sqrt(x*x+y*y+z*z) give you a vector

Don't worry, it's me, I've not been clear enough. The velocity vector of
the
ship is stored as the vector [x y z] which represents the distance the
ship
moves in one second. The length of this vector is then equal to the
above
formula, which is also the velocity of this ship.

> Unless you meant sqrt(x1*x2+y1*y2+z1*z2) where x1,y1,z1 represents the
> starting point of your last move and x2,y2,z2 represents the end point
of
> your last move (x1 should be x sub 1, and x2 should be x sub 2, etc.
but
> plain text is limiting).
>
> If sqrt(x1*x2+y1*y2+z1*z2) is what you meant, then you still have to
> maintain
> 3 variables previous x, y, & z (instead of 360x,360y,Velocity).

In fact you only need store [180x 360y Vely].

I agree about storage of the same number of variables, but the maths is
much
simpler if the course is stored as a vector.

[Example]

The VKK Lenin is flying through space at a constant 100m/s and applies a
right
push using its manouevering thrusters. Under your system we'd store the
course
as (say) [0.0deg, 45.0deg, 100.0]. Under my system we'd store [70.71,
0.0,
70.71]. The push is equivalent to a 10m/s push to the right - under your
system
this would be [0.0deg, 135.0deg, 10.0], under mine [7.07, 0.0, -7.07].

To derive the final velocity under my system you simply add the vectors
together
to get [77.78, 0.0, 63.64]. Under yours ... errr, I'll let you work it
out (any
solution I derive would involve converting your course format into a
vector,
calculating the sum and converting it back again). The answer is
[0.0deg,
50.71deg, 100.49] (I think - it's Monday and I've just done this on a
scrap of
paper).

[Quick list of assumptions for anyone who wants to try this for
themselves. I
work in a universe with left-hand rule axes, eg +ve X is right, +ve Y is
up, +ve
Z is forward. I've assumed instantaneous application of the push vector,
eg no
acceleration / momentum problems. Under Brian's system I've taken X
rotation to
be pitch and Y rotation to be azimuth which corresponds with the left
hand rule
axes.]

[/Example]

An additional problem with your system that's just occurred to me is one
of
ambiguity. A course of [90deg 0deg 100] actually gives the same result
as one of
[90deg 90deg 100], or in fact [90deg ANYdeg 100]. This may or may not be
a
problem depending on what you want to do with the course.

Tony
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