RE: Vector definition

["Paul Robson" <probson@powerup.com.au>]

Just to confuse you a little more, you can also define a vector in polar
co-ordinates, and this can be useful at times.

eg, the vector K can be defined in either Cartesian coordinates (x,y) or in
polar coordinate (r, theta)  where r is the magnitude and theta is the
angle.  Similarly for 3d coordinates (although I'm not quite sure how polar
coordinates are defined in 3d.. I assume with two angles, one from the x
axis and one from the z)

it is easy enough to convert between the two... :

K(r, theta) <--polar coordinates
is the same as:
K(r*cos(theta), r*sin(theta))  <-- Cartesian coordinates

just an extra little note for anyone interested :)

I could have the cos and sin mixed up.. but I think I'm right.  cos is
always x and sin is y.  wasn't Pythagoras just a genius??

Paul Robson

> -----Original Message-----
> From: gameprogrammer-owner@gameprogrammer.com
> [mailto:gameprogrammer-owner@gameprogrammer.com]On Behalf Of Kamel
> Serend
> Sent: Tuesday, September 21, 1999 12:10
> To: gameprogrammer@gameprogrammer.com
> Subject: Vector definition
>
>
> Hi Philippe,
>
> A vector is a mathematical object. We usually represent it using
> a sort of arrow. A vector is
> thus defined by its length (or magnitude), its direction (the
> line supporting it), and its
> orientation (positive or negative compared with the progression
> of the line).
> As you can imagine, if we note K a vector, the vector that is
> twice as long will be 2*K or 2K
> in short. We say that the two vectors are colinear because they
> can define the same line. A
> trick: K and -K are also colinear, even if they do not have the
> same orientation.
> A vector is useful to define a line. all you need is then this
> vector and a point belonging to
> the line.
> A vector is defined also as two extremities A and B (for
> instance). A and B can be two points
> in either 2D or 3D. The resulting vector will then have the
> following co-ordinates:
>     K=AB=(xb-xa, yb-ya, zb-za) in the 3D vector/points case, and
>     K=AB=(xb-xa, yb-ya) in the 2D vector/points one.
>
> Apart from that, vectors are also used to compute angles between
> lines, or between lines and
> planes (CF ray-tracing), we can also use them to define matrices
> as an association of vectors,
> and positions (a point can be a vector with its origin in O(0,0,0)).
> If you want any other information, let me know.
>
> Kamel.
>
> PHILIPPE NGUE wrote:
>
> > Hi
> > i don't know what's a vector?. I don't know anything about programming.
> > i know how to use karel,beeper,wall,and turbo pascal,robotical
> that's the only thing i know
> >
> > So teach me.
> >
> > Thanks
> >
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