On Thu, May 04, 2023 at 08:02:38AM +0000, '68th' via FriCAS - computer algebra
system wrote:
> On Wednesday, May 3rd, 2023 at 7:48 PM, Waldek Hebisch
> [email protected] wrote:
>
> > There is also another thing: when given option 'polar' our code
> > treat treats argument and function as giving polar coordinates
> > and transforms this to cartesion.
>
> that's right. you can transform one pair of coordinates from the polar or
> elliptic coordinate system to the Cartesian one. i guess that's what
> polar(pt) and elliptic(a) functions from the CoordinateSystems package do.
>
> > However, I understand "drawing
> > curve in polar coordinates" as producting curve in cartesian
> > coordinates and then transforming this to polar coordinates, that
> > is reverse of transformation our code is doing.
>
> what do you mean by producing a curve?
Here by curve I mean set of points. Of course normally such sets
are infinite so we need some internal representation (which for
plotting is only approximate).
> how is that different from the above-mentioned transformation of coordinates?
Curve is an abstract object which exist independenty of any coordinates.
To draw it we use coordinates, so we need to compute coordinates of
points. So "drawing curve in polar coordinates" means that we need
to compute polar coordinates of each point, and draw pixel with
computed coordinates (again this for each point of curve).
As I wrote above, we need some way to represent curves and points.
We use coordinates for this, this time cartesion coordinates.
That is why "drawing in polar coordinates" involves transformation
from cartesion coordiantes to polar coordinates.
--
Waldek Hebisch
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