drawing curves with visible dots

[Ralf Hemmecke]

It is somewhat related to the production of the book, but it is an issue
maybe deserves its own thread.

When running

vp:=draw(cos(5*t/8),t=0..16*%pi,coordinates==polar)

the output is the picture from chapter 1.4 of the book.

What bothers me, is the visible red dots. Maybe these points are needed
to actually draw the curve, but why must they be visible? And even in
red? In the Jenks&Sutor book the graphics is black and white, but I
cannot find visible dots.

I can remove the points via

points(vp,1,"off")

but I wonder why the drawing default is not "off".

Unfortunately, I also haven't yet found a way to change the commands in
the book such that I could simply rewrite the draw command to something like

draw(..., points=="off")

in order to achieve a better output for the picture in the book.
Yes, I can add points(vp,1,"off") silently during the automatic picture
generation, but that would be lying to the reader. The command in the
book would not agree with the shown picture. I rather argue that
points=="off" should be the default.

Opinions?

Ralf

[Waldek Hebisch]

On Sat, Jun 22, 2024 at 11:47:22AM +0200, Ralf Hemmecke wrote:
> It is somewhat related to the production of the book, but it is an issue
> maybe deserves its own thread.
>
> When running
>
> vp:=draw(cos(5*t/8),t=0..16*%pi,coordinates==polar)
>
> the output is the picture from chapter 1.4 of the book.
>
> What bothers me, is the visible red dots. Maybe these points are needed to
> actually draw the curve, but why must they be visible? And even in red? In
> the Jenks&Sutor book the graphics is black and white, but I cannot find
> visible dots.
>
> I can remove the points via
>
> points(vp,1,"off")
>
> but I wonder why the drawing default is not "off".

I agree that without points graphs look nicer. But points may
give valuable information, in particular heavy concentration
of points indicates numerical instability (bad conditioning).
And of course points tell you which values were computed and
which are merely interpolation.


--
Waldek Hebisch

[Ralf Hemmecke]

> I agree that without points graphs look nicer.

Certainly.

> But points may give valuable information, in particular heavy
> concentration of points indicates numerical instability (bad
> conditioning). And of course points tell you which values were
> computed and which are merely interpolation.

I do not question that. My point is

(a) dots seem to be slightly "visually out-of-place" (i.e. not
really on the curve). Or they are drawn too fat.
(b) The default should be "points=off". The user can turn points on
using the 2D control panel.

Unfortunately, I cannot simply give another option to draw, to turn of
points. I only know to kill them after creating the viewport. Any idea
how to achieve the graph directly without points by just *one* command.

Ralf