lilypond-devel
[Top][All Lists]

## Re: [PATCHES] Re: Harp Pedals?

 From: Trevor Daniels Subject: Re: [PATCHES] Re: Harp Pedals? Date: Fri, 29 Aug 2008 09:03:24 +0100

```Carl

Why not use an ellipse that just fits _inside_ the rectangle?

The values of x-extent and y-extent of the grob are also given
immediately.

Trevor, puzzled ||%-/

```
```Cc: <address@hidden>
Sent: Friday, August 29, 2008 4:17 AM
Subject: Re: [PATCHES] Re: Harp Pedals?

I want the equation of an ellipse that circumscribes a box 2a by 2b.

needs to pass through the points (a,b), (-a,b), (a,-b), (-a,-b).

Because of the squared terms, all four points have the same equation.

There is an infinite number of ellipses that circumscribe the ellipse.

I want one with the aspect ratio being the same as the box.  So my second
equation is

Solve for a.

substitute into equation (1)

By symmetry, xrad = sqrt(2) a.

Your counterexample didn't apply because of the 0 in the denominator.

HTH,

Carl

On 8/28/08 3:42 PM, "Reinhold Kainhofer" <address@hidden> wrote:

```
```-----BEGIN PGP SIGNED MESSAGE-----
Hash: SHA1

Am Donnerstag, 28. August 2008 schrieb Valentin Villenave:
```
```2008/8/19 Carl D. Sorensen <address@hidden>:
```
```I've been looking at ellipse code.  Once I can get rhythms.itely off my
plate (which is waiting on the beatGrouping patch, one way or the other)
I'll add an ellipse in place of the circle.
```
```
I've been looking at a way to draw ellipses, but I've just seen you
have pushed a much better-looking implementation than mine; I hope the
docs will be recompiled soon so we can appreciate your nice ellipse in
the documentation!
```
```
```
Yes, I saw that, too. I even generalized it to allow different paddings in X- and Y-direction. However, what I don't understand about the ellipse code in ellipse-stencil is the factor 0.707 (supposedly from sqrt(2)/2) for x-radius
```and y-radius. If that factor comes from scaling the ellipse so that it
```
surrounds the stencil, then it only works for square stencils, for all other
```stencils it will be too large. As an extreme case consider a line stencil
```
("box" from (0 . -1) to (0 . 1) ). The ellipse will have half-axes of length
```1.414 and 0 (without padding), so in X-direction it will overshoot by far.

```
For a square, of course, the ellipse will degenerate to a circle, touching all
```corners, but for stencils with other rectangular extents, the ellipse will
not touch the corners of the bounding box any more.

Cheers,
Reinhold

- --
- ------------------------------------------------------------------
Reinhold Kainhofer, Vienna University of Technology, Austria
```
* Financial and Actuarial Mathematics, TU Wien, http://www.fam.tuwien.ac.at/
``` * K Desktop Environment, http://www.kde.org, KOrganizer maintainer
* Chorvereinigung "Jung-Wien", http://www.jung-wien.at/
-----BEGIN PGP SIGNATURE-----
Version: GnuPG v1.4.6 (GNU/Linux)

iD8DBQFItxvJTqjEwhXvPN0RAp3YAKDPLWkKDtIwL9kXJ2ewllV145hAiQCfcgtJ
9HT0TA/6i916CtT0vlnWZUk=
=UbNn
-----END PGP SIGNATURE-----
```
```

_______________________________________________
lilypond-devel mailing list