Re: How to put text on a curved surface?

• To: mathgroup at smc.vnet.net
• Subject: [mg87238] Re: How to put text on a curved surface?
• From: Narasimham <mathma18 at hotmail.com>
• Date: Sat, 5 Apr 2008 04:22:17 -0500 (EST)
• References: <fsvels\$sto\$1@smc.vnet.net> <ft2aok\$pbg\$1@smc.vnet.net>

```On Apr 3, 3:15 pm, Narasimham <mathm... at hotmail.com> wrote:
> On Apr 2, 1:04 pm, P_ter <peter_van_summe... at yahoo.co.uk> wrote:
>
> > I would like to put "Mathematica" on a curved surface, e.g. a torus.
> > Can anyone help here?
> > with friendly greetings,
> > P_ter
>
> You mean the projected/mapped letters should be curved ? Try
> projecting stencil slots onto the torus from a suitable bright point
> as light source, which can be even at infinity.. as intersection with
> the conical rays.

It should be mentioned that the mapping can never be faithful ( per
isometric mappings between flat to flat or curvrd to curved surfaces )
as there is bound to be alteration due to:

1) magnification/reduction ( strain of tension or compression),

2) distortion ( angle changes in shear).

It is in other words so stated by Gauss Egregium theorem. After
writing or printing the text on a flat label when you try to stick it
on a torus of suitable size, a tendency to tear on areas outside the
crown (Gauss Curvature > 0) and some folds/frills on the inside ( G.C
< 0) is inevitable. The most faithful reproduction takes place at the
crown ( G.C ~ 0).

```

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