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: <firstname.lastname@example.org> <email@example.com>
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).