supply issues

I’ve had a number of mugs printed by Zazzle, and most of them came out gorgeous; but last summer I was peeved enough by a delivery cock-up to want to take my business elsewhere. Recently I got around to doing something about it, with even more disappointing results.

Threadless would not let me sign up. I can’t tell which of my address, handle and password offends it, let alone how.

Cafepress failed to upload my design.

Spreadshirt and CustomInk cannot do a wraparound design on a mug.

Who else is out there? Maybe I have cooled off enough to go back to Zazzle.

a poster


Sometimes I search my blog for this picture and scratch my head in puzzlement that it’s not here, before remembering that I posted it on Google Plus back when I used that.

So here it is. Stephen Guerin (the shaven one) displays his canvas print of one of my designs.

The colors came out better than I hoped, in stark contrast to a couple of mugs with related designs that I got from the same shop.

Klein bagel, mark N


I’ve had other designs made in steel but not this one. (The sintering leaves the steel highly porous, so liquid bronze is brought in by capillary action to fill it; the result is about three parts steel to two parts bronze – if I understand right. Hence the color.) (Later: I was mistaken: the steel powder is not sintered but glued; I guess the bronze burns away the glue.)

While it was on its way to me, I thought of some improvements. Continue reading “Klein bagel, mark N”

elusive avoidance

I’ve been designing printable models of the Lawson-Klein surface

w = cos(u) cos(2v)
x = cos(u) sin(2v)
y = sin(u) cos(v)
z = sin(u) sin(v)

As you can plainly see, this figure lives in S3 (positively curved 3-space), so stereographic projection can bring it into E3 (Euclidean 3-space) without adding more self-intersections. (It crosses itself at u=nπ.)

To minimize the distortion of the projection, I want the projection center to be as far as possible from the surface. One thing I tried was pursuit: starting with an arbitrary point P in S3 and an arbitrary point L(u,v) in the surface, move (u,v) to bring L closer to P while simultaneously moving P away from L. This gets me nowhere so far: either it fails to converge or P converges to the antipodes of L, which is also in the surface (change u by π).