# MAPS 40

Taco Hoekwater
MAPS 2010.1 (English/Dutch)
MAPS 40, 2010, 1-83
keywords: NTG, MAPS
abstract: NTG's magazine
40/maps.pdf (6323kb)

Taco Hoekwater
Redactioneel (Dutch)
MAPS 40, 2010, 1-1
40/01.pdf (92kb)

Hans Hagen
The font name mess (English)
MAPS 40, 2010, 2-8
keywords: ConTeXt mkiv, luatex, font names
40/02.pdf (53kb)

Kees van der Laan
Circle Inversions (English)
MAPS 40, 2010, 9-65
keywords: Apollonius, Cabri, circle inversion, circle covered by touching circles, circle limit, circle of anti-similitude, Coxeter, Descartes circle theorem, Escher, Java, Mathematica, Metafont, MetaPost, minimal markup, mixed-language programming, orthogonal circles, overloading polymorphic operator, Peaucellier-Lipkin linkage, (partial) pivoting, plain TeX, PostScript library, radical circle, reflection, Rerich, Sandaku, Soddy, solving 3X3 linear equations
abstract: Circle inversions are exercised and drawn with
PostScript operators which are also included in this
plain TeX document. Interesting pictures will be shown,
resulting from inversion of straight line pieces and
other procedures. I demonstrate a way to calculate
the circle of anti-similitude, by which two circles are
inverses of each other. Furthermore, I show how one can
transform two distinct circles into two concentric circles.
How to draw a circle orthogonal to a circle which passes
through one or two points within the circle is done via
the circle inversion technique. The above is generalized
into finding the circle which cuts the boundary at an
arbitrary angle, e.g. 80 degrees, and passes through a
point within the circle. Orthogonal circular arcs can
form an Escher-like grid, as he used in his Circle Limits.
Four variants of the grid of Circle Limits III have been
included. The first cuts the boundary at 80 degrees, the
second at 90 degrees, and the third with a mixture of both.
The fourth is Coxeter's solution. A smiley pattern is
inverted in (orthogonal) circular arcs within a circle
with the aid of PostScript's pathforall by
(repeated use of) circle inversion. How to draw a circle
orthogonal to 1, 2 or 3 other distinct circles is shown.
Apollonius problem is solved by the use of the circle
inversion transformation and also by transforming the 3
quadratic equations into 1 non-linear equation and a 2x2
system of linear equations, and solving these equations
in PostScript and MetaPost. A closer look yielded that we
of the wanted circle, in order to obtain the solution of
Apollonius problem. Coding problems in MetaPost will be
mentioned and circumvented. I demonstrate the way one can
create and use a PostScript library. A plea is made for
creating and maintaining a PostScript library of operators,
graphics and utilities. A snapshot of this growing library
is included. A few tiny but handy PostScript operators
are given next to a (numerical) PostScript operator to
solve a 3x3 linear system of equations, where partial
pivoting is implemented and the calculations are done with
the accuracy of the underlying computer arithmetic, which
is much better than MetaPost's accuracy for the moment. How
to overload a PostScript operator, e.g. length,
is given. The question whether the PostScript library can
be used in MetaPost will be answered. The pearl of the
paper is twofold: first the rediscovery that Apollonius
problem is solved by the solution of a quadratic
equation, and second the operator Apollonius,
which reflects this rediscovery and can be used to obtain
all 8 solutions of Apollonius problem. Another gem is
Apollonius2, which is suited for the case that
one circle contains the other two. The culmination of
it all is the operator radical for drawing the
radical circle of three given distinct circles.
40/03.pdf (2437kb)

(anonymous)
EuroTeX 2010 (English)
MAPS 40, 2010, 66-66
40/04.pdf (324kb)

Hans Hagen
Grouping in hybrid environments (English)
MAPS 40, 2010, 67-71
keywords: ConTeXt mkiv, luatex, grouping, underbar, overbar, overstrike, text backgrounds
40/05.pdf (60kb)

(anonymous)
Announcement: 4th ConTeXt Meeting (English)
MAPS 40, 2010, 72-72
40/06.pdf (2213kb)

Luigi Scarso
OpenType PostScript fonts with unusual units-per-em values (English)
MAPS 40, 2010, 73-79
keywords: LuaTeX, ConTeXt Mark IV, OpenType, FontMatrix.
abstract: OpenType fonts with Postscript outline are usually defined
in a dimensionless workspace of 1000x1000 units per em
pdf documents that embed an OpenType PostScript font with
unusual upm: this paper describes a solution implemented
by LuaTeX that resolves this problem.
40/07.pdf (417kb)

Piet van Oostrum
Een uittreksel uit de recente bijdragen in het CTAN archief (Dutch)
MAPS 40, 2010, 80-83