# 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

only have to solve one quadratic equation in r, the radius

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

(upm). Adobe Reader exhibits a strange behaviour with

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
**abstract:**This article describes some recent contributions to the

CTAN archive (and other internet sources.) The selection

reflects what interests me and what I think others may

be interested in. It is, therefore, a personal choice,

not a comprehensive review.- 40/08.pdf (1035kb)