Perl - 388 characters
Since it wouldn't be fair to pose a challenge I couldn't solve myself, here's a solution that uses string substitution instead of trigonometric functions, and making heavy use of your friendly neighbourhood Perl's ability to treat barewords as strings. It's necessarily a little long, but perhaps interesting for the sake of uniqueness:
($x,$y,$r)=split/\D/,<>;for(0..$r-1){$t=$r-1-$_;
$a.=L x$_.D.K x$t.C.J x$t.B.I x$_."\n";
$b.=M x$t.F.N x$_.G.O x$_.H.P x$t."\n"}
$_=$a.E x$r.o.A x$r."\n".$b;$x/=45;$y/=45;$S=' ';
sub A{$v=$_[0];$x==$v||$y==$v?$_[1]:$x<$v&&$y>$v?x:$S}
sub B{$x<=$_[0]&&$y>$_[0]?x:$S}
@a=!$x||$y==8?'-':$S;
push@a,map{A$_,'\\'.qw(- / | \\)[$_%4]}1..7;
push@a,!$x?x:$S,map{B$_}1..7;
eval"y/A-P/".(join'',@a)."/";print
All newlines are optional. It's fairly straightforward:
- Grab user input.
- Build the top (
$a) and bottom ($b) parts of the pattern.
- Build the complete pattern (
$_).
- Define a
sub A to get the fill character for an angle.
- Define a
sub B to get the fill character for a region.
- Build an array (
@a) of substitution characters using A and B.
- Perform the substitution and print the results.
The generated format looks like this, for R = 4:
DKKKCJJJB
LDKKCJJBI
LLDKCJBII
LLLDCBIII
EEEEoAAAA
MMMFGHPPP
MMFNGOHPP
MFNNGOOHP
FNNNGOOOH
Where A-H denote angles and I-P denote regions.
(Admittedly, this could probably be golfed further. The operations on @a gave me incorrect output when written as one list, presumably having something to do with how map plays with $_.)
