Find a way to make circles of a given radius using characters in a console. Please specify the font name and size. Also, please provide at least one example of the output.
For example:
Input:
3
Output:
******
** **
** **
* *
** **
** **
******
...Well, something better looking than that "hand drawn" "circle" with a radius of 3.
Bonus question: Ellipses. :)
The Bresenham - algorithm has 2 major points:
How to do it:
2 1
DCBABCD
GFE | EFG
IJ y|----JI
GJ | /JG
F | / |F
DE | r/ |ED
C | / | C
B 4 |/ | B 3
A +-------A
B 4' x B 3'
C C
DE ED
F F
GJ JG
IJ JI
GFE EFG
DCBABCD
2'1'
This isn't code golf, but all those numbers at the top of the existing solutions made me think it is, so I spent useless time in golfing my solution. Therefore I added a useless number at the top too. It's 11 times Pi rounded.
object BresenhamCircle extends App {
var count = 0
val r = args(0).toInt
// ratio > 1 means expansion in horizontal direction
val ratio = args(1).toInt
val field = ((0 to 2 * r).map (i=> (0 to 2 * r * ratio).map (j=> ' ').toArray)).toArray
def square (x: Int, y: Int): Int = x * x + y * y
def setPoint (x: Int, y: Int) {
field (x)(y*ratio) = "Bresenham"(count)
field (y)(x*ratio) = "Bresenham"(count)
}
def points (x: Int, y: Int)
{
setPoint (r + x, r + y)
setPoint (r - x, r + y)
setPoint (r + x, r - y)
setPoint (r - x, r - y)
}
def bresenwalk () {
var x = 0;
var y = r;
val rxr = r * r
points (x, y);
do
{
val (dx, dy) = { if (math.abs (rxr - square ((x+1), y)) < math.abs (rxr - square (x, (y-1))))
(1, 0)
else
(0, -1)
}
count = (count + 1) % "Bresenham".length
x += dx
y += dy
points (x, y)
}while ((x <= y))
}
bresenwalk ()
println (field.map (_.mkString ("")).mkString ("\n"))
}
The font-question is decided by sites webserver and your browser settings. Now, that I'm looking it is
'Droid Sans Mono',Consolas,Menlo,Monaco,Lucida Console,Liberation Mono,DejaVu Sans Mono,Bitstream Vera Sans Mono,Courier New,monospace,serif
Font-size is 12px. Pretty useless information, if you ask me, but who does?
Bonus: ellipses and sample output:
The invocation is
scala BresenhamCircle SIZE RATIO
for example
scala BresenhamCircle 10 2
s e r B r e s
h n e e n h
e m a a m e
e r r e
m m
h a a h
n n
s e e s
e e
r r
B B
r r
e e
s e e s
n n
h a a h
m m
e r r e
e m a a m e
h n e e n h
s e r B r e s
A ratio of 2 will print a circular shape for most fonts which happen to be about twice as tall than wide. To compensate for that, we widen by 2.
# As smaller value than 2 only 1 is available:
scala BresenhamCircle 6 1
erBre
aes sea
ah ha
e e
es se
r r
B B
r r
es se
e e
ah ha
aes sea
erBre
# widening it has more freedom:
scala BresenhamCircle 12 5
s e r B r e s
a h n e e n h a
B m m B
e r r e
e s s e
B r r B
a m m a
h h
n n
s e e s
e e
r r
B B
r r
e e
s e e s
n n
h h
a m m a
B r r B
e s s e
e r r e
B m m B
a h n e e n h a
s e r B r e s
I restricted the ratio parameter for Int to keep it simple, but it can easily be widened to allow floats.
function c(r){var f=1.83;var e=2*Math.PI/(r*r*r*r*r);var s=r*2+1;var g=Array(s);for(var i=0;i<s;i++){g[i]=Array(Math.round(s*f))};for(var i=0;i<=2*Math.PI;i+=e) {var x=Math.round(f*r*Math.cos(i)+f*r);var y=Math.round(r*Math.sin(i))+r;g[y][x]=1;}for(var j=0;j<g.length;j++){for(var i=0;i<g[j].length;i++)document.write((g[j][i]==1)?'*':' ');document.writeln()}}
http://jsfiddle.net/YssSb/3/ (f is a correction factor for the line-height / font-width ratio. If you use a square font setting, i.e., set line-height = font-size, you can set f=1 and get "square" circles. Or set f arbitrarily for ellipses.)
Output for 3 (interestingly enough, accidentally exactly the same shape as OP), 5, 15:
******
** **
** **
* *
** **
** **
******
*********
*** ****
*** **
** **
* *
* *
* *
** **
*** **
*** ****
*********
***************
****** ******
**** *****
*** ***
*** ***
*** ***
** **
** **
** **
** **
** **
* *
** **
* *
* *
* *
* *
* *
** **
* *
** **
** **
** **
** **
** **
*** ***
*** ***
*** ***
**** *****
****** ******
***************
172 chars including the two mandatory newlines. Uses the Bresenham algorithm for conic curves (no divisions or multiplications); it only outputs circles for square fonts, but should be exempt from staircase effects (ie. always has the same width).
y=input();t=[y*[' ']for x in range(y)];x=0;y-=1;p=3-2*y
while x<=y:t[x][y]=t[y][x]='*';n,y=((x-y+1,y-1),(x,y))[p<0];p+=4*n+6;x+=1
for s in t[::-1]+t:print"".join(s[::-1]+s)
Not very pretty, but well, I thought I'd give it a shot.
****
* *
* *
* *
* *
* *
* *
****
********
*** ***
* *
* *
* *
* *
* *
* *
* *
* *
* *
* *
* *
* *
* *
* *
* *
* *
* *
* *
* *
* *
* *
* *
* *
* *
*** ***
********
Edit: typo, replaced addition with division.
I went for the “bonus question” and made it exploit the character aspect ratio to draw ellipses :)
($w)=@ARGV;for$x(-$w..$w){$p.=abs($x*$x+$_*$_-$w*$w)<$w?'*':$"for(-$w..$w);$p.=$/;}print $p;
Example outputs:
>perl circle.pl 3
***
* *
* *
* *
* *
* *
***
>perl circle.pl 5
*****
* *
* *
* *
* *
* *
* *
* *
* *
* *
*****
>perl circle.pl 8
*****
** **
* *
* *
* *
* *
* *
* *
* *
* *
* *
* *
* *
* *
* *
** **
*****
g n=map(zipWith(?)f.repeat)f where x?y|abs(x^2+y^2-n^2)<n='*'|0<1=' ';f=[-n..n]
main=interact$unlines.g.read
This works by checking, whether x² + y² - r² < n for all points. All points for which this is true are stars, all others are blanks.
$ echo 3 | runhaskell circ.hs
***
* *
* *
* *
* *
* *
***
$ echo 10 | runhaskell circ.hs
*******
** **
* *
* *
* *
* *
* *
* *
* *
* *
* *
* *
* *
* *
* *
* *
* *
* *
* *
** **
*******
See here for big example: http://www.ideone.com/t042u
This code makes circles if the font is square. It's pretty easy to modify to generate nominal ellipses if you know your font height/width ratio.
import math
r=input()
d=2*r+1
c=[' '*d]*d
for a in xrange(9*d):f=math.pi*a/r/9; x=int(r+r*math.sin(f)+.5);y=int(r+r*math.cos(f)+.5);c[y]=c[y][:x]+'*'+c[y][x+1:]
for s in c:print s
Examples:
4:
*****
** **
** **
* *
* *
* *
** **
** **
*****
7:
*****
** **
** **
** **
** **
* *
* *
* *
* *
* *
** **
** **
** **
** **
*****
#include<math.h>
main(){int r=10,c=r*2+1,q=c*c,d;for(;q--;)d=hypot(r-q%c,r-q/c),printf("%c%s",d>r-4&&d<=r?42:32,q%c?"":"\n");}
Result:
*********
*************
***************
*****************
****** ******
***** *****
***** *****
**** ****
**** ****
**** ****
**** ****
**** ****
**** ****
**** ****
***** *****
***** *****
****** ******
*****************
***************
*************
*********
