Question

I need to draw a polygon in Pascal(dev-pascal) which has semicircles at its sides. I’ll give the code I have come up so far. It has diagonals too.

uses crt,graph;
var a,b:smallint;
    x0,y0,n,j,k,r:integer;
    xevi,yoni:array[1..50] of integer;
    i:real;

begin
 write('n?.. ');readln(n);
 detectgraph(a,b);
 initgraph(a,b,'');
 x0:=getmaxx div 2;
 y0:=getmaxy div 2;
 j:=0;
 i:=0;
 repeat
  inc(j);
  xevi[j]:=trunc( x0+200*cos(i) );
  yoni[j]:=trunc( y0-200*sin(i) );
  i:=i+2*pi/n;
 until i>2*pi;


 r:=trunc( sqrt( sqr((xevi[1]-xevi[2])) + sqr((yoni[1]-yoni[2])))) div 2;

 for j:=1 to n do begin
    if (xevi[j+1]-xevi[j])<>0 then begin
    k:=trunc( arctan(
    //abs(
    ((yoni[j+1]-yoni[1])/(xevi[j+1]-xevi[j])-1)
    /(1+(yoni[j+1]-yoni[1])/(xevi[j+1]-xevi[j]))
    //)
    )*180/pi); end
    else k:=90;
    if k>0 then arc( (xevi[j]+xevi[j+1]) div 2, (yoni[j]+yoni[j+1]) div 2, k, k+180, r )
           else begin
                k:=360+k;
                if k+180>360 then k:=360-k;
                arc( (xevi[j]+xevi[j+1]) div 2, (yoni[j]+yoni[j+1]) div 2, k, k+180, r );
                end;

 end;


 for j:=1 to n do
     for k:=1 to n do
         line( xevi[j],yoni[j],xevi[k],yoni[k]);


 readln;
 closegraph;
end.

As you can see, I tried using analytic geometry to find the slope between two adjacent vertices of the polygon, then calculating the angle of a line with that slope, and then using the angle to draw an arc.

So basically, I don’t know why it doesn’t work, and I’m also sure there’s a much simpler way to do it! Any help at all will be appreciated!

Thank you!

Answer 1

i don’t know pascal so will just use pseudo-code.

x0, y0 = ... # one end of side
x1, y1 = ... # other end of side
x, y = (x0 + x1) / 2, (y0 + y1) / 2 # midpoint
angle1 = atan2(y0 - y, x0 - x) # angle from midpt back to start
angle2 = atan2(y1 - y, x1 - x) # angle from midpt forwards to end

given that, the call to arc should be either:

arc(x, y, angle1, angle2)

or

arc(x, y, angle1, angle1 + 180)

and i think you shouldn’t need to adjust for different angles.

this is very similar to what you have, except that you have some strange +1 and -1 values in your atan2, and you shouldn’t need to worry so much about the angle.