javascript - Extract vertices from an ARC in generic way -

i want vertices arc. have data (for ex : start point, end point, start angle, end angle, radius) used draw arc need have generate vertices arc data.

i have tried 1 or 2 algorithm failed exact vertices arc data.

i used bresenham's algorithm failed.

right using below code not working ..

            double theta = 2 * 3.1415926 / 100;              double c = math.cos(theta);             double s = math.sin(theta);             double t;              double x = ((arcto) element).getradius();//we start @ angle = 0              double y = 0;               for(int ii = 0; ii < 100; ii++) {                coordinates.add(new coordinate(x + element.getcenterpoint().getx(), y + element.getcenterpoint().gety()));//output vertex                 //apply rotation matrix               t = x;               x = c * x - s * y;               y = s * t + c * y;             } 

please me. thank you.

1. first clarifications

   i assume vertices mean pixels , arc standard 2d circular arc (not elliptic arc !!!) , input data are:

   int (x0,y0),(x1,y1) // star/end points on curve !!! float a0,a1         // start end angles [rad] int (xc,yc)         // center of circle int r               // radius 

2. do not use bresenham

   because need start 0 angle , compute pixels until start point hit. flip draw flag start filling pixel point , stop on end point hit. need handle winding match arc direction.

3. you can use circle parametric equation

   // arc data test float r=25.0; float a0= 45.0*m_pi/180.0; float a1=270.0*m_pi/180.0; int xc=100,x0=xc+floor(r*cos(a0)),x1=xc+floor(r*cos(a1)); int yc=100,y0=yc+floor(r*sin(a0)),y1=yc+floor(r*sin(a1)); // arc rasterize code int x,y; float a,da; // here draw pixels x0,y0 , x1,y1 avoid rounding holes ... if (r) da=0.75/float(r); else da=0.1; // step less pixel avoid holes (a=a0;;a+=da)  {  x=xc+int(floor(r*cos(a)));  y=yc+int(floor(r*sin(a)));  // here draw pixel x,y  if ((x==x1)&&(y==y1)) // stop if endpoint reach   if (fabs(a-a1)<da)   // ignore stop if not @ end angle (full or empty circle arc)    break;  } 

   may round instead of floor have less pixel position error. if endpoint not match loop infinitely. if tweak bit end conditions can avoid or recompute x1,y1 a1 have ...

4. you can use equation (x-xc)^2+(y-yc)^2=r^2

   you need divide arc quadrants , handle each separate arc looping through x or y , computing other coordinate. loop through coordinate changing more

   

   so in blue areas loop y , in red loop x. example red area code can this:

   int x,y; (x=_x0;;x++)  {  y=sqrt((r*r)-((x-xc)*(x-xc)));  // here draw pixel x,y  if (x==_x1) // stop if endpoint reach   break;  } 

   you need compute (_x0,_y0),(_x1,_y1) start end points of cut part of arc inside quadrant , make _x0<=_x1.

   
   the value _x looped start/end point coordinate xc +/- sqrt(r) or x0 or x1
   the value _y looped start/end point coordinate yc +/- sqrt(r) or y0 or y1

   the blue parts done in analogically manner (just swap/replace x , y). approach bit more complicated due cutting can done solely on integers. sqrt can speed lut (limiting max radius) , ^2 can further optimized.

[notes]

so if recapitulate parametric equation simplest implement slowest. sqrt approach can done fast bresenham (and may faster lut) need code cutting arc quadrants need few ifs prior rendering.

all codes in c++ , can further improved avoiding int/float conversions, pre-compute values before loop, etc ...

the last goes bresenham need change few things inside , when not know doing can lost. need cut octant's complexity of change far bigger sqrt approach