# Circular arc approximation by cubic Bezier curve

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Approximating a circular by a single Bezier curve only is sufficiently exakt if the arc is less or equal than a quarter circle.

### The underlying JavaScript code

var brd = JXG.JSXGraph.initBoard('jxgbox',{axis:false,boundingbox:[-2,2,2,-2],keepaspectratio:true});

var M = brd.create('point', [0,0], {name:'M'});
var C = brd.create('point', [0,-1], {name:'D'});
var c = brd.create('circle', [M,C], {strokeWidth:1});
var A = brd.create('glider', [1,0,c], {name:'A'});
var B = brd.create('glider', [0,1,c], {name:'B'});

var k = function(M, A, B) {
var ax = A.X()-M.X(),
ay = A.Y()-M.Y(),
bx = B.X()-M.X(),
by = B.Y()-M.Y(),
d, r;
r = M.Dist(A);
d = Math.sqrt((ax+bx)*(ax+bx) + (ay+by)*(ay+by));
if (JXG.Math.Geometry.rad(A,M,B)>Math.PI) { d *= -1; }

if (Math.abs(by-ay)>JXG.Math.eps) {
return (ax+bx)*(r/d-0.5)*8.0/3.0/(by-ay);
} else {
return (ay+by)*(r/d-0.5)*8.0/3.0/(ax-bx);
}
};
var P1 = brd.create('point', [
function(){ return A.X()-k(M,A,B)*(A.Y()-M.Y()); },
function(){ return A.Y()+k(M,A,B)*(A.X()-M.X()); }
], {color:'blue'});
var P2 = brd.create('point', [
function(){ return B.X()+k(M,A,B)*(B.Y()-M.Y()); },
function(){ return B.Y()-k(M,A,B)*(B.X()-M.X()); }
], {color:'blue'});

var b = brd.create('curve', JXG.Math.Numerics.bezier([A,P1,P2,B]),
{strokecolor:'black', strokeOpacity:1, strokeWidth:3});

var l1 = brd.create('segment', [A,P1], {dash:2});
var l2 = brd.create('segment', [B,P2], {dash:2});