在 HTML 5 画布上创建 Reuleaux 多边形的函数

var taget = document.getElementById('target');
var context = target.getContext('2d');

var sides = 3;
var radius = 100;
var center = new Position(150,150);

// normal polygon
context.beginPath();
draw_sharp_polygon(center, radius, sides);
context.strokeStyle = 'silver';
context.stroke();

// circle
context.beginPath();
context.arc(center.x, center.y, radius, 0, 2*Math.PI, false);
context.strokeStyle = 'silver';
context.stroke();

// reuleaux polygon
context.beginPath();
draw_reuleaux_polygon(center,radius,sides);
context.strokeStyle = 'black';
context.stroke();

function Position(x, y)
{
    this.x = x || 0;
    this.y = y || 0;
}

function draw_reuleaux_polygon(center_position, radius, number_of_sides)
{
    if(typeof center_position == 'undefined')
        throw new Error("center_position not defined");
    if(typeof radius == 'undefined')
        throw new Error("radius not defined");
    if(typeof number_of_sides == 'undefined' || number_of_sides < 3)
        throw new Error("number_of_sides not defined");

    context.moveTo(center_position.x + radius, center_position.y);
    for (var index1 = 0; index1 < number_of_sides; index1++)
    {
        // point 1 = arc start
        // point 2 = tangent intersection
        // point 3 = arc end
        var index2 = (index1 + 0.5) % number_of_sides;
        var index3 = (index1 + 1) % number_of_sides;
        var angle1 = index1*2*Math.PI/number_of_sides;
        var angle2 = index2*2*Math.PI/number_of_sides;
        var angle3 = index3*2*Math.PI/number_of_sides;
        var p1 = new Position(center_position.x + radius*Math.cos(angle1), center_position.y + radius*Math.sin(angle1));
        var p2 = new Position(center_position.x + radius*Math.cos(angle2), center_position.y + radius*Math.sin(angle2));
        var p3 = new Position(center_position.x + radius*Math.cos(angle3), center_position.y + radius*Math.sin(angle3));

        var reuleaux_radius = radius*Math.sqrt(2 + 2*Math.cos(Math.PI/number_of_sides));
        
        context.arcTo(p2.x, p2.y, p3.x, p3.y, reuleaux_radius);
    }
    
    context.closePath();
}

function draw_sharp_polygon(center_position, radius, number_of_sides)
{
    if(typeof center_position == 'undefined')
        throw new Error("center_position not defined");
    if(typeof radius == 'undefined')
        throw new Error("radius not defined");
    if(typeof number_of_sides == 'undefined' || number_of_sides < 3)
        throw new Error("number_of_sides not defined");
    
    context.moveTo(center_position.x + radius, center_position.y);
    var circular_angle_division = (Math.PI * 2)/number_of_sides;
    for(var i = 1; i < number_of_sides; i++)
    {
        var x = center_position.x + radius * Math.cos(circular_angle_division * i);
        var y = center_position.y + radius * Math.sin(circular_angle_division * i);
        console.log(i,x,y);
        context.lineTo(x,y);
    }
    
    context.closePath();
}

<canvas id="target" width="300" height="300"></canvas>