#1に答えるために、パス内のランダムなポイントを見つけるためのそれほど優れていない方法があります:http://jsfiddle.net/Aj7Rw/
var points = [[73, 192],
[73, 160],
[340, 23],
[500, 109],
[499, 139],
[342, 93]],
minX,maxX,minY,maxY;
// find min and max values
for (var i = 0; i < points.length; i++){
var point = points[i];
if (minX == undefined || point[0] < minX)
minX = point[0];
if (maxX == undefined || point[0] > maxX)
maxX = point[0];
if (minY == undefined || point[1] < minY)
minY = point[1];
if (maxY == undefined || point[1] > maxY)
maxY = point[1];
}
// draw the path so we can use isPointInPath
var can = document.getElementById("test"),
ctx = can.getContext('2d');
ctx.beginPath();
ctx.moveTo(points[0][0],points[0][1]);
for (var i = 1; i < points.length; i++)
ctx.lineTo(points[i][0],points[i][1]);
ctx.closePath();
ctx.stroke();
// generate some random points.
for (var i = 0; i < 250; i++){
var found = false, iterations = 0;
while(!found){
iterations++;
var x = Math.floor(Math.random()*(maxX-minX)+minX);
var y = Math.floor(Math.random()*(maxY-minY)+minY);
if (ctx.isPointInPath(x,y)){
found = true;
ctx.fillRect(x-3,y-3,6,6);
console.log(x,y, iterations); // I'm logging the number of iterations it took to generate a point within the poly so you can get an idea of the lack of efficiency.
}
}
}