function drawCircle(x0,y0,r,res) {
  if (res==undefined) res = 50; //circle resolution
  beginShape();
  var step = Math.PI * 2.0 / res;
  for (var a=0; a<Math.PI*2; a+=step) {
    var x = Math.sin(a+Math.PI) * r + x0;
    var y = Math.cos(a+Math.PI) * r + y0;
    if (a==0) shapeMoveTo(x,y);
    else shapeLineTo(x,y);
  }

  //close shape
  var x = Math.sin(0+Math.PI) * r + x0;
  var y = Math.cos(0+Math.PI) * r + y0;
  shapeLineTo(x,y);
  
  endShape();
}

function beginShape(x,y) {
  setSketchModified(true);
}

function shapeMoveTo(x,y) {
  _points.push([x, y, true]);
  adjustBounds(x, y);
  adjustPreviewTransformation();
  draw(x, y, -1);
}

function shapeLineTo(x,y) {
  _points.push([x, y, false]);
  adjustBounds(x, y);
  adjustPreviewTransformation();
  draw(x, y);
}

function endShape() {
  renderToImageDataPreview();
}

function getBounds(points) {    
  var xMin = Infinity, xMax = -Infinity, yMin = Infinity, yMax = -Infinity;
  for (var i=0; i<points.length; i++) {
    var p = points[i];
    xMin = Math.min(xMin,p[0]);
    xMax = Math.max(xMax,p[0]);
    yMin = Math.min(yMin,p[1]);
    yMax = Math.max(yMax,p[1]);
  }
  return {x:xMin,y:yMin,width:xMax-xMin,height:yMax-yMin};
}

function translatePoints(points,x,y) {
  for (var i=0; i<points.length; i++) {
    points[i][0] += x;
    points[i][1] += y;
  }
}

function scalePoints(points,x,y) {
  if (y==undefined) y = x;
  for (var i=0; i<points.length; i++) {
    points[i][0] *= x;
    points[i][1] *= y;
  }
}

function rotatePoints(points, radians, cx, cy) {
  if (cx==undefined) cx = 0;
  if (cy==undefined) cy = 0;

  var cos = Math.cos(radians);
  var sin = Math.sin(radians);

  for (var i=0; i<points.length; i++) {
      var x = points[i][0];
      var y = points[i][1];
      var nx = (cos * (x - cx)) - (sin * (y - cy)) + cx;
      var ny = (sin * (x - cx)) + (cos * (y - cy)) + cy;
      points[i][0] = nx;
      points[i][1] = ny;
  }
}

function moveShape(x,y) {
	var bounds = getBounds(_points);
	var delta = reduceTransformToFit(x, y, 1.0, bounds);
	
	if (delta.x != 0 || delta.y != 0) {
		translatePoints(_points, delta.x, delta.y);
		updateView();
	}
}

//TODO: reduction of zoomValue is still not completely correct (but acceptable?)
//TODO: bounds should be cached and marked dirty on modification of points array; translations could be combined in several places
function zoomShape(zoomValue) {
	var bounds = getBounds(_points);
	var transform = reduceTransformToFit(0, 0, zoomValue, bounds);
	
	translatePoints(_points, transform.x, transform.y); //move points towards center as far as necessary to avoid clipping
	translatePoints(_points, -bounds.x, -bounds.y);
	translatePoints(_points, -bounds.width / 2, -bounds.height / 2);
	scalePoints(_points, transform.zf, transform.zf);
	translatePoints(_points, bounds.width / 2, bounds.height / 2);
	translatePoints(_points, bounds.x, bounds.y);
	updateView();
}

function rotateShape(radians) {
  var bounds = getBounds(_points);
  var cx = bounds.x + bounds.width/2;
  var cy = bounds.y + bounds.height/2;
  rotatePoints(_points, radians, cx, cy);
  
  var bounds = getBounds(_points);
  var transform = reduceTransformToFit(0, 0, 1.0, bounds);
  translatePoints(_points, transform.x, transform.y);
  scalePoints(_points, transform.zf, transform.zf);

  updateView();
}

function updateView() {
  setSketchModified(true);
  redrawDoodle(true);
  adjustPreviewTransformation();
  renderToImageDataPreview();
  
  if (debugMode) {
    var bounds = getBounds(_points);
  	drawCircleTemp(bounds.x + bounds.width / 2, bounds.y + bounds.height / 2, 5, 'red');
  }
}

//when x,y!=0,0: reduces them such that transformed bounds will still fit on canvas (given that they fit prior to the transform)
//otherwise: calculate translation + zoom reduce such that given bounds will fit on canvas after transformation
function reduceTransformToFit(x, y, zf, bounds) {
	var zw = bounds.width * zf; zh = bounds.height * zf;
	var newBounds = { x: bounds.x - (zw - bounds.width) / 2, y: bounds.y - (zh - bounds.height) / 2, width: zw, height: zh };
//	console.log("bounds: " + bounds.x + ", " + bounds.y + ", " + bounds.width + ", " + bounds.height);
//	console.log("newBounds: " + newBounds.x + ", " + newBounds.y + ", " + newBounds.width + ", " + newBounds.height);
	
	var ldx = Math.max(x, -newBounds.x);
	var rdx = Math.min(x, canvasWidth - (newBounds.x + newBounds.width));
	var tdy = Math.max(y, -newBounds.y);
	var bdy = Math.min(y, canvasHeight - (newBounds.y + newBounds.height));
	
	if (x != 0 || y != 0) { //movement was requested
		return { x: nearestZero(ldx, rdx), y: nearestZero(tdy, bdy) };
	} else { //no movement requested
		var delta = { x: ldx + rdx, y: tdy + bdy };
		if (ldx != 0 && rdx != 0) delta.x /= 2;
		if (tdy != 0 && bdy != 0) delta.y /= 2;
		
		delta.x /= zf;
		delta.y /= zf;
	
		var zxMax = Math.min(zf, canvasWidth / newBounds.width);
		var zyMax = Math.min(zf, canvasHeight / newBounds.height);
//		var oldZF = zf;
//		var dir = zf >= 1.0 ? 1 : 0;
		zf = Math.min(zxMax, zyMax);
//		if (dir == 1 && zf < 1.0) zf = 1;
//		console.log("orgZF, zxMax, zyMax, finZF: " + oldZF + ", " + zxMax + ", " + zyMax + ", " + zf);
		
		return { x: delta.x, y: delta.y, zf: zf };
	}
}

function nearestZero(v1, v2) { return Math.abs(v1) < Math.abs(v2) ? v1 : v2; }

//*draws* a circle (i.e. it is not added as points to shape)
function drawCircleTemp(x, y, r, color) {
	ctx.beginPath();
	ctx.lineWidth = 1;
	ctx.fillStyle = color;
	ctx.arc(x, y, r, 0, 2 * Math.PI, false);
	ctx.fill();
	ctx.stroke();
	ctx.fillStyle = 'black';
}