How to draw dashed lines with using rectangles in AS3? - actionscript-3

I'm using starling framework for my game project and it hasn't got any draw dashed line method. Because of this they suggest me to draw dashed lines with using small rectangles which is called quads.
My math is not enough for it, could you give a sample method for rectangles with dashed lines occurring.
Thanks..

This class by Andy Woodruff draws dashed lines
/*
DashedLine class
by Andy Woodruff (http://cartogrammar.com/blog || awoodruff#gmail.com)
May 2008
Still in progress; I'll get a more perfected version eventually. For now take it as is.
This is a Sprite with the capability to do basic lineTo drawing with dashed lines.
Example:
var dashy:DashedLine = new DashedLine(2,0x333333,new Array(3,3,10,3,5,8,7,13));
dashy.moveTo(120,120);
dashy.beginFill(0xcccccc);
dashy.lineTo(220,120);
dashy.lineTo(220,220);
dashy.lineTo(120,220);
dashy.lineTo(120,120);
dashy.endFill();
*/
package com.cartogrammar.drawing {
import flash.display.Shape;
import flash.display.Sprite;
import flash.geom.Point;
import flash.display.CapsStyle;
public class DashedLine extends Sprite {
var lengthsArray:Array = new Array(); // array of dash and gap lengths (dash,gap,dash,gap....)
var lineColor:uint; // line color
var lineWeight:Number; // line weight
var lineAlpha:Number = 1; // line alpha
var curX:Number = 0; // stores current x as it changes with lineTo and moveTo calls
var curY:Number = 0; // same as above, but for y
var remainingDist:Number = 0; // stores distance between the end of the last full dash or gap and the end coordinates specified in lineTo
var curIndex = null; // current index in the length array, so we know which dash or gap to draw
var arraySum:Number = 0; // total length of the dashes and gaps... not currently being used for anything, but maybe useful?
var startIndex:int = 0; // array index (the particular dash or gap) to start with in a lineTo--based on the last dash or gap drawn in the previous lineTo (along with remainingDist, this is so our line can properly continue around corners!)
var fill:Shape = new Shape(); // shappe in the background to be used for fill (if any)
var stroke:Shape = new Shape(); // shape in the foreground to be used for the dashed line
public function DashedLine(weight:Number = 0, color:Number = 0, lengthsArray:Array = null){
if (lengthsArray != null){ // if lengths array was specified, use it
this.lengthsArray = lengthsArray;
} else { // if unspecified, use a default 5-5 line
this.lengthsArray = [5,5];
}
if (this.lengthsArray.length % 2 != 0){ // if array has more dashes than gaps (i.e. an odd number of values), add a 5 gap to the end
lengthsArray.push(5);
}
// sum the dash and gap lengths
for (var i:int in lengthsArray){
arraySum += lengthsArray[i];
}
// set line weight and color properties from constructor arguments
lineWeight = weight;
lineColor = color;
// set the lineStyle according to specified properties - beyond weight and color, we use the defaults EXCEPT no line caps, as they interfere with the desired gaps
stroke.graphics.lineStyle(lineWeight,lineColor,lineAlpha,false,"none",CapsStyle.NONE);
// add fill and stroke shapes
addChild(fill);
addChild(stroke);
}
// basic moveTo method
public function moveTo(x:Number,y:Number):void{
stroke.graphics.moveTo(x,y); // move to specified x and y
fill.graphics.moveTo(x,y);
// keep track of x and y
curX = x;
curY = y;
// reset remainingDist and startIndex - if we are moving away from last line segment, the next one will start at the beginning of the dash-gap sequence
remainingDist = 0;
startIndex = 0;
}
// lineTo method
public function lineTo(x:Number,y:Number):void{
var slope:Number = (y - curY)/(x - curX); // get slope of segment to be drawn
// record beginning x and y
var startX:Number = curX;
var startY:Number = curY;
// positive or negative direction for each x and y?
var xDir:int = (x < startX) ? -1 : 1;
var yDir:int = (y < startY) ? -1 : 1;
// keep drawing dashes and gaps as long as either the current x or y is not beyond the destination x or y
outerLoop : while (Math.abs(startX-curX) < Math.abs(startX-x) || Math.abs(startY-curY) < Math.abs(startY-y)){
// loop through the array to draw the appropriate dash or gap, beginning with startIndex (either 0 or determined by the end of the last lineTo)
for (var i:int = startIndex; i < lengthsArray.length; i++){
var dist:Number = (remainingDist == 0) ? lengthsArray[i] : remainingDist; // distance to draw is either the dash/gap length from the array or remainingDist left over from the last lineTo if there is any
// get increments of x and y based on distance, slope, and direction - see getCoords()
var xInc:Number = getCoords(dist,slope).x * xDir;
var yInc:Number = getCoords(dist,slope).y * yDir;
// if the length of the dash or gap will not go beyond the destination x or y of the lineTo, draw the dash or gap
if (Math.abs(startX-curX) + Math.abs(xInc) < Math.abs(startX-x) || Math.abs(startY-curY) + Math.abs(yInc) < Math.abs(startY-y)){
if (i % 2 == 0){ // if even index in the array, it is a dash, hence lineTo
stroke.graphics.lineTo(curX + xInc,curY + yInc);
} else { // if odd, it's a gap, so moveTo
stroke.graphics.moveTo(curX + xInc,curY + yInc);
}
// keep track of the new x and y
curX += xInc;
curY += yInc;
curIndex = i; // store the current dash or gap (array index)
// reset startIndex and remainingDist, as these will only be non-zero for the first loop (through the array) of the lineTo
startIndex = 0;
remainingDist = 0;
} else { // if the dash or gap can't fit, break out of the loop
remainingDist = getDistance(curX,curY,x,y); // get the distance between the end of the last dash or gap and the destination x/y
curIndex = i; // store the current index
break outerLoop; // break out of the while loop
}
}
}
startIndex = curIndex; // for next time, the start index is the last index used in the loop
if (remainingDist != 0){ // if there is a remaining distance, line or move from current x/y to the destination x/y
if (curIndex % 2 == 0){ // even = dash
stroke.graphics.lineTo(x,y);
} else { // odd = gap
stroke.graphics.moveTo(x,y);
}
remainingDist = lengthsArray[curIndex] - remainingDist; // remaining distance (which will be used at the beginning of the next lineTo) is now however much is left in the current dash or gap after that final lineTo/moveTo above
} else { // if there is no remaining distance (i.e. the final dash or gap fits perfectly), we're done with the current dash or gap, so increment the start index for next time
if (startIndex == lengthsArray.length - 1){ // go to the beginning of the array if we're at the end
startIndex = 0;
} else {
startIndex++;
}
}
// at last, the current x and y are the destination x and y
curX = x;
curY = y;
fill.graphics.lineTo(x,y); // simple lineTo (invisible line) on the fill shape so that the fill (if one was started via beginFill below) follows along with the dashed line
}
// returns a point with the vertical and horizontal components of a diagonal given the distance and slope
private function getCoords(distance:Number,slope:Number):Point {
var angle:Number = Math.atan(slope); // get the angle from the slope
var vertical:Number = Math.abs(Math.sin(angle)*distance); // vertical from sine of angle and length of hypotenuse - using absolute value here and applying negative as needed in lineTo, because this number doesn't always turn out to be negative or positive exactly when I want it to (haven't thought through the math enough yet to figure out why)
var horizontal:Number = Math.abs(Math.cos(angle)*distance); // horizontal from cosine
return new Point(horizontal,vertical); // return the point
}
// basic Euclidean distance
private function getDistance(startX:Number,startY:Number,endX:Number,endY:Number):Number{
var distance:Number = Math.sqrt(Math.pow((endX-startX),2) + Math.pow((endY-startY),2));
return distance;
}
// clear everything and reset the lineStyle
public function clear():void{
stroke.graphics.clear();
stroke.graphics.lineStyle(lineWeight,lineColor,lineAlpha,false,"none",CapsStyle.NONE);
fill.graphics.clear();
moveTo(0,0);
}
// set lineStyle with specified weight, color, and alpha
public function lineStyle(w:Number=0,c:Number=0,a:Number=1):void{
lineWeight = w;
lineColor = c;
lineAlpha = a;
stroke.graphics.lineStyle(lineWeight,lineColor,lineAlpha,false,"none",CapsStyle.NONE);
}
// basic beginFill
public function beginFill(c:uint,a:Number=1):void{
fill.graphics.beginFill(c,a);
}
// basic endFill
public function endFill():void{
fill.graphics.endFill();
}
}
}

Thanks For Your Replies, I Wrote My Own Class Which Draws Rectangles To Create A Dashed Lines.
Thanks..

Related

if a ball is hitting a box from every side, how to know which side hittest is true

i am creating a brick breaker game in which ball is hitting a square object. i want to change the direction of ball when he hit square object.
square is of 15 px. and
ball is of 10 px.
for example
if hits on the right side, Speed in x direction will reverse
if hits on the left side, Speed in x direction will reverse
if hits on the up side, Speed in y direction will reverse
if hits on the down side , Speed in y direction will reverse.
I tried it hard but found nothing. any help will be appreciated. here is the code:
import flash.events.*;
import flash.display.*;
stop();
// speed of ball in x and y
var speedx : Number = 10;
var speedy : Number = 10;
// start running
function begin_code (event:MouseEvent):void{
addEventListener(Event.ENTER_FRAME,move_ball);
stage.addEventListener(MouseEvent.MOUSE_DOWN,by_key);
addEventListener(Event.ENTER_FRAME,ht_mc);
start_game.alpha=0;
}
start_game.addEventListener(MouseEvent.CLICK, begin_code) ;
//start ball moving
function move_ball(e:Event):void{
Ball.x += speedx;
Ball.y += speedy;
Ball.rotation +=speedx;
var ballposition : Number = Ball.x -Hitbar.x;
var ballhitpercent : Number = (ballposition /(Hitbar.width-Ball.width));
if(Ball.x <= x1.x+Ball.width/2){
speedx = speedx *-1;
}
if(Ball.x >= x2.x-Ball.width/2){
speedx = speedx *-1;
}
if(Ball.y <=(55)){
speedy = speedy *-1;
}
else if (Ball.y >= stage.stageHeight-Ball.height){
speedy = speedy *-1;
trace("hit y");
}
//start ball angle
else if(Ball.hitTestObject(Hitbar)){
speedx = ballhitpercent*10;
speedy = speedy *-1;
}
}
//start hitbar moving
// code for keys!!!!!!!!!
var distance : Number = 0;
function by_key(e:MouseEvent):void{
if (mouseX>Hitbar.x){
distance = (mouseX-Hitbar.x);
Hitbar.x += distance;
}
else if (mouseX<Hitbar.x){
distance = (Hitbar.x-mouseX);
Hitbar.x -= distance;
}
}
//restart
function by_key_up(e:MouseEvent):void{
}
stage.addEventListener(MouseEvent.MOUSE_UP, by_key_up);
function pLimiter(e:Event):void{
Hitbar.y = 406.2;
if (Hitbar.hitTestObject(x1)){
Hitbar.x = 32.6;
}
if (Hitbar.hitTestObject(x2)){
Hitbar.x = 287.55;
}
}
addEventListener(Event.ENTER_FRAME, pLimiter);
// Bricks set hit
var pickup:Array =new Array();
for (var i = 0;i<numChildren;i++){
if(getChildAt(i) is abc){
pickup.push(getChildAt(i));
}
}
function hittest_box(e:Event):void{
for (var f = 0;f<pickup.length;f++){
if (Ball.hitTestObject(pickup[f])){
if(pickup[f].parent) {
pickup[f].parent.removeChild(pickup[f]);
}
}
}
}
function ht_mc(e:Event):void{
for (var j = 0;j<pickup.length;j++){
var ball_pos_x: Number = ( Ball.x - pickup[j].x);
var ball_pos_y: Number = ( Ball.y - pickup[j].y);
if( ball_pos_x < 11.5 && ball_pos_x > -11.5){
speedy = speedy *-1;
trace("box y");
addEventListener(Event.ENTER_FRAME,hittest_box);
}
else if ( ball_pos_y < 11.5 && ball_pos_y > -11.5){
speedx = speedx *-1;
trace("boxx");
addEventListener(Event.ENTER_FRAME,hittest_box);
}
}
}
edit
To turn my two point example into a one-ball-moving version, the main thing you need to do is to declare the p1 then move the ball and then declare p2.
p1.x = ball.x;
p1.y = ball.y;
moveBall();
p2.x = ball.x;
p2.y = ball.y;
Now you have p1 and p2. Run the calculations as below to find which brick is hit and which side was hit.
A few more calculations will be needed (and you'll have to loop through this whole thing for every collision that occurs in between frames). But I can't post all that here.
Original Answer
My answer is meant to be able to be used in any situation in which you have a point object that is moving and needs to detect when it collides with sides of a square. Simple hitTest solutions are inadequate because a point object moving fast enough could "jump over" a corner. Additionally, if the walls of the object are infinitely thin, there couldn't easily be a "collision", so what we really want to calculate is whether or not the point passed through a wall during the last tick. Also, if the ball is going fast enough to jump over an entire brick, you'll get collision with bricks that are surrounded by other bricks. This method fixes that. Here we go...
My illustration shows the basic method I'm using. It breaks down like this:
define end points for each line segment (corners of block and 2 positions of ball)
check first if ball bounding box and block overlap with simple hit test type of conditional statement
if they do, determine which edge the ball passed through by comparing the 3 angles as shown in the diagram (angle 1 just has to be between angle 2 and 3)
then determine which of the points that make up the lines that the ball passed through during the last frame transition and determine which of these points is nearest the where the ball was on the previous frame (this will be a point contained in the line that the ball will hit!)
lastly, determine which line contains that point
There could certainly be some optimizations added, but this works like a charm for what it is.
This code will add a bunch of LineTestBlock objects to the stage as well as 2 Point objects associated with circles. Move the Points such that 1 will represent the first frame location of the ball, and the second Point can be dragged to a place representing where the ball will be on the 2nd frame. You will see that wherever the line between these passes through, the closest edge of a block will light up.
And here is the code. It is a main document class named BlockDoc and a LineTestBlock class.
package {
import flash.display.MovieClip;
import flash.geom.Point;
import flash.events.Event;
import flash.display.Sprite;
import flash.events.MouseEvent;
import flash.text.TextField;
import flash.text.TextFormat;
import flash.geom.Rectangle;
import flash.display.Shape;
public class BlockDoc extends MovieClip {
// this holds the circle handles (the actual sprite objects)
var cArray = new Array();
// this holds all the bricks
var brickArray = new Array();
//ball position in frame 1
//these are just point objects. p1 will need to represent where the ball was on the last frame
var p1:Point = new Point();
// and p2 will need to be where the ball is "going" to be on the next frame
// although, if it hits something, the ball will not end up p2 on the next screen update, obviously
var p2:Point = new Point();
// just an array used for putting the 1 and 2 on the handles
// you won't eventually need this, of course
var pointNameArray:Array = new Array();
// this is the Sprite object that holds the rectangle
// which describes the bounding box made by the ball in the two frames
var recASprite:Sprite = new Sprite();
// rec is the Sprite that holds the bricks, or you could just put the bricks on the stage. I like having them in a container so I can remove them all or move them all or change them all just by changing the container
var rec:Sprite = new Sprite();
// lines is the Shape object that all the bricks edge lines are drawn to
var lines:Shape = new Shape();
// mainLine is the Shape object that the line connecting the two ball positions is drawn to
var mainLine:Shape = new Shape();
// you won't need either of these lines in your version
public function BlockDoc() {
// just a background so you can see the alpha better.
// you won't need this in yours
var bkgnd:Sprite = new Sprite();
bkgnd.graphics.lineStyle();
bkgnd.graphics.beginFill(0x0);
bkgnd.graphics.drawRect(0,0,stage.stageWidth,stage.stageHeight);
bkgnd.graphics.endFill();
addChild(bkgnd);
makeBricks();
createArray();
addChild(mainLine);
addChild(lines);
createHandles(); // creates the circle handles
addEventListener(Event.ENTER_FRAME,gameTick);
}
private function drawLine(container:Shape,p1:Point,p2:Point,color:uint=0xffbbee):void{
container.graphics.clear();
container.graphics.lineStyle(2,color);
container.graphics.moveTo(p1.x,p1.y);
container.graphics.lineTo(p2.x,p2.y);
}
private function makeBricks():void{
// creates rectangle object defined by frame 1 and 2 of ball position
updateBallBoundingBox(recASprite,p1,p2);
addChild(rec); // the parent for all bounding boxes
makeSimpleRectangle(recASprite); // this is the bounding box for the 2 positions of the ball
// these are the bricks
for (var i:int = 0; i < 5; i++){
for (var j: int = 0; j < 3; j++){
var b: LineTestBlock = new LineTestBlock(50,25);
rec.addChild(b);
b.alpha = .5;
brickArray.push(b);
b.x = 100 * i + 50;
b.y = 80 * j +100;
// top left corner of brick
b._p1.x = b.x;
b._p1.y = b.y;
// top right corner of brick
b._p2.x = b.x + b.width;
b._p2.y = b.y;
// bottom right corner of brick
b._p3.x = b.x + b.width;
b._p3.y = b.y + b.height;
// bottom left corner of brick
b._p4.x = b.x;
b._p4.y = b.y + b.height;
}
}
}
private function makeSimpleRectangle(rect:Sprite,color:uint = 0x0):void{
rect.graphics.lineStyle(0,0x0,0);
rect.graphics.beginFill(color,.5);
rect.graphics.drawRect(0,0,50,50);
rect.graphics.endFill();
}
private function updateBallBoundingBox(rec:Sprite,p1:Point,p2:Point):void{
rec.x = Math.min(p2.x,p1.x);
rec.y = Math.min(p2.y,p1.y);
rec.width = Math.max(p2.x,p1.x)-rec.x;
rec.height = Math.max(p2.y,p1.y)-rec.y;
}
private function checkIntersection(A1:Point,A2:Point,B1:Point,B2:Point):Boolean{
// adjusts the current "bounding box" using the position 1 and position 2 of the ball
updateBallBoundingBox(recASprite,A1,A2);
// if bounding boxes hit
// define the angles to be used (further optimization can easily be done here by
// only checking the 2 possible sides of contact, or using a look up table
// instead of using Math.atan2)
// angle between position 1 and 2 of the ball
var A1_A2_r:Number = Math.atan2(A2.y - A1.y,A2.x - A1.x);
// angle between position 1 and one corner
var A1_B1_r:Number = Math.atan2(B1.y - A1.y,B1.x - A1.x);
// angle between position 1 and the second corner
var A1_B2_r:Number = Math.atan2(B2.y - A1.y,B2.x - A1.x);
// and if angle from position 1 to position 2 is between angle from one corner to the other corner...
if (A1_A2_r > A1_B1_r && A1_A2_r < A1_B2_r){
// return true
return true;
} else {
return false;
}
}
private function gameTick(e:Event):void{
// p1 and p2 are the point objects that describe frame 1 and frame 2 of the moving ball
// for actual moving ball:
//p1.x = Ball.x;
//p1.y = Ball.y;
//move_ball();
//p2.x = Ball.x;
//p2.y = Ball.y;
//or use this for experimenting with the handles
//p1.x = cArray[0].x;
//p1.y = cArray[0].y;
//p2.x = cArray[1].x;
//p2.y = cArray[1].y;
// draw line between position 1 and 2
drawLine(mainLine,p1,p2);
checkCollision();
}
private function checkCollision():void{
// clears previously drawn lines on bricks
lines.graphics.clear();
var xDir:int;
var yDir:int;
// determine direction of ball (you probably already have this as a variable somewhere so probably don't need this
if (p1.x < p2.x){
xDir = 1;
} else if (p1.x > p2.x){
xDir = -1;
} else {
xDir = 0;
}
if (p1.y < p2.y){
yDir = 1;
} else if (p1.y > p2.y){
yDir = -1;
} else {
yDir = 0;
}
// this array will hold all the Point objects involved in true collision
var arr:Array = new Array();
var arrLines:Array = new Array();
var nearestDistance:Number = 2000; // change this to something sensible (maybe the speed of the ball...);
var nearestPoint:Point = new Point(); // change this to something sensible
// first check bounding boxes
for (var i:int = 0; i < brickArray.length; i++){
var b:LineTestBlock = brickArray[i];
var a:Sprite = recASprite;
updateBallBoundingBox(a,p2,p1);
// this is just a bounding box hittest, and hitTestObject used to work, but I broke something, so I have to do it like this now
if (a.x+a.width > b.x && a.y + a.height > b.y && a.x < b.x+b.width && a.y<b.y+b.height){
// now that we know the rectangles overlap, we check the two sides that are hittable
// instead of xDir and yDir just use your variable or property that holds the x and y speeds;
// I use xDir and yDir because my example doesn't actually use motion.
if (xDir > 0){
if (checkIntersection(p1,p2,b._p1,b._p4)){
// ball hits left wall of brick
//drawLine(lines,b._p1,b._p4,0x00ffee);
// instead of drawLine above, put in your function for collision of left wall
arr.push(b._p1,b._p4);
arrLines.push({p1:b._p1,p2:b._p4,brick:brickArray[i]});
// that last array there simply holds an object with 3 properties
// for use later in comparing what should actually receive the hit.
}
if (yDir > 0) {
if (checkIntersection(p2,p1,b._p1,b._p2)){
// ball hits top wall of brick
arr.push(b._p1,b._p2);
arrLines.push({p1:b._p1,p2:b._p2,brick:brickArray[i]});
}
} else if (yDir < 0){
if(checkIntersection(p2,p1,b._p3,b._p4)){
// ball hits bottom wall of brick
arr.push(b._p3,b._p4);
arrLines.push({p1:b._p3,p2:b._p4,brick:brickArray[i]});
}
}
} else if (xDir < 0){
if(checkIntersection(p2,p1,b._p2,b._p3)){
// ball hits right edge of brick
arr.push(b._p2,b._p3);
arrLines.push({p1:b._p2,p2:b._p3,brick:brickArray[i]});
}
if (yDir > 0) {
if (checkIntersection(p2,p1,b._p1,b._p2)){
// ball hits top edge of brick
arr.push(b._p1,b._p2);
arrLines.push({p1:b._p1,p2:b._p2,brick:brickArray[i]});
}
} else if (yDir < 0){
if(checkIntersection(p2,p1,b._p3,b._p4)){
// ball hits bottom edge of brick
arr.push(b._p3,b._p4);
arrLines.push({p1:b._p3,p2:b._p4,brick:brickArray[i]});
}
}
}
}
}
for (var i:int = 0; i < brickArray.length; i++){
brickArray[i].alpha = 0.3;
}
for (var i:int = 0; i < arr.length; i++){
var d:Number = dist(arr[i],p1);
if(d < nearestDistance){
nearestDistance = d;
nearestPoint = arr[i];
}
}
for (var j:int = 0; j < arrLines.length; j++){
if (arrLines[j].p1 == nearestPoint){
drawLine(lines,nearestPoint,arrLines[j].p2);//THIS IS THE EDGE THAT GETS HIT!!
arrLines[j].brick.alpha = 0.7; // THIS IS THE BRICK THAT GETS HIT!!
} else if (arrLines[j].p2 == nearestPoint){
drawLine(lines,nearestPoint,arrLines[j].p1); //THIS IS THE EDGE THAT GETS HIT!!
arrLines[j].brick.alpha = 0.7; // THIS IS THE BRICK THAT GETS HIT!!
}
}
}
private function dist(p1:Point, p2:Point):Number{
var dx:Number = p1.x - p2.x;
var dy:Number = p1.y - p2.y;
return Math.sqrt(dx * dx + dy * dy);
}
private function createHandles():void{
// these are the circle handles for moving the balls around
for (var i:int = 0; i < 2; i++){
var c:Sprite = new Sprite();
var tf:TextField = new TextField();
c.graphics.lineStyle();
c.graphics.beginFill(0x5555ff+0x5555*i);
c.graphics.drawCircle(0,0,10);
c.graphics.endFill();
addChild(c);
c.addChild(tf);
c.x = 50*i+50;
c.y = 50;
c.addEventListener(MouseEvent.MOUSE_DOWN,dragObject);
c.addEventListener(MouseEvent.MOUSE_UP,dragStopObject);
cArray.push(c);
tf.height = 20;
tf.width = 10;
tf.text = pointNameArray[i];
tf.x = -5;
tf.y = -10;
tf.mouseEnabled = false;
}
}
private function createArray():void{
// just used for putting the fancy 1 and 2 on the handles
pointNameArray = ["1","2"];
}
private function radsFromPoints(p1:Point,p2:Point):Number{
return Math.atan2(p1.y - p2.y, p1.x - p2.y);
}
private function dragObject(me:MouseEvent):void{
me.target.startDrag(true);
}
private function dragStopObject(me:MouseEvent):void{
me.target.stopDrag();
}
}
}
and the LineTestBlock class:
package {
import flash.display.*;
import flash.text.*;
import flash.geom.Point;
public class LineTestBlock extends Sprite{
var _p1:Point = new Point();
var _p2:Point = new Point();
var _p3:Point = new Point();
var _p4:Point = new Point();
public function LineTestBlock(w:Number,h:Number) {
var s:Sprite = new Sprite();
s.graphics.lineStyle();
s.graphics.beginFill(0xff5599,0.5);
s.graphics.drawRect(0,0,w,h);
s.graphics.endFill();
addChild(s);
}
}
}
Obviously the stuff about lines and alpha are just for display purposes. You'll be able to erase a bunch of this code and will need to replace some of it with actual bounce functions.
One thing to keep in mind is how you deal with the bouncing off of the ball. You can't simply reverse the x or y speed of the ball, as you might think because then it is inside of a brick, or on the opposite side of the brick trying to come back out, which will work, but could look funny and actually allow the ball access to bricks that should be off limits because the are surrounded by other bricks. But I've already answered the question at hand, so I'll stop there.

HTML5 Canvas - Anti-aliasing and Paint Bucket / Flood Fill

Having trawled Stack Overflow and Google it seems to me that there is no way to disable antialiasing when drawing lines on an HTML5 canvas.
This makes for nice looking lines, but causes me a problem when it comes time to applying a paint bucket / flood fill algorithm.
Part of my application requires that users draw on a canvas, freestyle drawing with basic tools like line size, color... and a paint bucket.
Because lines are rendered with antialiasing they are not a consistent color... with that in mind consider the following:
Draw a thick line in black
Decide at some point later that the line should be red
Apply flood fill to black line
My flood fill algorithm fills the bulk of the line with red, but the edges that were antialiased are detected as being outside the area that should be filled... hence remain (greys / blues(?) left over from the black line).
The flood fill algorithm does not incorporate something akin to 'tolerance' like Photoshop does... I have considered something like that but am unsure it would help as I don't think the anti-aliasing does something simple like render grey next to a black line, I think it's more advanced than that and the anti-aliasing takes into consideration the surrounding colors and blends.
Does anyone have any suggestions as to how I can end up with a better paint bucket / flood fill that COMPLETELY flood fills / replaces an existing line or section of a drawing?
If you simply want to change a color of a line: don't use bucket paint fill at all.
Store all your lines and shapes as objects/arrays and redraw them when needed.
This not only allow you to change canvas size without losing everything on it, but to change a color is simply a matter of changing a color property on your object/array and redraw, as well as scaling everything based on vectors instead of raster.
This will be faster than a bucket fill as redrawing is handled in most part internally and not by pixel-by-pixel in JavaScript as is needed with a bucket fill.
That being said: you cannot, unfortunately, disable anti-alias for shapes and lines, only for images (using the imageSmoothingEnabled property).
An object could look like this:
function myLine(x1, y1, x2, y2, color) {
this.x1 = x1;
this.y1 = y1;
this.x2 = x2;
this.y2 = y2;
this.color = color;
return this;
}
And then allocate it by:
var newLine = new myLine(x1, y1, x2, y2, color);
Then store this to an array:
/// globally:
var myLineStack = [];
/// after x1/x2/y1/y2 and color is achieved in the draw function:
myLineStack.push(new myLine(x1, y1, x2, y2, color));
Then it is just a matter of iterating through the objects when an update is needed:
/// some index to a line you want to change color for:
myLineStack[index].color = newColor;
/// Redraw all (room for optimizations here...)
context.clearRect( ... );
for(var i = 0, currentLine; currentLine = myLineStack[i]; i++) {
/// new path
context.beginPath();
/// set the color for this line
context.strokeStyle = currentLine.color;
/// draw the actual line
context.moveTo(currentLine.x1, currentLine.y1);
context.lineTo(currentLine.x2, currentLine.y2);
context.stroke();
}
(For optimizations you can for example clear only the area that needs redraw and draw a single index. You can also group lines/shapes with the same colors and draw then with a single setting of strokeStyle etc.)
You can not always redraw the canvas, you may have used filters that can not be reversed, or just use so many fill and stroke calls it would be impractical to redraw.
I have my own flood fill based on a simple fill stack that paints to a tolerances and does its best to lessen anti-aliasing artifacts. Unfortunately if you have anti-aliasing on repeated fills will grow the filled region.
Below is the function, adapt it as suited, it is a direct lift from my code with comments added.
// posX,posY are the fill start position. The pixel at the location is used to test tolerance.
// RGBA is the fill colour as an array of 4 bytes all ranged 0-255 for R,G,B,A
// diagonal if true the also fill into pixels that touch at the corners.
// imgData canvas pixel data from ctx.getImageData method
// tolerance Fill tolerance range 0 only allow exact same colour to fill to 255
// fill all but the extreme opposite.
// antiAlias if true fill edges to reduce anti-Aliasing artifacts.
Bitmaps.prototype.floodFill = function (posX, posY, RGBA, diagonal,imgData,tolerance,antiAlias) {
var data = imgData.data; // image data to fill;
antiAlias = true;
var stack = []; // paint stack to find new pixels to paint
var lookLeft = false; // test directions
var lookRight = false;
var w = imgData.width; // width and height
var h = imgData.height;
var painted = new Uint8ClampedArray(w*h); // byte array to mark painted area;
var dw = w*4; // data width.
var x = posX; // just short version of pos because I am lazy
var y = posY;
var ind = y * dw + x * 4; // get the starting pixel index
var sr = data[ind]; // get the start colour tha we will use tollerance against.
var sg = data[ind+1];
var sb = data[ind+2];
var sa = data[ind+3];
var sp = 0;
var dontPaint = false; // flag to indicate if checkColour can paint
// function checks a pixel colour passes tollerance, is painted, or out of bounds.
// if the pixel is over tollerance and not painted set it do reduce anti alising artifacts
var checkColour = function(x,y){
if( x<0 || y < 0 || y >=h || x >= w){ // test bounds
return false;
}
var ind = y * dw + x * 4; // get index of pixel
var dif = Math.max( // get the max channel differance;
Math.abs(sr-data[ind]),
Math.abs(sg-data[ind+1]),
Math.abs(sb-data[ind+2]),
Math.abs(sa-data[ind+3])
);
if(dif < tolerance){ // if under tollerance pass it
dif = 0;
}
var paint = Math.abs(sp-painted[y * w + x]); // is it already painted
if(antiAlias && !dontPaint){ // mitigate anti aliasing effect
// if failed tollerance and has not been painted set the pixel to
// reduce anti alising artifact
if(dif !== 0 && paint !== 255){
data[ind] = RGBA[0];
data[ind+1] = RGBA[1];
data[ind+2] = RGBA[2];
data[ind+3] = (RGBA[3]+data[ind+3])/2; // blend the alpha channel
painted[y * w + x] = 255; // flag pixel as painted
}
}
return (dif+paint)===0?true:false; // return tollerance status;
}
// set a pixel and flag it as painted;
var setPixel = function(x,y){
var ind = y * dw + x * 4; // get index;
data[ind] = RGBA[0]; // set RGBA
data[ind+1] = RGBA[1];
data[ind+2] = RGBA[2];
data[ind+3] = RGBA[3];
painted[y * w + x] = 255; // 255 or any number >0 will do;
}
stack.push([x,y]); // push the first pixel to paint onto the paint stack
while (stack.length) { // do while pixels on the stack
var pos = stack.pop(); // get the pixel
x = pos[0];
y = pos[1];
dontPaint = true; // turn off anti alising
while (checkColour(x,y-1)) { // find the bottom most pixel within tolerance;
y -= 1;
}
dontPaint = false; // turn on anti alising if being used
//checkTop left and right if alowing diagonal painting
if(diagonal){
if(!checkColour(x-1,y) && checkColour(x-1,y-1)){
stack.push([x-1,y-1]);
}
if(!checkColour(x+1,y) && checkColour(x+1,y-1)){
stack.push([x+1,y-1]);
}
}
lookLeft = false; // set look directions
lookRight = false; // only look is a pixel left or right was blocked
while (checkColour(x,y)) { // move up till no more room
setPixel(x,y); // set the pixel
if (checkColour(x - 1,y)) { // check left is blocked
if (!lookLeft) {
stack.push([x - 1, y]); // push a new area to fill if found
lookLeft = true;
}
} else
if (lookLeft) {
lookLeft = false;
}
if (checkColour(x+1,y)) { // check right is blocked
if (!lookRight) {
stack.push([x + 1, y]); // push a new area to fill if found
lookRight = true;
}
} else
if (lookRight) {
lookRight = false;
}
y += 1; // move up one pixel
}
// check down left
if(diagonal){ // check for diagnal areas and push them to be painted
if(checkColour(x-1,y) && !lookLeft){
stack.push([x-1,y]);
}
if(checkColour(x+1,y) && !lookRight){
stack.push([x+1,y]);
}
}
}
// all done
}
There is a better way that gives high quality results, the above code can be adapted to do this by using the painted array to mark the paint edges and then after the fill has completed scan the painted array and apply a convolution filter to each edge pixel you have marked. The filter is directional (depending on which sides are painted) and the code too long for this answer. I have pointed you in the right direction and the infrastructure is above.
Another way to improve the image quality is to super sample the image you are drawing to. Hold a second canvas that is double the size of the image being painted. Do all you drawing to that image and display it to the user on another canvas with CTX.imageSmoothingEnabled and ctx.setTransform(0.5,0,0,0.5,0,0) half size, when done and the image is ready half its size manually with the following code (don't rely on canvas imageSmoothingEnabled as it gets it wrong.)
Doing this will greatly improve the quality of your final image and with the above fill almost completely eliminate anti-aliasing artifacts from flood fills.
// ctxS is the source canvas context
var w = ctxS.canvas.width;
var h = ctxS.canvas.height;
var data = ctxS.getImageData(0,0,w,h);
var d = data.data;
var x,y;
var ww = w*4;
var ww4 = ww+4;
for(y = 0; y < h; y+=2){
for(x = 0; x < w; x+=2){
var id = y*ww+x*4;
var id1 = Math.floor(y/2)*ww+Math.floor(x/2)*4;
d[id1] = Math.sqrt((d[id]*d[id]+d[id+4]*d[id+4]+d[id+ww]*d[id+ww]+d[id+ww4]*d[id+ww4])/4);
id += 1;
id1 += 1;
d[id1] = Math.sqrt((d[id]*d[id]+d[id+4]*d[id+4]+d[id+ww]*d[id+ww]+d[id+ww4]*d[id+ww4])/4);
id += 1;
id1 += 1;
d[id1] = Math.sqrt((d[id]*d[id]+d[id+4]*d[id+4]+d[id+ww]*d[id+ww]+d[id+ww4]*d[id+ww4])/4);
id += 1;
id1 += 1;
d[id1] = Math.sqrt((d[id]*d[id]+d[id+4]*d[id+4]+d[id+ww]*d[id+ww]+d[id+ww4]*d[id+ww4])/4);
}
}
ctxS.putImageData(data,0,0); // save imgData
// grab it again for new image we don't want to add artifacts from the GPU
var data = ctxS.getImageData(0,0,Math.floor(w/2),Math.floor(h/2));
var canvas = document.createElement("canvas");
canvas.width = Math.floor(w/2);
canvas.height =Math.floor(h/2);
var ctxS = canvas.getContext("2d",{ alpha: true });
ctxS.putImageData(data,0,0);
// result canvas with downsampled high quality image.

How to have an object hover back and forth constrained within a specific radius?

I have a sprite in a movie symbol that I would like to hover back and forth within a 360 radius. I was hoping to make it smooth and random. Never really venturing from its original xy cordinates.
I've tried to create some stipulations with if statements and a starting momentum. Like this:
var num = 2;
stage.addEventListener(Event.ENTER_FRAME, hover);
function hover(evt:Event):void{
//start it moving
cloudWhite.y += num;
cloudWhite.x += num;
//declare these variables
var cX = cloudWhite.x;
var cY = cloudWhite.y;
// object travels 10 pixels
var cXP = cX + 10;
var cXN = cX - 10;
var cYP = cY + 10;
var cYN = cY - 10;
// if object goes 10 pixels reverse direction of momentum (maybe)
if (cX >= cXP) {
num = -2;
}
if (cX <= cXN){
num = 2;
}
if (cY >= cYP) {
num = 2;
}
if (cY <= cYN){
num = 2;
}
Clearly this is super wrong because when it runs the object just either goes to 0,0 or to some place that only the math gods know of.
I am clearly a noob at this kind of math so i apologize but I am very excited to learn the trig behind this.
Thank you for your help and thank you for reading.
You are setting all your variables inside the ENTER_FRAME loop, so none of your conditions ever evaluates to true. On every single frame you are doing this:
cloudWhite.x += 2;
cX = cloudWhite.x;
cXP = cX + 10; // Must == cloudWhite's previous x + 10 + 2;
cXN = cX - 10; // Must == cloudWite's previous x -10 + 2;
if(cX > cXP)... // Can never be true.
if(cX < cXN)... // Can never be true.
What you need to do is:
1) Store the original position of cloudWhite somewhere outside the loop, and store it before the loop begins.
2) Define your bounds relative to the original position of cloudWhite, again before your loop begins. Also define the amount you are going to change the position with each iteration.
3) Start your loop.
4) Increment the current position of cloudWhite on each iteration. Add a little random in here if you want the shape to move in a random manner.
5) Check if the new position of cW is outside your bounds and adjust the direction if it is.
The sample below is crude and jerky but I don't know exactly what effect you're looking for. If you want smoother, longer movements in each direction, consider using the Tween class or a Tween library such as the popular Greensock one, instead of incrementing / decrementing the position manually. There's a useful discussion of this here: http://www.actionscript.org/forums/archive/index.php3/t-163836.html
import flash.display.MovieClip;
import flash.events.Event;
// Set up your variables
var original_x:Number = 100; // Original x
var original_y:Number = 100; // Original y
var x_inc:Number = 5; // X Movement
var y_inc:Number = 5; // Y Movenent
var bounds:Number = 50; // Distance from origin allowed
// Doesn't take into account width of object so is distance to nearest point.
// Create an MC to show the bounds:
var display:MovieClip = addChild(new MovieClip()) as MovieClip;
display.graphics.lineStyle(1, 0x0000FF);
display.graphics.beginFill(0x0000FF, 0.5);
display.graphics.drawRect(0-bounds, 0-bounds, bounds * 2, bounds *2);
display.x = original_x;
display.y = original_y;
addChild(display);
// Create our moving mc:
var mc:MovieClip = addChild(new MovieClip()) as MovieClip;
mc.graphics.beginFill(0xFF0000, 1);
mc.graphics.drawCircle(-10, -10, 20);
// Position it:
mc.x = original_x;
mc.y = original_y;
addChild(mc);
// Loop:
function iterate($e:Event = null):void
{
// Move the mc by a random amount related to x/y inc
mc.x += (Math.random() * (2 * x_inc))/2;
mc.y += (Math.random() * (2 * y_inc))/2;
// If the distance from the origin is greater than bounds:
if((Math.abs(mc.x - original_x)) > bounds)
{
// Reverse the direction of travel:
x_inc == 5 ? x_inc = -5 : x_inc = 5;
}
// Ditto on the y axis:
if((Math.abs(mc.y - original_y)) > bounds)
{
y_inc == 5 ? y_inc = -5 : y_inc = 5;
}
}
// Start the loop:
addEventListener(Event.ENTER_FRAME, iterate);
This should get you started. I'm sure there are any number of other ways to do this with formal trig, but this has the benefit of being very simple, and just an extension of your existing method.

Rotate bitmap data in AS3 180deg for export

I have a bitmap in AS3 flash and I am sending it over to javascript using a base64 encoded jpg string.
All that works great. I need to send the img over scaled down, and rotated 180deg. The scaling works, but not the rotation. The rotation never takes. I know Im am obviously doing it wrong, but don't know the right way.
So basically I just need to rotate the image 180deg so when it is sent to javascript it is upside down.
Here is my transform code
var scaleFactor:int = 5;
var tempBitmap:BitmapData = new BitmapData(img.width/scaleFactor, img.height/scaleFactor);
var drawMatrix:Matrix = new Matrix(1/scaleFactor, 0, 0, 1 /scaleFactor );
drawMatrix.rotate(Math.PI); //180deg
tempBitmap.draw(img, drawMatrix);
I think you need to translate your object after rotation otherwise it gets clipped so you don't see it, I did an example with a bitmap in a MovieClip just on the stage using CS5.
import flash.display.Bitmap;
import flash.display.BitmapData;
import flash.display.MovieClip;
var scaleFactor:int = 1;
var tempBitmap:BitmapData = new BitmapData(img.width, img.height);
var rotationMatrix:Matrix = new Matrix();
rotationMatrix.rotate(Math.PI);
rotationMatrix.translate(img.width, img.height);
tempBitmap.draw(box_mc, rotationMatrix);
var output:Bitmap = new Bitmap(tempBitmap);
addChild(output);
I didn't mess with the scaling, you can do that yourself I guess. The one I put on the stage is on the right, the bitmapData drawn one is top left of stage, and correctly inverted.
UPDATE
Also have a look at fl.motion.MatrixTransformer as per 32bitkid comment below!
/** flips individual blocks within a bitmap. Specifically used for doing sprite sheets. But I am sure you could find another use if you wanted.
* #param inBM
* #param spritePixelWidth
* #param spritePixelHeight
* #param inTransformType :An enum from TransFiveConstants. Example: TransFiveConstants.VERTICAL_FLIP
* #return a bitmap data object where all the sprites within the sprite sheet bitmap have been rotated or transformed **/
public static function makeTransformedCopyOfSpriteSheet(inSpriteSheet:BitmapData, spritePixelWidth:int, spritePixelHeight:int, inTransformType:int):BitmapData
{
//Do error check to make sure we evenly fit into the bitmap we are doing transforms on.
CONFIG::debug{
if ( (inSpriteSheet.width % spritePixelWidth ) != 0) { throw new Error("input error: width does not go in evenly! Fix it."); }
if ( (inSpriteSheet.height % spritePixelHeight) != 0) { throw new Error("input error: height does not go in evenly! Fix it."); }
}//CONFIG_debug
//Calculate width and height in sprites of the inSpriteSheet.
var widthInSprites :int = inSpriteSheet.width / spritePixelWidth ;
var heightInSprites:int = inSpriteSheet.height / spritePixelHeight;
/** Bitmap that takes rectangle chunks out of inSpriteSheet, one at a time. **/
var inBM:BitmapData = new BitmapData(spritePixelWidth, spritePixelHeight, true, 0x00);
//Inlined copy of code in makeTransformedCopy
////////////////////////////////////////////////////////////////////
var flipWidthHeight:Boolean = false;
if (inTransformType == TransFiveConstants.ROTATE_NEG_90 ||
inTransformType == TransFiveConstants.ROTATE_POS_90 )
{
flipWidthHeight = true;
}
var outWID:int = (flipWidthHeight ? inBM.height : inBM.width );
var outHGT:int = (flipWidthHeight ? inBM.width : inBM.height);
////////////////////////////////////////////////////////////////////
/** Bitmap that is a [rotated||transformed] version of inputBitmap: **/
var outBM:BitmapData = new BitmapData(outWID, outHGT, true, 0x00);
var outputSpriteSheetWidth :int = outBM.width * widthInSprites;
var outputSpriteSheetHeight:int = outBM.height * heightInSprites;
/** The output of this function **/
var outputSpriteSheet :BitmapData = new BitmapData(outputSpriteSheetWidth, outputSpriteSheetHeight, true, 0x00);
//scan through the sheet with a rectangle and make all the transformed copies you need.
//Every time you make a transformed chunk/copy, move it from the inSpriteSheet to the outputSpriteSheet
/** Places the [rotated||transformed] chunk in correct spot on outputSpriteSheet **/
var finalDestination:Point = new Point();
var cookieCutter:Rectangle = new Rectangle();
cookieCutter.width = spritePixelWidth ;
cookieCutter.height = spritePixelHeight;
for (var xx:int = 0; xx < widthInSprites ; ++xx){
for (var yy:int = 0; yy < heightInSprites; ++yy){
cookieCutter.x = xx * spritePixelWidth;
cookieCutter.y = yy * spritePixelHeight;
//Cut chunk out of main sprite sheet:
inBM.copyPixels(inSpriteSheet, cookieCutter, ZZ, null, null, true);
//Transform the chunk you cut out of the main sprite sheet:
makeTransformedCopy(inBM, inTransformType, outBM);
//Paste the transformed copy into the output sheet:
finalDestination.x = xx * outBM.width; //if outBM is rotated, this width will NOT BE SAME AS spritePixelWidth
finalDestination.y = yy * outBM.height;
outputSpriteSheet.copyPixels(outBM, outBM.rect, finalDestination, null, null, true);
}}//next [xx, yy]
return outputSpriteSheet;
}//makeTransformedCopyOfSpriteSheet
/** Flips/Mirrors and Rotates using a 1D index scan remap. "transformUsingScanRemap"
*
* Meaning, I put data into a 1D array, then change my assumptions on the "scan order" ( left-right, then top-bottom is default convention),
* I can effectively rotate or transform the pixel input.
*
* All we have to do is pack the bitmap into a 1D array. (scanning left-right, top-to-bottom)
* And then convert it BACK to the 2D array using a different formula assuming the data is packed via a different scan order.
*
* EXAMPLE:
* If we change our assumption to assume it is left-right, then BOTTOM-to-top, and make a formula for mapping 1D indexes
* to 2D values based on that scan order assumption, we achieve a vertical flip.
*
* #param inBM :Bitmap we are making a transformed copy of.
* #param inTransformType :The enum for the type of [transform||rotation] to use. For values check TransFiveConstants.as
* #param outputBitmap :Supply this to OVERWRITE an existing bitmap instead of create a NEW bitmap for output.
* #return a transformed or rotated bitmap **/
public static function makeTransformedCopy(inBM:BitmapData, inTransformType:int, outputBitmap:BitmapData = null):BitmapData
{
//If the bitmap is being ROTATED, we will have to flip the output width and height.
var flipWidthHeight:Boolean = false;
if (inTransformType == TransFiveConstants.ROTATE_NEG_90 ||
inTransformType == TransFiveConstants.ROTATE_POS_90 )
{
flipWidthHeight = true;
}
var outWID:int = (flipWidthHeight ? inBM.height : inBM.width );
var outHGT:int = (flipWidthHeight ? inBM.width : inBM.height);
//You can supply a reference to the OUTPUT of this function if you are doing some type of batch processing
//And want to avoid repetitively constructing new intermediary bitmaps:
if (outputBitmap == null)
{
var outputBitmap:BitmapData = new BitmapData(outWID, outHGT, true, 0x00);
}
else
{
if (outputBitmap.width != outWID) { ICU.error("Bad output bitmap supplied. Size is wrong."); }
if (outputBitmap.height != outHGT) { ICU.error("Bad output bitmap supplied. Size is wrong."); }
}
/** Max x index when remapping 1D values. **/
var maxXXX:int = outWID - 1;
/** Max y index when remapping 1D values. **/
var YYYmax:int = outHGT - 1;
/** Number of full columns, using 1D scan order for this orientation. **/
var fullColumns:int = 0;
/** Number of full rows, using 1D scan order for orientation specified. **/
var fullRows:int = 0;
/**What is left over after we have calculated the rows or collumns we have. **/
var remainder:int = 0;
var curPix:uint;
var index:int = ( -1);
var trans:IntPoint = new IntPoint();
inBM.lock();
outputBitmap.lock();
for (var yy:int = 0; yy < inBM.height; yy++) {
for (var xx:int = 0; xx < inBM.width ; xx++) {
++index;
//using 1D index position, remap that to correct 2D position.
//To do different transforms and rotations, simply change your assumptions on how we
//map from 1D to 2D.
//Standard 1D to 2D assumes scan lines go left-right, then top-bottom. Row by row.
//2D to 1D formula for standard:
//1D = (Y * width) + X.
//how many full widths you can get out of 1D == Y. Remainder == X.
//2D.Y = (1D/width);
//2D.X = 1D - (2D.Y * width);
if (inTransformType == TransFiveConstants.NO_TRANSFORM)
{ //[1][2] Assumed scan order (AKA 1D to 2D Mapping)
fullRows = (index / outWID); //[3][4] used to get full
remainder = index - (fullRows * outWID); //[5][6] rows and remainder.
trans.iy = fullRows;
trans.ix = remainder;
}else
if (inTransformType == TransFiveConstants.VERTICAL_FLIP)
{ //[5][6] Assumed scan order (AKA 1D to 2D Mapping)
fullRows = (index / outWID); //[3][4] used to get full
remainder = index - (fullRows * outWID); //[1][2] rows and remainder.
trans.iy = YYYmax - fullRows;
trans.ix = remainder;
}else
if (inTransformType == TransFiveConstants.ROTATE_NEG_90)
{ //[2][4][6] Assumed scan order (AKA 1D to 2D Mapping)
fullColumns = (index / outHGT); //[1][3][5] used to get full rows and remainder.
remainder = index - (fullColumns * outHGT);
trans.ix = fullColumns;
trans.iy = YYYmax - remainder;
}else
if (inTransformType == TransFiveConstants.ROTATE_POS_90)
{ //[5][3][1] Assumed scan order (AKA 1D to 2D Mapping)
fullColumns = (index / outHGT); //[6][4][2] used to get full rows and remainder.
remainder = index - (fullColumns * outHGT);
trans.ix = maxXXX - fullColumns;
trans.iy = remainder;
}else
if (inTransformType == TransFiveConstants.FLOOR_MIRROR)
{ //[2][1] Assumed scan order (AKA 1D to 2D Mapping)
fullRows = (index / outWID); //[4][3] used to get full
remainder = index - (fullRows * outWID); //[6][5] rows and remainder.
trans.iy = fullRows;
trans.ix = maxXXX - remainder;
}
else
{
throw new Error("Transform type not recognized");
}
//Copy and paste the pixel now that we know where to put it:
curPix = inBM.getPixel32(xx, yy);
outputBitmap.setPixel32(trans.ix, trans.iy, curPix);
}}//next [xx, yy]
inBM.unlock();
outputBitmap.unlock();
return outputBitmap;
}//transformUsingScanRemap

Algorithm to solve the points of a evenly-distributed / even-gaps spiral?

First, just to give a visual idea of what I'm after, here's the closest result (yet not exactly what I'm after) image that I've found:
Here's the entire site-reference: http://www.mathematische-basteleien.de/spiral.htm
BUT, it doesn't exactly solve the problem I'm after. I would like to store an array of points of a very specific spiral algorithm.
The points are evenly distributed
The 360 degree cycles have an even gap
If I'm not mistaken, the first two points would be:
point[ 0 ] = new Point(0,0);
point[ 1 ] = new Point(1,0);
But where to go from here?
The only arguments I'd like to provide are:
the quantity of points I wish to resolve (length of array).
the distance between each points (pixels gap).
the distance between cycles.
It almost sounds, to me, that I have to calculate the "spiral-circumference" (if there's such a term) in order to plot the evenly distributed points along the spiral.
Can 2*PI*radius be reliably used for this calculation you think?
If it's been done before, please show some code example!
Fun little problem :)
If you look at the diagram closer, the sequence is clearly stated:
There are probably many solutions to drawing these, maybe more elegant, but here's mine:
You know the hypotenuse is square root of the current segment count+1
and the opposite side of the triangle is always 1.
Also you know that Sine(Math.sin) of the angle is equal to the opposite side divided by the hypotenuse.
from the old mnenonic SOH(Sine,Opposite,Hypotenuse),-CAH-TOA.
Math.sin(angle) = opp/hyp
You know the value of the sine for the angle, you know the two sides, but you don't know the angle yet, but you can use the arc sine function(Math.asin) for that
angle = Math.asin(opp/hyp)
Now you know the angle for each segment, and notice it increments with each line.
Now that you have an angle and a radius(the hypotenuse) you can use for polar to cartesian formula to convert that angle,radius pair to a x,y pair.
x = Math.cos(angle) * radius;
y = Math.sin(angle) * radius;
Since you asked for an actionscript solution, there Point class already provides this function for you through the polar() method. You pass it a radius and angle and it returns your x and y in a Point object.
Here's a little snippet which plots the spiral. You can control the number of segments by moving the mouse on the Y axis.
var sw:Number = stage.stageWidth,sh:Number = stage.stageHeight;
this.addEventListener(Event.ENTER_FRAME,update);
function update(event:Event):void{
drawTheodorus(144*(mouseY/sh),sw*.5,sh*.5,20);
}
//draw points
function drawTheodorus(segments:int,x:Number,y:Number,scale:Number):void{
graphics.clear();
var points:Array = getTheodorus(segments,scale);
for(var i:int = 0 ; i < segments; i++){
points[i].offset(x,y);
graphics.lineStyle(1,0x990000,1.05-(.05+i/segments));
graphics.moveTo(x,y);//move to centre
graphics.lineTo(points[i].x,points[i].y);//draw hypotenuse
graphics.lineStyle(1+(i*(i/segments)*.05),0,(.05+i/segments));
if(i > 0) graphics.lineTo(points[i-1].x,points[i-1].y);//draw opposite
}
}
//calculate points
function getTheodorus(segments:int = 1,scale:Number = 10):Array{
var result = [];
var radius:Number = 0;
var angle:Number = 0;
for(var i:int = 0 ; i < segments ; i++){
radius = Math.sqrt(i+1);
angle += Math.asin(1/radius);//sin(angle) = opposite/hypothenuse => used asin to get angle
result[i] = Point.polar(radius*scale,angle);//same as new Point(Math.cos(angle)*radius.scale,Math.sin(angle)*radius.scale)
}
return result;
}
This could've been written in less lines, but I wanted to split this into two functions:
one that deals only with computing the numbers, and the other which deals with drawing the lines.
Here are some screenshots:
For fun I added a version of this using ProcessingJS here.
Runs a bit slow, so I would recommend Chromium/Chrome for this.
Now you can actually run this code right here (move the mouse up and down):
var totalSegments = 850,hw = 320,hh = 240,segments;
var len = 10;
points = [];
function setup(){
createCanvas(640,480);
smooth();
colorMode(HSB,255,100,100);
stroke(0);
noFill();
//println("move cursor vertically");
}
function draw(){
background(0);
translate(hw,hh);
segments = floor(totalSegments*(mouseY/height));
points = getTheodorus(segments,len);
for(var i = 0 ; i < segments ; i++){
strokeWeight(1);
stroke(255-((i/segments) * 255),100,100,260-((i/segments) * 255));
line(0,0,points[i].x,points[i].y);
// strokeWeight(1+(i*(i/segments)*.01));
strokeWeight(2);
stroke(0,0,100,(20+i/segments));
if(i > 0) line(points[i].x,points[i].y,points[i-1].x,points[i-1].y);
}
}
function getTheodorus(segments,len){
var result = [];
var radius = 0;
var angle = 0;
for(var i = 0 ; i < segments ; i++){
radius = sqrt(i+1);
angle += asin(1/radius);
result[i] = new p5.Vector(cos(angle) * radius*len,sin(angle) * radius*len);
}
return result;
}
<script src="https://cdnjs.cloudflare.com/ajax/libs/p5.js/0.4.4/p5.min.js"></script>
George's answer was excellent! I was looking for the solution for quite a while.
Here's the same code adjusted for PHP, in case it helps someone. I use the script to draw dots (= cities) for a map with X, Y coordinates. X starts from left, Y starts from bottom left.
<?
/**
* Initialize variables
**/
// MAXIMUM width & height of canvas (X: 0->400, Y: 0->400)
$width = 400;
// For loop iteration amount, adjust this manually
$segments = 10000;
// Scale for radius
$radiusScale = 2;
// Draw dot (e.g. a city in a game) for every N'th drawn point
$cityForEveryNthDot = 14;
/**
* Private variables
**/
$radius = 0;
$angle = 0;
$centerPoint = $width/2;
/**
* Container print
**/
print("<div style=\"width: ${width}px; height: ${width}px; background: #cdcdcd; z-index: 1; position: absolute; left: 0; top: 0;\"></div>");
/**
* Looper
**/
for($i=0;$i<$segments;$i++) {
// calculate radius and angle
$radius = sqrt($i+1) * $radiusScale;
$angle += asin(1/$radius);
// skip this point, if city won't be created here
if($i % $cityForEveryNthDot != 0) {
continue;
}
// calculate X & Y (from top left) for this point
$x = cos($angle) * $radius;
$y = sin($angle) * $radius;
// print dot
print("<div style=\"width: 1px; height: 1px; background: black; position: absolute; z-index: 2; left: " . round($x+$centerPoint) . "; top: " . round($y+$centerPoint) . ";\"></div>");
// calculate rounded X & Y (from bottom left)
$xNew = round($x+$centerPoint);
$yNew = round($width - ($y+$centerPoint));
// just some internal checks
if($xNew > 1 && $yNew > 1 && $xNew < $width && $yNew < $width) {
/**
* do something (e.g. store to database). Use xNew and yNew
**/
}
}