I'm using Matter.js and I want two rectangles with a constraint to make them act if they where a single rigid object.
I am basically setting stiffness to 1, so the contraint acts like a rigid bar instead of a spring.
Also to prevent the object from rotating, I'm setting the intertia to Infinity.
// a 20x20 square with 0 friction and infinite inertia
let objectA = Bodies.rectangle(0, 0, 20, 20, {
frictionAir: 0,
inertia: 'Infinity'
});
let objectB = Bodies.rectangle(30, 0, 20, 20, {
frictionAir: 0,
inertia: 'Infinity'
});
let constraint = Constraint.create({
bodyA: objectB,
bodyB: objectB,
length: 30,
stiffness: 1);
This indeed creates 2 objects with a fixed distance and they do not rotate (both squares always have the same absolute orientation)
However the objects can rotate between them, the constrain acts as a linear constraint but not as an angular constraint.
This picture shows how the distance between objects is kept, how the absolute orientation of the objects has not changed but how the objects rotate around each other.
How can I get rid of this rotation and have the two objects act if they were a single object?
I use a different approach: building a Body from parts instead of using constraints. The result is a single rigid object. Matter handles the parts still separately, so you can e.g. drop a ball in the cart created with the code below.
let cart = bodyWithParts(200, 150, { isStatic: true, friction: 0.0 });
function bodyWithParts(x, y, options) {
options = options || {}
let w = 4;
options.parts = [];
options.parts.push(Matter.Bodies.rectangle(w, 20, 5, 20));
options.parts.push(Matter.Bodies.rectangle(40 - w, 20, 5, 20));
options.parts.push(Matter.Bodies.rectangle(20, 40 - w, 50, 5))
let body = Matter.Body.create(options)
Matter.Body.setPosition(body, { x: x, y: y });
return body;
}
Building a Body to of parts can be useful, however, the strength of the orientation "constraint" cannot be lowered. The orientation stays fixed in any situation.
Therefore, I've written the following TypeScript function which adds two constraints of zero length to two Body objects. Constraints allows us to set the stiffness parameter.
Note that removing one the constraints allows one of the bodies to rotate around its own position ("midpoint") but it cannot change its position relative the other body.
/**
* Adds constraints to `bodyA` and `bodyB` such that their current
* relative position and orientaion is preseved (depending on `stiffness`).
*
* #param bodyA the first body of the constraint
* #param bodyB the second body of the constraint
* #param stiffness the stiffness of the constraint connecting `bodyA` and `bodyB`
* #param offsetA the constraint offset on `bodyA` in its coordinate system
* #param offsetB the constraint offset on `bodyB` in its coordinate system
*/
function addRigidBodyConstraints(
bodyA: Body, bodyB: Body,
stiffness: number = 0.1,
offsetA: Vector = Vector.create(0, 0),
offsetB: Vector = Vector.create(0, 0)
) {
function makeConstraint(posA: Vector, posB: Vector): Constraint {
return Constraint.create({
bodyA: bodyA, bodyB: bodyB,
pointA: posA, pointB: posB,
// stiffness larger than 0.1 is sometimes unstable
stiffness: stiffness
})
}
// add constraints to world or compound body
World.add(world, [
makeConstraint(Vector.sub(bodyB.position, bodyA.position), offsetB),
makeConstraint(offsetA, Vector.sub(bodyA.position, bodyB.position))
])
}
I am using Leaflet.js for desktop and mobile browser-based maps, and need to support a variety of map tile services. Some of these tile services are defined with coarse zoom levels (like 1, 5, 10, 15), and if I make a request for an unsupported zoom level, the service does not return a tile. (For example, if I request service/tiles/6/x/y when zoom level 6 is not supported).
Leaflet tile layers support minZoom and maxZoom but I'm trying to figure out if there is a best practice for doing coarse zoom levels, and if other folks have encountered this.
I found this post on GitHub that addresses tile scaling for unsupported zoom levels: https://github.com/Leaflet/Leaflet/pull/1802
But I am not sure if this applies. (I'm not sure I want to scale or 'tween' the zoom levels... but if this makes sense and is not too difficult I am willing to try.)
I've started experimenting with this approach which gets messy because zooming can cause more zooming and I have to differentiate user-driven zooms from system-driven zooms:
// layer metadata (assumption: Levels is in ascending order of zoom)
var layerDef = { Title: 'Service lines', Levels: [10, 15, 19] };
// create Leaflet Tile Layer and show on map
var layer = L.tileLayer('://host/service/{z}/{x}/{y}');
layer.minZoom = layerDef.Levels[0];
layer.maxZoom = layerDef.Levels[layerDef.Levels-1];
layer.addTo(map);
// initialize lastZoom for coarse zoom management
var lastZoom = map.getZoom();
var userZoom = true;
// handle supported zoom levels when zoom changes
map.on('zoomend', function (e)
{
// get new zoom level
var z = e.target._zoom || map.getZoom();
if (userZoom) // assume user initiated this zoom
{
// is this zoom level supported?
var zIdx = $.inArray(z, layerDef.Levels);
if (zIdx === -1)
{
// zoom level is not supported; zoom out or in to supported level
// delta: < 0 for zoom out, > 0 for zoom in
var zDelta = z - lastZoom;
var zLastIdx = $.inArray(lastZoom, layerDef.Levels);
var newZoom = -1;
if (zDelta > 0)
{
// user zoomed in to unsupported level.
// zoom in to next supported level (rely on layer.maxZoom)
newZoom = layerDef.Levels[zLastIdx + 1];
}
else
{
// user zoomed out to unsupported level.
// zoom out to next supported level (rely on layer.minZoom)
newZoom = layerDef.Levels[zLastIdx - 1];
}
if (newZoom !== -1)
{
userZoom = false; // set flag
setTimeout(function ()
{
map.setZoom(newZoom); // set zoom -- seems to not work if called from within zoomend handler
}, 100); // delay call to setZoom() to fix issue
}
}
}
else
{
userZoom = true; // clear flag
}
lastZoom = z;
});
(Side note: I hope the reason for coarse zoom levels is obvious: it can get expensive to create and store raster tiles at each zoom level, especially for large geographic areas, and especially when used with offline mobile devices with their own [local] tile servers, limited wireless data plans, limited storage capacity, etc. This is perhaps not something you might encounter with toy apps and Google maps, for example, but rather with domain-specific and mobile applications in which space and bandwidth are at a premium.)
Thanks!
UPDATE: I found that the problem I was having with this code is that map.setZoom(z) does not work right when called from within the zoomEnd handler (it does set the zoom, but causes display issue with gray/nonexistent tiles, perhaps because Leaflet is still in process of scaling / zooming). Fix was to use setTimeout to delay the call to setZoom() a bit. However, I'm still really curious if anybody else has dealt with this, and if there is a 'better way'... (I updated above code to work with setZoom fix)
There is currently a commit under review in Leaflet's repository on GitHub. It adds zoomFactor to the map's options. Maybe that's what you're looking for. At least, i think it will work just as long as your available tileset has zoomlevels which are (don't know if this is the correct technical term) multiples of the lowest available zoomlevel.
See: https://github.com/Leaflet/Leaflet/pull/3285
The following (no guarantees, based on this) should work with Leaflet v1.7.3 but probably not with current master.
It uses a serverZooms option to specify available zoom levels on the tile server as an ordered array.
Overrides L.TileLayer._getZoomForUrl to return a matching or the next lower available server zoom. Also overrides L.TileLayer._getTileSize to increase tile size in order to scale the tiles in between server zooms.
L.TileLayer.Overzoom = L.TileLayer.extend({
options: {
// List of available server zoom levels in ascending order. Empty means all
// client zooms are available (default). Allows to only request tiles at certain
// zooms and resizes tiles on the other zooms.
serverZooms: []
},
// add serverZooms (when maxNativeZoom is not defined)
// #override
_getTileSize: function() {
var map = this._map,
options = this.options,
zoom = map.getZoom() + options.zoomOffset,
zoomN = options.maxNativeZoom || this._getServerZoom(zoom);
// increase tile size when overscaling
return zoomN && zoom !== zoomN ?
Math.round(map.getZoomScale(zoom) / map.getZoomScale(zoomN) * options.tileSize) :
options.tileSize;
},
// #override
_getZoomForUrl: function () {
var zoom = L.TileLayer.prototype._getZoomForUrl.call(this);
return this._getServerZoom(zoom);
},
// Returns the appropriate server zoom to request tiles for the current zoom level.
// Next lower or equal server zoom to current zoom, or minimum server zoom if no lower
// (should be restricted by setting minZoom to avoid loading too many tiles).
_getServerZoom: function(zoom) {
var serverZooms = this.options.serverZooms || [],
result = zoom;
// expects serverZooms to be sorted ascending
for (var i = 0, len = serverZooms.length; i < len; i++) {
if (serverZooms[i] <= zoom) {
result = serverZooms[i];
} else {
if (i === 0) {
// zoom < smallest serverZoom
result = serverZooms[0];
}
break;
}
}
return result;
}
});
(function () {
var map = new L.Map('map');
map.setView([50, 10], 5);
new L.TileLayer.Overzoom('http://{s}.tile.openstreetmap.org/{z}/{x}/{y}.png', {
serverZooms: [0, 1, 2, 3, 6, 9, 12, 15, 17],
attribution : '© <a target="_parent" href="http://www.openstreetmap.org/copyright">OpenStreetMap</a> contributors'
}).addTo(map);
})();
body {
margin: 0;
}
html, body, #map {
width: 100%;
height: 100%;
}
<link rel="stylesheet" href="http://cdn.leafletjs.com/leaflet-0.7.3/leaflet.css" />
<script src="http://cdn.leafletjs.com/leaflet-0.7.3/leaflet.js"></script>
<div id="map"></div>
Struggeling translating the position of the mouse to the location of the tiles in my grid. When it's all flat, the math looks like this:
this.position.x = Math.floor(((pos.y - 240) / 24) + ((pos.x - 320) / 48));
this.position.y = Math.floor(((pos.y - 240) / 24) - ((pos.x - 320) / 48));
where pos.x and pos.y are the position of the mouse, 240 and 320 are the offset, 24 and 48 the size of the tile. Position then contains the grid coordinate of the tile I'm hovering over. This works reasonably well on a flat surface.
Now I'm adding height, which the math does not take into account.
This grid is a 2D grid containing noise, that's being translated to height and tile type. Height is really just an adjustment to the 'Y' position of the tile, so it's possible for two tiles to be drawn in the same spot.
I don't know how to determine which tile I'm hovering over.
edit:
Made some headway... Before, I was depending on the mouseover event to calculate grid position. I just changed this to do the calculation in the draw loop itself, and check if the coordinates are within the limits of the tile currently being drawn. creates some overhead tho, not sure if I'm super happy with it but I'll confirm if it works.
edit 2018:
I have no answer, but since this ha[sd] an open bounty, help yourself to some code and a demo
The grid itself is, simplified;
let grid = [[10,15],[12,23]];
which leads to a drawing like:
for (var i = 0; i < grid.length; i++) {
for (var j = 0; j < grid[0].length; j++) {
let x = (j - i) * resourceWidth;
let y = ((i + j) * resourceHeight) + (grid[i][j] * -resourceHeight);
// the "+" bit is the adjustment for height according to perlin noise values
}
}
edit post-bounty:
See GIF. The accepted answer works. The delay is my fault, the screen doesn't update on mousemove (yet) and the frame rate is low-ish. It's clearly bringing back the right tile.
Source
Intresting task.
Lets try to simplify it - lets resolve this concrete case
Solution
Working version is here: https://github.com/amuzalevskiy/perlin-landscape (changes https://github.com/jorgt/perlin-landscape/pull/1 )
Explanation
First what came into mind is:
Just two steps:
find an vertical column, which matches some set of tiles
iterate tiles in set from bottom to top, checking if cursor is placed lower than top line
Step 1
We need two functions here:
Detects column:
function getColumn(mouseX, firstTileXShiftAtScreen, columnWidth) {
return (mouseX - firstTileXShiftAtScreen) / columnWidth;
}
Function which extracts an array of tiles which correspond to this column.
Rotate image 45 deg in mind. The red numbers are columnNo. 3 column is highlighted. X axis is horizontal
function tileExists(x, y, width, height) {
return x >= 0 & y >= 0 & x < width & y < height;
}
function getTilesInColumn(columnNo, width, height) {
let startTileX = 0, startTileY = 0;
let xShift = true;
for (let i = 0; i < columnNo; i++) {
if (tileExists(startTileX + 1, startTileY, width, height)) {
startTileX++;
} else {
if (xShift) {
xShift = false;
} else {
startTileY++;
}
}
}
let tilesInColumn = [];
while(tileExists(startTileX, startTileY, width, height)) {
tilesInColumn.push({x: startTileX, y: startTileY, isLeft: xShift});
if (xShift) {
startTileX--;
} else {
startTileY++;
}
xShift = !xShift;
}
return tilesInColumn;
}
Step 2
A list of tiles to check is ready. Now for each tile we need to find a top line. Also we have two types of tiles: left and right. We already stored this info during building matching tiles set.
function getTileYIncrementByTileZ(tileZ) {
// implement here
return 0;
}
function findExactTile(mouseX, mouseY, tilesInColumn, tiles2d,
firstTileXShiftAtScreen, firstTileYShiftAtScreenAt0Height,
tileWidth, tileHeight) {
// we built a set of tiles where bottom ones come first
// iterate tiles from bottom to top
for(var i = 0; i < tilesInColumn; i++) {
let tileInfo = tilesInColumn[i];
let lineAB = findABForTopLineOfTile(tileInfo.x, tileInfo.y, tiles2d[tileInfo.x][tileInfo.y],
tileInfo.isLeft, tileWidth, tileHeight);
if ((mouseY - firstTileYShiftAtScreenAt0Height) >
(mouseX - firstTileXShiftAtScreen)*lineAB.a + lineAB.b) {
// WOHOO !!!
return tileInfo;
}
}
}
function findABForTopLineOfTile(tileX, tileY, tileZ, isLeftTopLine, tileWidth, tileHeight) {
// find a top line ~~~ a,b
// y = a * x + b;
let a = tileWidth / tileHeight;
if (isLeftTopLine) {
a = -a;
}
let b = isLeftTopLine ?
tileY * 2 * tileHeight :
- (tileX + 1) * 2 * tileHeight;
b -= getTileYIncrementByTileZ(tileZ);
return {a: a, b: b};
}
Please don't judge me as I am not posting any code. I am just suggesting an algorithm that can solve it without high memory usage.
The Algorithm:
Actually to determine which tile is on mouse hover we don't need to check all the tiles. At first we think the surface is 2D and find which tile the mouse pointer goes over with the formula OP posted. This is the farthest probable tile mouse cursor can point at this cursor position.
This tile can receive mouse pointer if it's at 0 height, by checking it's current height we can verify if this is really at the height to receive pointer, we mark it and move forward.
Then we find the next probable tile which is closer to the screen by incrementing or decrementing x,y grid values depending on the cursor position.
Then we keep on moving forward in a zigzag fashion until we reach a tile which cannot receive pointer even if it is at it's maximum height.
When we reach this point the last tile found that were at a height to receive pointer is the tile that we are looking for.
In this case we only checked 8 tiles to determine which tile is currently receiving pointer. This is very memory efficient in comparison to checking all the tiles present in the grid and yields faster result.
One way to solve this would be to follow the ray that goes from the clicked pixel on the screen into the map. For that, just determine the camera position in relation to the map and the direction it is looking at:
const camPos = {x: -5, y: -5, z: -5}
const camDirection = { x: 1, y:1, z:1}
The next step is to get the touch Position in the 3D world. In this certain perspective that is quite simple:
const touchPos = {
x: camPos.x + touch.x / Math.sqrt(2),
y: camPos.y - touch.x / Math.sqrt(2),
z: camPos.z - touch.y / Math.sqrt(2)
};
Now you just need to follow the ray into the layer (scale the directions so that they are smaller than one of your tiles dimensions):
for(let delta = 0; delta < 100; delta++){
const x = touchPos.x + camDirection.x * delta;
const y = touchPos.y + camDirection.y * delta;
const z = touchPos.z + camDirection.z * delta;
Now just take the tile at xz and check if y is smaller than its height;
const absX = ~~( x / 24 );
const absZ = ~~( z / 24 );
if(tiles[absX][absZ].height >= y){
// hanfle the over event
}
I had same situation on a game. first I tried with mathematics, but when I found that the clients wants to change the map type every day, I changed the solution with some graphical solution and pass it to the designer of the team. I captured the mouse position by listening the SVG elements click.
the main graphic directly used to capture and translate the mouse position to my required pixel.
https://blog.lavrton.com/hit-region-detection-for-html5-canvas-and-how-to-listen-to-click-events-on-canvas-shapes-815034d7e9f8
https://code.sololearn.com/Wq2bwzSxSnjl/#html
Here is the grid input I would define for the sake of this discussion. The output should be some tile (coordinate_1, coordinate_2) based on visibility on the users screen of the mouse:
I can offer two solutions from different perspectives, but you will need to convert this back into your problem domain. The first methodology is based on coloring tiles and can be more useful if the map is changing dynamically. The second solution is based on drawing coordinate bounding boxes based on the fact that tiles closer to the viewer like (0, 0) can never be occluded by tiles behind it (1,1).
Approach 1: Transparently Colored Tiles
The first approach is based on drawing and elaborated on here. I must give the credit to #haldagan for a particularly beautiful solution. In summary it relies on drawing a perfectly opaque layer on top of the original canvas and coloring every tile with a different color. This top layer should be subject to the same height transformations as the underlying layer. When the mouse hovers over a particular layer you can detect the color through canvas and thus the tile itself. This is the solution I would probably go with and this seems to be a not so rare issue in computer visualization and graphics (finding positions in a 3d isometric world).
Approach 2: Finding the Bounding Tile
This is based on the conjecture that the "front" row can never be occluded by "back" rows behind it. Furthermore, "closer to the screen" tiles cannot be occluded by tiles "farther from the screen". To make precise the meaning of "front", "back", "closer to the screen" and "farther from the screen", take a look at the following:
.
Based on this principle the approach is to build a set of polygons for each tile. So firstly we determine the coordinates on the canvas of just box (0, 0) after height scaling. Note that the height scale operation is simply a trapezoid stretched vertically based on height.
Then we determine the coordinates on the canvas of boxes (1, 0), (0, 1), (1, 1) after height scaling (we would need to subtract anything from those polygons which overlap with the polygon (0, 0)).
Proceed to build each boxes bounding coordinates by subtracting any occlusions from polygons closer to the screen, to eventually get coordinates of polygons for all boxes.
With these coordinates and some care you can ultimately determine which tile is pointed to by a binary search style through overlapping polygons by searching through bottom rows up.
It also matters what else is on the screen. Maths attempts work if your tiles are pretty much uniform. However if you are displaying various objects and want the user to pick them, it is far easier to have a canvas-sized map of identifiers.
function poly(ctx){var a=arguments;ctx.beginPath();ctx.moveTo(a[1],a[2]);
for(var i=3;i<a.length;i+=2)ctx.lineTo(a[i],a[i+1]);ctx.closePath();ctx.fill();ctx.stroke();}
function circle(ctx,x,y,r){ctx.beginPath();ctx.arc(x,y,r,0,2*Math.PI);ctx.fill();ctx.stroke();}
function Tile(h,c,f){
var cnv=document.createElement("canvas");cnv.width=100;cnv.height=h;
var ctx=cnv.getContext("2d");ctx.lineWidth=3;ctx.lineStyle="black";
ctx.fillStyle=c;poly(ctx,2,h-50,50,h-75,98,h-50,50,h-25);
poly(ctx,50,h-25,2,h-50,2,h-25,50,h-2);
poly(ctx,50,h-25,98,h-50,98,h-25,50,h-2);
f(ctx);return ctx.getImageData(0,0,100,h);
}
function put(x,y,tile,image,id,map){
var iw=image.width,tw=tile.width,th=tile.height,bdat=image.data,fdat=tile.data;
for(var i=0;i<tw;i++)
for(var j=0;j<th;j++){
var ijtw4=(i+j*tw)*4,a=fdat[ijtw4+3];
if(a!==0){
var xiyjiw=x+i+(y+j)*iw;
for(var k=0;k<3;k++)bdat[xiyjiw*4+k]=(bdat[xiyjiw*4+k]*(255-a)+fdat[ijtw4+k]*a)/255;
bdat[xiyjiw*4+3]=255;
map[xiyjiw]=id;
}
}
}
var cleanimage;
var pickmap;
function startup(){
var water=Tile(77,"blue",function(){});
var field=Tile(77,"lime",function(){});
var tree=Tile(200,"lime",function(ctx){
ctx.fillStyle="brown";poly(ctx,50,50,70,150,30,150);
ctx.fillStyle="forestgreen";circle(ctx,60,40,30);circle(ctx,68,70,30);circle(ctx,32,60,30);
});
var sheep=Tile(200,"lime",function(ctx){
ctx.fillStyle="white";poly(ctx,25,155,25,100);poly(ctx,75,155,75,100);
circle(ctx,50,100,45);circle(ctx,50,80,30);
poly(ctx,40,70,35,80);poly(ctx,60,70,65,80);
});
var cnv=document.getElementById("scape");
cnv.width=500;cnv.height=400;
var ctx=cnv.getContext("2d");
cleanimage=ctx.getImageData(0,0,500,400);
pickmap=new Uint8Array(500*400);
var tiles=[water,field,tree,sheep];
var map=[[[0,0],[1,1],[1,1],[1,1],[1,1]],
[[0,0],[1,1],[1,2],[3,2],[1,1]],
[[0,0],[1,1],[2,2],[3,2],[1,1]],
[[0,0],[1,1],[1,1],[1,1],[1,1]],
[[0,0],[0,0],[0,0],[0,0],[0,0]]];
for(var x=0;x<5;x++)
for(var y=0;y<5;y++){
var desc=map[y][x],tile=tiles[desc[0]];
put(200+x*50-y*50,200+x*25+y*25-tile.height-desc[1]*20,
tile,cleanimage,x+1+(y+1)*10,pickmap);
}
ctx.putImageData(cleanimage,0,0);
}
var mx,my,pick;
function mmove(event){
mx=Math.round(event.offsetX);
my=Math.round(event.offsetY);
if(mx>=0 && my>=0 && mx<cleanimage.width && my<cleanimage.height && pick!==pickmap[mx+my*cleanimage.width])
requestAnimationFrame(redraw);
}
function redraw(){
pick=pickmap[mx+my*cleanimage.width];
document.getElementById("pick").innerHTML=pick;
var ctx=document.getElementById("scape").getContext("2d");
ctx.putImageData(cleanimage,0,0);
if(pick!==0){
var temp=ctx.getImageData(0,0,cleanimage.width,cleanimage.height);
for(var i=0;i<pickmap.length;i++)
if(pickmap[i]===pick)
temp.data[i*4]=255;
ctx.putImageData(temp,0,0);
}
}
startup(); // in place of body.onload
<div id="pick">Move around</div>
<canvas id="scape" onmousemove="mmove(event)"></canvas>
Here the "id" is a simple x+1+(y+1)*10 (so it is nice when displayed) and fits into a byte (Uint8Array), which could go up to 15x15 display grid already, and there are wider types available too.
(Tried to draw it small, and it looked ok on the snippet editor screen but apparently it is still too large here)
Computer graphics is fun, right?
This is a special case of the more standard computational geometry "point location problem". You could also express it as a nearest neighbour search.
To make this look like a point location problem you just need to express your tiles as non-overlapping polygons in a 2D plane. If you want to keep your shapes in a 3D space (e.g. with a z buffer) this becomes the related "ray casting problem".
One source of good geometry algorithms is W. Randolf Franklin's website and turf.js contains an implementation of his PNPOLY algorithm.
For this special case we can be even faster than the general algorithms by treating our prior knowledge about the shape of the tiles as a coarse R-tree (a type of spatial index).