I've been experimenting with animation.
It's very simple to animate an object across the canvas by clearing the entire canvas and redrawing it in a new location every frame (or "tick"):
// Inside requestAnimationFrame(...) callback
// Clear canvas
canvas.selectAll('*').remove();
// ... calculate position of x and y
// x, y = ...
// Add object in new position
canvas.append('circle')
.attr('cx', x)
.attr('cy', y)
.attr('r', 10)
.attr('fill', '#ffffff');
Is this a bad practice or am I doing it right?
For instance, if you were making a screen full of objects moving around, is it better practice to animate them by updating their attributes (e.g., x, y coordinates) in each frame?
Or, perhaps there is some other method I'm entirely unaware of, no?
Note: my animation might include 100-200 objects in view at a time.
It is better to move them, because that is the only way you can animate without errors.
In d3.js the idea is that the objects are data-bound. Clearing and redrawing the 'canvas' is not the correct approach. Firstly its not a canvas, its a web page, and any clearing and redrawing is handled by the browser itself. You job is to bind data to SVG, basically.
You need to make use of the d3 events, enter, exit, update which handles how the SVG behaves when the databound underlying data is modified and let d3 handle the animations.
the most simple example is here: https://bost.ocks.org/mike/circles/
select your elements, and store the selction in a variable
var svg= d3.select("svg");
var circles = svg.selectAll('circle');
now we need to databind something to the circle.
var databoundCircles = circles.data([12,13,14,15,66]);
This data can be anything. Usually I would expect a list of object, but these are simple numbers.
handle how things 'are made' when data appears
databoundCircles.enter().append('circle');;
handle what happens to them when data is removed
databoundCircles.exit().remove()
handle what happens when the data is updated
databoundCircles.attr('r', function(d, i) { return d * 2; })
this will change the radius when the data changes.
And recap from that tutorial:
enter - incoming elements, entering the stage.
update - persistent elements, staying on stage.
exit - outgoing elements, exiting the stage.
so in conclusion: don't do it like you are. Make sure you are using those events specifically to handle the lifecycle of elements.
PRO TIP: if you're using a list of objects make sure you bind the data by id, or some unique identifier, or the animations might behave unusually over time. Remember you are binding data to SVG you are not just wiping and redrawing a canvas!
d3.selectAll('circle').data([{id:1},{id:2}], function(d) { return d.id; });
Make note the optional second argument, that tells us how to bind the data! very important!
var svg = d3.select("svg");
//the data looks like this.
var data = [{
id: 1,
r: 3,
x: 35,
y: 30
}, {
id: 2,
r: 5,
x: 30,
y: 35
}];
//data generator makes the list above
function newList() {
//just make a simple array full of the number 1
var items = new Array(randoNum(1, 10)).fill(1)
//make the pieces of data. ID is important!
return items.map(function(val, i) {
var r = randoNum(1, 16)
return {
id: i,
r: r,
x: randoNum(1, 200) + r,
y: randoNum(1, 100) + r
}
});
}
//im just making rando numbers with this.
function randoNum(from, to) {
return Math.floor(Math.random() * (to - from) + from);
}
function update(data) {
//1. get circles (there are none in the first pass!)
var circles = svg.selectAll('circle');
//2. bind data
var databoundCircles = circles.data(data, function(d) {
return d.id;
});
//3. enter
var enter = databoundCircles.enter()
.append('circle')
.attr('r', 0)
//4. exit
databoundCircles.exit()
.transition()
.attr('r', 0)
.remove();
//5. update
//(everything after transition is tweened)
databoundCircles
.attr('fill', function(d, i){
var h = parseInt(i.toString(16));
return '#' + [h,h,h].join('');
})
.transition()
.duration(1000)
.attr('r', function(d, i) {
return d.r * 4
})
.attr('cx', function(d, i) {
return d.x * 2;
})
.attr('cy', function(d, i){
return d.y * 2
})
;
}
//first time I run, I use my example data above
update(data);
//now i update every few seconds
//watch how d3 'keeps track' of each circle
setInterval(function() {
update(newList());
}, 2000);
<script src="https://cdnjs.cloudflare.com/ajax/libs/d3/3.4.11/d3.min.js"></script>
<svg width="500" height="300">
</svg>
Is this a bad practice or am I doing it right?
Yes, it is a bad practice. In a normal circumstance I like to call it lazy coding: clearing the SVG (or whatever) and painting the dataviz again.
But, in your case, it's even worse: you will end up writing a huge amount of code (not exactly laziness, though), ignoring d3.transition(), which can easily do what you want. And that takes us to your second question:
Or, perhaps there is some other method I'm entirely unaware of, no?
Yes, as I just said, it's called transition(): https://github.com/d3/d3-transition
Then, at the end, you said:
Note: my animation might include 100-200 objects in view at a time.
First, modern browsers can handle that very well. Second, you still have to remove and repaint manually all that elements. If you benchmark the two approaches, maybe this is even worse.
Thus, just use d3.transition().
You can change the data (or the attributes) of the elements anytime you want, and "moving" (or transitioning) them to the new value calling a transition. For instance, to move this circle around, I don't have to remove it and painting it again:
var circle = d3.select("circle")
setInterval(() => {
circle.transition()
.duration(900)
.attr("cx", Math.random() * 300)
.attr("cy", Math.random() * 150)
.ease(d3.easeElastic);
}, 1000)
<script src="https://d3js.org/d3.v4.min.js"></script>
<svg>
<circle r="10" cx="100" cy="50" fill="teal"></circle>
</svg>
I am trying to create something similar to this
http://demo.joostkiens.com/het-parool-4g/
Where the plotted circles have outer lines throbbing outwards.
This is my demo so far.
http://jsfiddle.net/NYEaX/95/
I've plotted the circles with some dummy data. On top are red based circles. How do I invoke the animation and make it more vibrant per the alarm data .. eg. alarmLevel.
I am unsure as to how to create a looping animation with the radius bouncing off past the circumference and then fading out - having this variety based on the alarmLevel threshold
Would ideally need the transition to occur like this in a loop., http://jsfiddle.net/pnavarrc/udMUx/
var speedLineGroup = sampleSVG.append("g")
.attr("class", "speedlines");
speedLineGroup.selectAll("circle.dl-speed-static")
.data(dataset)
.enter().append("circle")
.style("stroke", "red")
.style("fill", "black")
.attr("r", function(d){
return d.value;
})
.attr("cx", function(d){
return d.xcoord;
})
.attr("cy", function(d){
return d.ycoord;
})
.attr("class", "dl-speed-static")
.attr("stroke-opacity", function (e) {
return 1;
//return var
})
.attr("fill-opacity", function (e) {
return 1;
//return var
})
.transition()
.ease("linear")
.duration(200)
.attr("r", function (e) {
return 1;
//return var
})
I've merged the ideas in the post. I've placed the ring creation in its own function and removed the time out. I've also started to try and hook into the alarm threshold per marker.
http://jsfiddle.net/NYEaX/102/
but the application still seems delayed/buggy - not very clear as in the prime example. How could this be improved further. Some of the alarm counts are low - but this method is causing the ring to throb too soon or flickery. Its almost like I need to invert the value to have a low alarm - create a slower response.
function makeRings() {
var datapoints = circleGroup.selectAll("circle");
var radius = 1;
function myTransition(circleData){
var transition = d3.select(this).transition();
speedLineGroup.append("circle")
.attr({"class": "ring",
"fill":"red",
"stroke":"red",
"cx": circleData.xcoord,
"cy": circleData.ycoord,
"r":radius,
"opacity": 0.4,
"fill-opacity":0.1
})
.transition()
.duration(function(){
return circleData.alarmLevel*100;
})
.attr("r", radius + 100 )
.attr("opacity", 0)
.remove();
transition.each('end', myTransition);
}
datapoints.each(myTransition);
}
This is the latest code..
makeRings()
var t = window.setInterval(makeRings, 10000);
function makeRings() {
var datapoints = mapSVG.selectAll("circle.location");
var radius = 1;
function myTransition(circleData){
console.log("circleData", circleData);
var transition = d3.select(this).transition();
speedLineGroup.append("circle")
.attr({"class": "ring",
"fill":"red",
"stroke":"red",
"cx": circleData.x * ratio,
"cy": circleData.y * ratio,
"r":radius,
"opacity": 0.4,
"fill-opacity":0.1
})
.transition()
.duration(function(){
return (circleData.redSum * 100);
})
.attr("r", radius + 30 )
.attr("opacity", 0)
.remove();
transition.each('end', myTransition);
}
datapoints.each(myTransition);
}
The example you linked to uses minified code, so it's a bit of a pain to figure out what they're doing. However, if you just watch the changes in the DOM inspector, you'll see that each ring is a new circle that gets added, grows in size and faces away, and then gets removed. The different points vary in how big the rings get before they fade away (and therefore in how many rings are visible at a time, since they all grow at the same speed).
The approach I would take to make this continue indefinitely is:
Use 'setInterval' to call a function on a regular basis (e.g., once or twice per second) that will create a new ring around each data circle.
Create the rings using an .each() call on your data circles, but add them to a different <g> element, and/or with different class names so there is no confusion between the rings and the data points.
Set the initial radius of the ring to be the same as the data point, but then immediately start a transition on it. Make the duration of the transition a function of the "intensity" data value for the associated data circle, and also make the final radius a function of that data value. Also transition the opacity to a value of 0.
Make the final line of the transition for the rings .remove() so that each ring removes itself after it has finished expanding.
Basic code:
window.setInterval(makeRings, 1000);
function makeRings() {
datapoints.each(function(circleData){
//datapoints is your d3 selection of circle elements
speedLineGroup.append("circle")
.attr({"class": "ring",
"fill":"red", //or use CSS to set fill and stroke styles
"stroke":"red",
"cx": circleData.xCoord,
"cy": circleData.yCoord,
//position according to this circle's position
"r":radius, //starting radius,
//set according to the radius used for data points
"opacity": 0.8, //starting opacity
"fill-opacity":0.5 //fill will always be half of the overall opacity
})
.transition()
.duration( intensityTimeScale(circleData.intensity) )
//Use an appropriate linear scale to set the time it takes for
//the circles to expand to their maximum radius.
//Note that you *don't* use function(d){}, since we're using the data
//passed to the .each function from the data point, not data
//attached to the ring
.attr("r", radius + intensityRadiusScale(circleData.intensity) )
//transition radius
//again, create an appropriate linear scale
.attr("opacity", 0) //transition opacity
.remove(); //remove when transition is complete
});
}
Because both the change in radius and the duration of the transition are linear functions of the intensity value, the change will have a constant speed for all the data points.
All you need to do to create looping transitions in d3 is to use the end callback on transitions. Create two functions, which each create a transition on your data, with one going from your start point to your end point, and the other going back, and have them call each other on completion, like so:
function myTransition(d){
var transition = d3.select(this).transition();
//Forward transition behavior goes here
//Probably create a new circle, expand all circles, fade out last circle
transition.each('end', myTransition); //This calls the backward transition
}
d3.select('myFlashingElement').each(myTransition);
This will encapsulate everything and keep looping at whatever the duration of your transition is. The next transition will always fire when the transition before it ends, so you don't have to worry about syncing anything.
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).