I've been doing web development for years now and I'm slowly getting myself involved with game development and for my current project I've got this isometric map, where I need to use an algorithm to detect which field is being clicked on. This is all in the browser with Javascript by the way.
The map
It looks like this and I've added some numbers to show you the structure of the fields (tiles) and their IDs. All the fields have a center point (array of x,y) which the four corners are based on when drawn.
As you can see it's not a diamond shape, but a zig-zag map and there's no angle (top-down view) which is why I can't find an answer myself considering that all articles and calculations are usually based on a diamond shape with an angle.
The numbers
It's a dynamic map and all sizes and numbers can be changed to generate a new map.
I know it isn't a lot of data, but the map is generated based on the map and field sizes.
- Map Size: x:800 y:400
- Field Size: 80x80 (between corners)
- Center position of all the fields (x,y)
The goal
To come up with an algorithm which tells the client (game) which field the mouse is located in at any given event (click, movement etc).
Disclaimer
I do want to mention that I've already come up with a working solution myself, however I'm 100% certain it could be written in a better way (my solution involves a lot of nested if-statements and loops), and that's why I'm asking here.
Here's an example of my solution where I basically find a square with corners in the nearest 4 known positions and then I get my result based on the smallest square between the 2 nearest fields. Does that make any sense?
Ask if I missed something.
Here's what I came up with,
function posInGrid(x, y, length) {
xFromColCenter = x % length - length / 2;
yFromRowCenter = y % length - length / 2;
col = (x - xFromColCenter) / length;
row = (y - yFromRowCenter) / length;
if (yFromRowCenter < xFromColCenter) {
if (yFromRowCenter < (-xFromColCenter))--row;
else++col;
} else if (yFromRowCenter > xFromColCenter) {
if (yFromRowCenter < (-xFromColCenter))--col;
else++row;
}
return "Col:"+col+", Row:"+row+", xFC:"+xFromColCenter+", yFC:"+yFromRowCenter;
}
X and Y are the coords in the image, and length is the spacing of the grid.
Right now it returns a string, just for testing.. result should be row and col, and those are the coordinates I chose: your tile 1 has coords (1,0) tile 2 is(3,0), tile 10 is (0,1), tile 11 is (2,1). You could convert my coordinates to your numbered tiles in a line or two.
And a JSFiddle for testing http://jsfiddle.net/NHV3y/
Cheers.
EDIT: changed the return statement, had some variables I used for debugging left in.
A pixel perfect way of hit detection I've used in the past (in OpenGL, but the concept stands here too) is an off screen rendering of the scene where the different objects are identified with different colors.
This approach requires double the memory and double the rendering but the hit detection of arbitrarily complex scenes is done with a simple color lookup.
Since you want to detect a cell in a grid there are probably more efficient solutions but I wanted to mention this one for it's simplicity and flexibility.
This has been solved before, let me consult my notes...
Here's a couple of good resources:
From Laserbrain Studios, The basics of isometric programming
Useful article in the thread posted here, in Java
Let me know if this helps, and good luck with your game!
This code calculates the position in the grid given the uneven spacing. Should be pretty fast; almost all operations are done mathematically, using just one loop. I'll ponder the other part of the problem later.
def cspot(x,y,length):
l=length
lp=length+1
vlist = [ (l*(k%2))+(lp*((k+1)%2)) for k in range(1,y+1) ]
vlist.append(1)
return x + sum(vlist)
Related
I'm trying to make an array of images 'spring' onto the canvas from the bottom of the screen and then land in random positions, like this image here:enter image description here (this is a screenshot of my canvas after you remove the physics)
Here is my attempt so far:
https://editor.p5js.org/holographicleah/sketches/DUY0EDnqN
I like the animation of the spring that i've managed, but I want the cats to be scattered across the whole screen like in the image above. I understand that i'm affecting the same 'force' on all of the objects, so it's natural that they all end up at the same height at the top of the screen. How could I randomise it so that they end up everywhere? Should I have used some kind of lerp to absolute positions instead? Open to trying something different if needs be. Still a beginner to code really so classes are still new to me!
Inspiration for this code came from both https://www.youtube.com/watch?v=Rr-5HiXquhw&t=937s for the spring physics and https://www.youtube.com/watch?v=cl-mHFCGzYk&t=149s for the 'particles'. I've adapted what I can but I've hit an experience wall!
You already have the x position covered in your linked code. In order to randomize the y position, change your constructor() method, by adding this line:
this.randomf = random(Math.floor(height/2) - 50);
Then, in the update() method, add this line:
this.pos.y += this.vel + this.randomf;
With the first line, you're giving individual objects a property which tells them what their (randomly chosen) y limit should be.
With the second line, you're limiting the y position. You would need to adjust it a bit, to fit your use case.
And some advice - with a large number of objects springing up, you might want to consider limiting the number of cycles, by dropping the updates, once the velocity falls below a certain value. Something like this:
update(){
if(this.vel <= 0.009) {
let force = - spring * this.pos.y;
this.vel+= force;
this.pos.y += this.vel;
this.vel*=0.9;
}
}
I'm putting together a p5 sketch with little wiggling snakes that move randomly across the screen.
Unfortunately, the tail keeps catching up to the head every time it does a sharpish turn.
Here is the function I'm using to calculate the move, I've tried with a few different ways of calculating the speed, fixed numbers, relative to the snake's length.
It's supposed to work by moving the snakes head (points[3]) in a semi-random direction and then having each body point move towards the one before it by the same amount. This isn't working, and I feel there's something wrong with my algorithm itself. I'm not familiar with these kinds of intermediate random-walks, so I've just been going by guesswork for the most part.
this["moveCurve"] = function() {
let newDir = this["oldDir"] + (random() - 1/2)*PI/6;
let velocity = createVector(1,0);
velocity.setMag(5);
velocity.setHeading(newDir);
this["points"][3].add(velocity);
for (let i = 2; i >= 0; i--) {
this["points"][i].add(p5.Vector.sub(this["points"][i + 1],this["points"][i]).setMag(5));
}
this["oldDir"] = newDir;
}
If you have any idea what I could do to make this work properly, I'd love to hear your advice. Thanks!
This does look like an algorithmic issue / not a bug with how you implemented it.
Here's my go at explaining why the gap between two points must decrease in this algorithm:
Let's consider just a two point snake, with two points Hi (head) and Ti (tail) at an initial locations Hi: (20, 0), and Ti: (0, 0). So, the heading here is 0 radians.
What happens when moveCurve is called? A new heading is chosen (let's use PI/2, a right angle to make it easy to imagine) and using a fixed velocity of 5 we calculate a new position for the head of (20, 5), let's call it Hf. T also moves, but it also moves toward Hf at the same 5 unit velocity, ending up at about (4.85, 1.21). The distance between these two final positions is now 15.62657, which is smaller than the initial distance.
To visualize this, think of the triangle formed between Ti, Hi, and Hf. Ti, and Hi, form the base of this triangle. Ti will move along the hypotenuse to get to Tf, while Hi will move along the other side. The directions they are moving in form an angle which is smaller than PI radians and both points are moving at the same speed so intuitively the points must be getting closer together.
So how to solve this? Well if we consider our tiny snake's movement, the tail moved in a decent direction but too far. One solution might be to scale the velocity vector in order to maintain a fixed distance between points instead of using a fixed velocity. For example instead of stepping 5 units along the hypotenuse from Ti toward Hf in the example, you could step 20 units along the hypotenuse from Hf toward Ti. I'm not sure how this would work out for your snake, just an idea!
Keep slithering!
Fortunately, it turns out p5's documentation itself had the answer for me. By adapting the code from here to use p5 Vectors, I was able to get it all working.
The segLengths property is defined when the object is made, just takes the distances between all the points.
this["moveCurve"] = function() {
let newDir = this["oldDir"] + (random() - 1/2)*PI/6;
let velocity = p5.Vector.fromAngle(newDir).setMag(5);
this["points"][3].add(velocity);
for (let i = 2; i >= 0; i--) {
this["points"][i].set(p5.Vector.sub(this["points"][i+1], p5.Vector.fromAngle(p5.Vector.sub(this["points"][i+1],this["points"][i]).heading()).setMag(this["segLengths"][i])));
}
this["oldDir"] = newDir;
}
I might spend a little time trying to clean up the code a bit, it's a jot messy for my tastes at the moment. But it works.
I am trying to calculate with higher precision numbers in JavaScript to be able to zoom in more on the Mandlebrot set.
(after a certain amount of zooming the results get "pixelated", because of the low precision)
I have looked at this question, so I tried using a library such as BigNumber but it was unusably slow.
I have been trying to figure this out for a while and I think the only way is to use a slow library.
Is there a faster library?
Is there any other way to calculate with higher precision numbers?
Is there any other way to be able to zoom in more on the Mandlebrot set?
Probably unneceseary to add this code, but this is the function I use to check if a point is in the Mandlebrot set.
function mandelbrot(x, y, it) {
var z = [0, 0]
var c1 = [x, y]
for (var i = 0; i < it; i++) {
z = [z[0]*z[0] - z[1]*z[1] + c1[0], 2*z[0]*z[1] + c1[1]]
if (Math.abs(z[0]) > 2, Math.abs(z[1]) > 2) {
break
}
}
return i
}
The key is not so much the raw numeric precision of JavaScript numbers (though that of course has its effects), but the way the basic Mandelbrot "escape" test works, specifically the threshold iteration counts. To compute whether a point in the complex plane is in or out of the set, you iterate on the formula (which I don't exactly remember and don't feel like looking up) for the point over and over again until the point obviously diverges (the formula "escapes" from the origin of the complex plane by a lot) or doesn't before the iteration threshold is reached.
The iteration threshold when rendering a view of the set that covers most of it around the origin of the complex plane (about 2 units in all directions from the origin) can be as low as 500 to get a pretty good rendering of the whole set at a reasonable magnification on a modern computer. As you zoom in, however, the iteration threshold needs to increase in inverse proportion to the size of the "window" onto the complex plane. If it doesn't, then the "escape" test doesn't work with sufficient accuracy to delineate fine details at higher magnifications.
The formula I used in my JavaScript implementation is
maxIterations = 400 * Math.log(1/dz0)
where dz0 is (arbitrarily) the width of the window onto the plane. As one zooms into a view of the set (well, the "edge" of the set, where things are interesting), dz0 gets pretty small so the iteration threshold gets up into the thousands.
The iteration count, of course, for points that do "escape" (that is, points that are not part of the Mandelbrot set) can be used as a sort of "distance" measurement. A point that escapes within a few iterations is clearly not "close to" the set, while a point that escapes only after 2000 iterations is much closer. That distance quality can be used in various ways in visualizations, either to provide a color value (common) or possibly a z-axis value if the set is being rendered as a 3D view (with the set as a sort of "mesa" in three dimensions and the borders being a vertical "cliff" off the sides).
Whatever it is I'm doing, I don't know what it's called, but I need help because I know it can be done with math. This is for a simulation I'm building, and the role it plays is very difficult to explain, but it has something to do with defining the properties of an object.
Here is my JavaScript: https://jsfiddle.net/vdocnmzu/
DM.prototype.get = function(coords){
var dist;
val = 0;
for(var j,i = 0; i < this.distortions.length; i += 1){
dist = 0;
for(j = 0; j < coords.length; j += 1){
dist += Math.pow( coords[j] - this.distortions[i].coords[j], 2);
}
dist = Math.pow(dist,.5);
if( dist <= this.distortions[i].range){
val += Math.cos( (dist/this.distortions[i].range) * Math.PI/2 ) * this.distortions[i].amp;//;
}
}
return val;
}
What's happening is this: I have this 3D cube, where I can pick x & y, and get Z(the grayscale pixel color). In this sample code, I'm picking a grid of points across the entire x,y plane of the cube. The "bubbles" you see (you may need to refresh a few times) are multiple points being picked and creating that image.
What I'm trying to do is not have bubbles, but rather, organic flows between bubbles.
Right now, the z value comes from these "distortion points" that each of these 3DCubes have. It can have any amount of these points.
These "distortion points" don't have to be points. They can be sets of points, or lines, or any type of base geometry to define the skeleton of some type of distance function.
I think that distance function is what I'm struggling with, because I only know how to do it with points. I feel like lines would still be too rigid. What's the math associated with doing this with curves? Distance to a curve? Are there more approaches to this? If there's not a good single 1 to pick, it's okay to have a collection as well.
Your question is very complicated to understand. The overall feeling is that your expectations are too high. Some advanced math 101 might help (feel free to google buzzwords):
Defining a curve is an very hard problem that challenged the brightest mathematicians of the history. From the naive approach of the greeks, through the calculus of Newton and Leibniz, passing by Euler and Gauss, to the mathematical analysis of Weisstreiss, the word curve changed meaning several times. The accepted definition nowadays says that curves are continous functions in two variables, where continous is a very special word that has an exact meaning coined in the 19th century (naively is a function without jumps from one value to another). Togheter with the notion of continuity, came the notions of connected, compact, differentiable (and so on) curves, which defined new conditions for special curves. The subject developed to what is now known as topology and mathematical analysis.
Mathematicians usually uses definitions to reproduce a class of ideas that can be brought and thought togheter. To their surprise, the definition of continuity did include really weird functions to be curves: space-filling-curves, fractals!!! They called them monsters at the time.
After this introduction, lets go back to your question. You need a geometrical object to calculate distances from a point. Lets avoid weird curves and go from continous to differentiable. Now it's better. A (conected compact) differentiable function can be expanded in Taylor series, for example, which means that all functions of this class can be written as an infinite sum of polynomial functions. In two dimensions, you need to calculate matrices involved in this expansion (Calculus in many variables is a pre-requisite). Another step further is truncating this expansion in some degree, lets say 3. Then the general curve in this case is: ax + by + cx^2 + dy^2 + ex^3 + fy^3 + gx^2y + hxy^2 + ixy + j = 0 (ab...j are free parameters). Oh! This is reasonable, you might think. Well, actually there is a name for this kind of curve: algebraic curve of deggre 3. This is an active research theme of algebraic geometry, which is a very hard field even among mathematicians. Generally speaking, there are milestone theorems about the general behavior of those curves, which involves singularities and intersection points that are allowed in the general case.
In essence, what you are looking for does not exist, and is a very hard subject. Your algorithm works with points (really cool pictures by the way) and you should baby step it into a straight line. This step already requires you to think about how to calculate distance between a point and a straight line. This is another subject that was developed in general in the 19th century, togheter with mathematical analysis: metric spaces. The straightfoward answer to this question is defining the distance between a point and a line to be the smallest distance from the point to all line points. In this case, it can be shown that the distance is the modulus of the vector that connects the point to the line in a 90 degrees angle. But this is just one definition among infinte possible ones. To be considered a distance (like the one I just described and the euclidean distance) there is a set of axioms that needs to be verified. You can have hyperbolic metrics, discrete metrics, metrics that count words, letters, LotsOfFamousPeople metric spaces... the possibilities are infinite.
So, baby steps. Do it with straight lines and euclidean minimum distance metric. Play around with other metrics you find on google. Understand the axioms and make your own!!! Going to second degree polynomials is already a big challenge, as you have to understand everything that those curves can make (they can really do weird unexpect stuff) and define a distance to it (metric space).
Well thats it! Good luck with your project. Looks really cool!
I need to implement a spatial data structure to store rectangles then be able to find all rectangles that intersect a given rectangle. This will be implemented in JavaScript.
So far I am developing a Quad Tree to cut down the search space but because it is for a game, all objects that move will need to update its position in the tree. Back to square one.
Are there any data-structures or methods to help? It will need to process around 10,000 objects so brute force isn't good enough.
A hash table works fairly well as an approximate intersection test. Hash tables are used as part of a more sophisticated algorithm for detecting collisions in ODE.
Logically, this test divides the space into a regular grid. Each grid cell is labeled with a list of objects that intersect that cell. The grid is initialized by scanning all objects. I don't know javascript, so I'll use python-ish pseudocode.
for each ob in objects:
for each x in [floor(ob.x_min / grid_size) .. floor(ob.x_max / grid_size)]:
for each y in [floor(ob.y_min / grid_size) .. floor(ob.y_max / grid_size)]:
hashtable[hash(x, y)].append(ob)
To find collisions with a given object, look up near-collisions in the hash table and then apply an exact collision test to each one.
near_collisions = []
for each x in [floor(ob.x_min / grid_size) .. floor(ob.x_max / grid_size)]:
for each y in [floor(ob.y_min / grid_size) .. floor(ob.y_max / grid_size)]:
near_collisions = near_collisions ++ hashtable[hash(x, y)]
remove duplicates from near_collisions
for each ob2 in near_collisions:
if exact_collision_test(ob, ob2):
do_something
You can still use quadtree even if you have moving objects – just remove and reinsert an object every time it moves or every time it crosses region boundary.
But quadtrees aren't very good at storing rectangles and I would recommend using an R-tree instead.