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Did you ever played the "Tank wars" game?
I'm programming this game with JavaScript + Canvas (for a personal challenge), and what I need is an algorithm for generating that random green land every time I start the game, but I'm not too good at maths, so I can't do it myself.
I don't want someone to give me the code, I only want the idea for the algorithm.
Thanks!
(9 segments)
Fiddle demo
(7 segments)
The main generation function look like this:
var numOfSegments = 9; // split horizontal space
var segment = canvas.width / numOfSegments; // calc width of each segment
var points = [], calcedPoints;
var variations = 0.22; // adjust this: lower = less variations
var i;
//produce some random heights across the canvas
for(i=0; i < numOfSegments + 1; i++) {
points.push(segment * i);
points.push(canvas.height / 2.8 + canvas.height * variations * Math.random());
}
//render the landscape
ctx.beginPath();
ctx.moveTo(canvas.width, canvas.height);
ctx.lineTo(0, canvas.height);
calcedPoints = ctx.curve(points); // see below
ctx.closePath();
ctx.fillStyle = 'green';
ctx.fill();
The curve() function is a separate function which generate a cardinal spline. In here you can modify it to also store tension values to make more spikes. You can also used the generated points as a basis for where and at what angle the tanks will move at.
The function for cardinal spline:
CanvasRenderingContext2D.prototype.curve = function(pts, tension, numOfSegments) {
tension = (tension != 'undefined') ? tension : 0.5;
numOfSegments = numOfSegments ? numOfSegments : 16;
var _pts = [], res = [], t, i, l, r = 0,
x, y, t1x, t2x, t1y, t2y,
c1, c2, c3, c4, st, st2, st3, st23, st32;
_pts = pts.concat();
_pts.unshift(pts[1]);
_pts.unshift(pts[0]);
_pts.push(pts[pts.length - 2]);
_pts.push(pts[pts.length - 1]);
l = (_pts.length - 4);
for (i = 2; i < l; i+=2) {
//overrides and modifies tension for each segment.
tension = 1 * Math.random() - 0.3;
for (t = 0; t <= numOfSegments; t++) {
t1x = (_pts[i+2] - _pts[i-2]) * tension;
t2x = (_pts[i+4] - _pts[i]) * tension;
t1y = (_pts[i+3] - _pts[i-1]) * tension;
t2y = (_pts[i+5] - _pts[i+1]) * tension;
st = t / numOfSegments;
st2 = st * st;
st3 = st2 * st;
st23 = st3 * 2;
st32 = st2 * 3;
c1 = st23 - st32 + 1;
c2 = -(st23) + st32;
c3 = st3 - 2 * st2 + st;
c4 = st3 - st2;
x = c1 * _pts[i] + c2 * _pts[i+2] + c3 * t1x + c4 * t2x;
y = c1 * _pts[i+1] + c2 * _pts[i+3] + c3 * t1y + c4 * t2y;
res[r++] = x;
res[r++] = y;
} //for t
} //for i
l = res.length;
for(i=0;i<l;i+=2) this.lineTo(res[i], res[i+1]);
return res; //return calculated points
}
Look into perlin noise generation, this in combination with a good smoothing algorithm can produce some pretty good terrain, and is fairly quick. There is a reference version of the code kicking around the net somewhere, which should provide you with a fairly hefty headstart
First you need a point that is random y (between 55,65); got x=0
So this is the origin point for the green, lets keep it as x1,y1 (x1 always 0).
Then you need a random integer between 30 to 40. This is x2. And a random y which is in the range y1 + 8 to y1 + 20.
Then x3 and y3 on same principle (lets call it formula type 1)
Now you need to first get a random either -1 or 1, this will be directions of y4. So y4 can go higher than y3 or lower ... this will be formula type 2.
You need to keep a max and min y for a new y, if it crosses that then go the other way -> this will be a correction type formula 3.
Xn keeps increasing till its >= width of board.
Join the lines in a eclipses ... and looks like web searches is the way to go !
I am sure there are a lot of coded libraries that you could use to make this easy. But if you are trying to code this by yourself, here is my idea.
You need to define terrain from everything else. So every part of your environment is a cluster for example. You need to define how are separated these clusters, by nodes(points) for example.
You can create a polygon from a sequence of points, and this polygon can become whatever you want, in this case terrain.
See that on the image you passed, there are peaks, those are the nodes (points). Remember to define also nodes on the borders of your environment.
There are surely a novel, written algorithms, either fractal as #DesertIvy pointed out or others, maybe there are libraries as well, but if you want toi generate what is in the image, it can be pretty straightforward, since it is just (slightly curved) lines between points. If you do it in phases, not trying to be correct at once, it is easy:
Split x region of your game screen into sections (with some minimal and maximal width) using random (you may be slightly off in last section, but it does not matter as much, I think). Remember the x-es where sections meet (including the ones at game screen border)
Prepare some data structure to include y-s as well, on previously remembered x-s. Start with leftmost.y = 0, slope = Math.random()-0.5;.
Generate each next undefined y beginning with 1: right.y = left.y + slope * (right.x-left.x); as well as update slope after each y: slope += Math.random()-0.5;. Do not bother, for the moment, if it all fits into game screen.
If you want arcs, you can generate "curviness" parameter for each section randomly which represent how much the middle of the line is bumped compared to straight lines.
Fit the ys into the game screen: first find maximal and minimal generated y (mingeny, maxgeny) (you can track this while generating in point 4). Choose where the max and min y in game screen (minscry, maxscry) (say at the top fourth and at the bottom fourth). Then transform generated ys so that it spans between minscry and maxscry: for every point, do apoint.y = minscry + (maxscry-minscry)/(maxgeny-mingeny)*(apoint.y-mingeny).
Now use lines between [x,y] points as a terrain, if you want to use "curviness", than add curvemodifier to y for any particular x in a section between leftx and rightx. The arc need not to be a circle: I would suggest a parabola or cosine which are easy to produce: var middle = (left.x+right.x)/2; var excess = (x-left)/(middle-left); and then either var curvemodifier = curviness * (1-excess*excess); or var curvemodifier = curviness * Math.cos(Math.PI/2*excess).
Wow...At one point I was totally addicted to tank wars.
Since you are on a learning adventure...
You might also learn about the context.globalCompositeOperation.
This canvas operation will let you grab an image of actual grass and composite it into your game.
You can randomize the grass appearance by changing the x/y of your drawImage();
Yes, the actual grass would probably be too distracting to include in your finished game, but learning about compositing would be valuable knowledge to have.
...and +1 for the question: Good for you in challenging yourself !
Related
I reached out for help recently on math.stackexchange.com with a question about 2 dimensional algebra. The answer was promptly provided but it's in mathematical notation unfamiliar to me and the person giving the answer has stopped responding to my questions. While I am extremely grateful to BStar for providing this information, he/she has stopped replying both on the site and the chat, and doesn't seem interested in helping me understand it to the point that I could write programming code to calculate the desired point P. I respect that, but it leaves me stuck for now. Could someone help me convert this sequence of steps into a programming language such as Javascript? (I am actually working in PHP, but Javascript would be more convenient to represent in a runnable Snippet on stackoverflow .. I'm happy with any current language that I can translate into PHP).
The post is at https://math.stackexchange.com/questions/4110517/trig-101-calculate-coords-of-point-p-such-that-it-is-distance-n-from-line-ab-an/4110550?noredirect=1#comment8504010_4110550
The answer given is in Latex but here's a screenshot of it:
The latest description of the process by the author BStar: "Here is the process: First calculate cos B and use arccos to get B. Second calculate tanθ to get θ with arctan by using |BP| is the same from two triangles. Knowing these, we can get vectors BA’ and B’P, thus vectors OA and OP. We get θ to grt vector BA’ in this case, not the other way around. "
I can follow up until step (5) where the comma notation comes in, i.e. k = (-xb, -yb)(xc - xb, yc - yb) / ac. This seems to make k a two dimensional vector but I don't think I ever worked with this notation. Later, k is used in step (6) and (6a) to calculate theta, appearing both in the numerator and denominator of a fraction. I have no idea how to expand this to get an actual value for theta.
(Edit Note: The author BStar assumed point A is at the origin, so (xa, ya) = (0, 0) but I cannot make that assumption in the real world. Thus the vector BA in Step 1 is actually (xa - xb, ya - yb) and his formula for k shown above is actually k = (xa - xb, ya - yb)(xc - xb, yc - yb) / ac. This expansion needs to be carried through the calculation but it's not a major change.)
If we were to frame this in Javascript, I could lay out a framework of what is known at the beginning of the calculation. It's not productive to represent every single step of the mathematical proof given by BStar, but I'm not sure exactly what steps can be left as processes in the mathematical proof and what steps need expounding in code.
/* Known points - A, B, C */
var xa = 10, ya = 10;
var xb = 100, yb = 500;
var xc = 700, yc = 400;
/* Known lengths m and n (distance perpendicularly from AB and AC) */
var m = 30;
var n = 50;
/* Point we want to calculate, P */
var px = 0, py = 0;
/* Calculation goes here - some Javascript notes:
* var a = Math.sin(angInRadians);
* var b = Math.asin(opposite / hypotenuse);
* var c = Math.pow(number, 2); // square a number
* var d = Math.sqrt(number);
*/
/* Print the result */
console.log('Result: P (' + px + ', ' + py + ')');
How would one express the maths from the diagram in the programming snippet above?
I think I can get you to the angle of B but I'm not very good with math and get lost with all those variables. If you are stuck at figuring out the angle try this and see if it does what you want. It seems to do what step 5 is asking but double check my work.
let pointA = {x: 100, y: 0};
let pointB = {x: 20, y: 20};
let pointC = {x: 0, y: 100};
let distBA_x = pointB.x - pointA.x;
let distBA_y = pointB.y - pointA.y;
//let BA_a = Math.sqrt(distBA_x*distBA_x + distBA_y*distBA_y);
let distBC_x = pointB.x - pointC.x;
let distBC_y = pointB.y - pointC.y;
//let BC_c = Math.sqrt(distBC_x*distBC_x + distBC_y*distBC_y);
var angle = Math.atan2(distBA_x * distBC_y - distBA_y * distBC_x, distBA_x * distBC_x + distBA_y * distBC_y);
if(angle < 0) {angle = angle * -1;}
var degree_angle = angle * (180 / Math.PI);
console.log(degree_angle)
I've laid it out on a canvas so you can see it visually and change the parameters. Hope it helps. Here's the Codepen https://codepen.io/jfirestorm44/pen/RwKdpRw
BA • BC is a "dot product" between two vectors. The result is a single number: It's the sum of the products of vector components. If the vectors are (x1,y1) and (x2,y2) the dot product is x1x2+y1y2.
Assuming you don't have a library for vector calculations and don't want to create one, the code for computing k would be:
k = (-xb*(xc - xb)-yb*(yc - yb)) / ac
I want to make a Tetradecagon, a polygon with 14 sides, with Processing.JS.
(I want to make the Tetradecagon like the one shown in the Image below!)
Using the numbers given in the image, which I would like to replicate, I concluded that each piece (I don't know it's proper name), has an angle of 25.714285714°.....25 and 10/14 = 25 and 5/7 - 5/7 in decimal form = 0.714285714So, I arrived at 25.714285714°
Now, in Processing.JS, I was wanting to use a while loop:
var r = 0;
var draw = function() {
translate(200,200);
while(r < 361){
rotate(r);
r = r + 25.714285714;
line(200,0,200,200);
}
};
Here, I have set one variable, r. r will be the variable for the rotate() function. The while loop will keep going until r meets 360 - this will allow for the the change in r, the angle, to increase by 25.714285714°, while r < 361.
But, sadly, this is not happening. What I see on my canvas is the line being shot off the screen.
(edit) I added translate(200,200); just above the while() loop - this helped, but the lines are still not looking like the picture above.
The second point of the line is not staying in the center; the whole line is being shifted. I only want the first (top) point to be shifted by the given change in angles.
How do I change the code in order to achieve the goal that I am striving for? Any help would be appreciated - Thanks for your time!
P.S. This is my result with the current code -
Processing.js is just for running Processing code. This looks like a mix of Processing and Javascript code so my first advice would be "write real Processing code".
With that said, if you want to do this based on coordinate rotation, look at your 14-gon: it's 14 repeated triangles, so analyze one triangle and draw that 14 times. Any triangular slice is defined by a line from "the center" to "a vertex on the 14-gon" at a (necessary) distance r, the radius of the circumscribing circle. So, given a vertex (r,0) on the 14-gon where is the next vertex (nx,ny)?
Simple maths:
first vertex = (x, y) = (r,0)
next vertex = (nx,ny) = (r,0) rotated over (0,0) by (phi = tau/14)
(I'm using tau here because it's a far more convenient constant for programming purposes. It's simply equal to 2*pi, and as such represents an entire circle, rather than a half circle)
Now, computing that rotate coordinate using basic trigonometry:
nx = r * cos(phi) - 0 * sin(phi) = r * cos(phi)
ny = r * sin(phi) + 0 * cos(phi) = r * sin(phi)
Alright, done. And this nx,ny computation is clearly not specific to the number 14, it about arbitrary angles, so let's code the solution and make it work for any n-sided polygon:
void setup() {
size(400,400);
noLoop();
}
void draw() {
background(255);
// offset the coordinate system so that (0,0) is the sketch center
translate(width/2,height/2);
// then draw a polygon. In this case, radius width/2, and 14 sided
drawNgon(width/2, 14);
}
void drawNgon(float r, float n) {
// to draw (r,0)-(x',y') we need x' and y':
float phi = TAU/n;
float nx = r * cos(phi);
float ny = r * sin(phi);
// and then we just draw that line as many times as there are sides
for(int a=0; a<n; a++) {
// draw line...
line(r,0, nx,ny);
// rotate the entire coordinate system...
rotate(phi);
// repeat until done.
}
}
And now we can freely change both the polygon radius and the number of sides by changing the input to drawNgon(..., ...).
I am working on a "rally" game where a car is drawing on hills made of cosine curves. I know the current xspeed of the car (without hills) but the problem is that I need to know the xspeed of the car on the hills to be able to draw the wheels on right places and keep the speed steady.
At the moment my solution looks like this.
function drawWheelOnBasicHill(hillStart, xLocWheel, wheelNro) {
var cw = 400 //the width of the hill
t_max = 2*Math.PI;
var scale = 80, step = cw, inc = t_max/step;
var t1 = (xLocWheel-hillStart)*inc
var y1 = -scale*0.5 * Math.cos(t1);
if(wheelNro == 1 ){ //backwheel
drawRotatedImage(wheel, car.wheel1x, car.wheel1y-y1-45,sx);
//drawing the wheel on canvas
} else { //frontwheel
drawRotatedImage(wheel, car.wheel2x, car.wheel2y-y1-45,sx);
}
for(var i=1; i<=car.speed; i++){ //finding the next xlocation of the wheel with the
//same distance (on the curve) to the previous location as the speed of the car(=the
//distance to the new point on the flat ground)
var t2 = (xLocWheel + i -hillStart)*inc
var y2 = -scale*0.5 * Math.cos(t2);
if(Math.round(Math.sqrt(i^2+(y2-y1)^2))==car.speed){
sx = sx+i; //the new xcoordinate break;
}
}
}
The for loop is the problem. It might bee too slow (animation with fps 24). I cant understand why the if statement isnt working at the moment. It works sometimes but most of the times the value of the condition newer reaches the actual xspeed.
Are there some more efficient and easier ways to do this? Or does this code contain some errors? I really appreciate your efforts to solve this! Ive been looking at this piece of code the whole day..
So i is the variable and
x2=x1+i
t2=t1+i*inc
y1=-scale*0.5 * Math.cos(t1)
y2=-scale*0.5 * Math.cos(t2)
which somehow is strange. The landscape should be time independent, that is, y should be a function of x only. The time step is external, determined by the speed of the animation loop. So a more logical model would have dx as variable and
dt = t2-t1
x2 = x1 + dx
y1 = f(x1) = -0.5*scale*cos(x1)
y2 = f(x2) = -0.5*scale*cos(x2)
and you would be looking for the intersection of
(x2-x1)^2+(y2-y1)^2 = (speed*dt)^2
which simplifies to
(speed*dt)^2=dx^2+0.25*scale^2*(cos(x1+dx)-cos(x1))^2
For small values of dx, which would be the case if dt or speed*dt is small,
cos(x1+dx)-cos(x1) is approx. -sin(x1)*dx
leading to
dx = (speed*dt) / sqrt( 1+0.25*scale^2*sin(x1)^2 )
To get closer to the intersection of curve and circle, you can then iterate the fixed point equation
dydx = 0.5*scale*(cos(x1+dx)-cos(x1))/dx
dx = (speed*dt) / ( 1+dydx^2 )
a small number of times.
The problem is currently solved. In case some one wants to see the colored fractal, the code is here.
Here is the previous problem:
Nonetheless the algorithm is straight forward, I seems to have a small error (some fractals are drawing correctly and some are not). You can quickly check it in jsFiddle that c = -1, 1/4 the fractal is drawing correctly but if I will take c = i; the image is totally wrong.
Here is implementation.
HTML
<canvas id="a" width="400" height="400"></canvas>
JS
function point(pos, canvas){
canvas.fillRect(pos[0], pos[1], 1, 1); // there is no drawpoint in JS, so I simulate it
}
function conversion(x, y, width, R){ // transformation from canvas coordinates to XY plane
var m = R / width;
var x1 = m * (2 * x - width);
var y2 = m * (width - 2 * y);
return [x1, y2];
}
function f(z, c){ // calculate the value of the function with complex arguments.
return [z[0]*z[0] - z[1] * z[1] + c[0], 2 * z[0] * z[1] + c[1]];
}
function abs(z){ // absolute value of a complex number
return Math.sqrt(z[0]*z[0] + z[1]*z[1]);
}
function init(){
var length = 400,
width = 400,
c = [-1, 0], // all complex number are in the form of [x, y] which means x + i*y
maxIterate = 100,
R = (1 + Math.sqrt(1+4*abs(c))) / 2,
z;
var canvas = document.getElementById('a').getContext("2d");
var flag;
for (var x = 0; x < width; x++){
for (var y = 0; y < length; y++){ // for every point in the canvas plane
flag = true;
z = conversion(x, y, width, R); // convert it to XY plane
for (var i = 0; i < maxIterate; i++){ // I know I can change it to while and remove this flag.
z = f(z, c);
if (abs(z) > R){ // if during every one of the iterations we have value bigger then R, do not draw this point.
flag = false;
break;
}
}
// if the
if (flag) point([x, y], canvas);
}
}
}
Also it took me few minutes to write it, I spent much more time trying to find why does not it work for all the cases. Any idea where I screwed up?
Good news! (or bad news)
You're implementation is completely. correct. Unfortunately, with c = [0, 1], the Julia set has very few points. I believe it is measure zero (unlike say, the Mandelbrot set). So the probability of a random point being in that Julia set is 0.
If you reduce your iterations to 15 (JSFiddle), you can see the fractal. One hundred iterations is more "accurate", but as the number of iterations increase, the chance that a point on your 400 x 400 grid will be included in your fractal approximation decreases to zero.
Often, you will see the Julia fractal will multiple colors, where the color indicates how quickly it diverges (or does not diverge at all), like in this Flash demonstration. This allows the Julia fractal to be somewhat visible even in cases like c = i.
Your choices are
(1) Reduce your # of iterations, possibly depending on c.
(2) Increase the size of your sampling (and your canvas), possibly depending on c.
(3) Color the points of your canvas according to the iteration # at which R was exceeded.
The last option will give you the most robust result.
I'm sorry to say that Math really isn't my strong suit. Normally I can get by, but this has got me totally stumped.
I'm trying to code up a quiz results screen in HTML/CSS/Javascript.
On my interface, I have a semicircle (the right hemisphere of a target).
I have a range of 'scores' (integers out of 100 - so 50, 80, 90 etc.).
I need to plot these points on the semicircle to be n% away from the centre, where n is the value of each score - the higher the score, the closer to the centre of the target the point will appear.
I know how wide my semicircle is, and have already handled the conversion of the % values so that the higher ones appear closer to the centre while the lower ones appear further out.
What I can't wrap my head around is plotting these points on a line that travels out from the centre point (x = 0, y = target height/2) of the target at a random angle (so the points don't overlap).
Any suggestions are gratefully received!
Do you have an example of what you want this to look like? It sounds like you want to divide up the circle into N slices where N is the number of points you need to display, then plot the points along each of those radii. So you might have something like:
Edit: code was rotating about the origin, not the circle specified
var scores = [];
//...
//assume scores is an array of distances from the center of the circle
var points = [];
var interval = 2 * Math.PI / N;
var angle;
for (var i = 0; i < N; i++) {
angle = interval * i;
//assume (cx, cy) are the coordinates of the center of your circle
points.push({
x: scores[i] * Math.cos(angle) + cx,
y: scores[i] * Math.sin(angle) + cy
});
}
Then you can plot points however you see fit.
After much headscratching, I managed to arrive at this solution (with the help of a colleague who's much, much better at this kind of thing than me):
(arr_result is an array containing IDs and scores - scores are percentages of 100)
for (var i = 0; i < arr_result.length; i++){
var angle = angleArray[i]; // this is an array of angles (randomised) - points around the edge of the semicircle
var radius = 150; // width of the semicircle
var deadZone = 25 // to make matters complicated, the circle has a 'dead zone' in the centre which we want to discount
var maxScore = 100
var score = parseInt(arr_result[i]['score'], 10)
var alpha = angle * Math.PI
var distance = (maxScore-score)/maxScore*(radius-deadZone) + deadZone
var x = distance * Math.sin(alpha)
var y = radius + distance * Math.cos(alpha)
$('#marker_' + arr_result[i]['id'], templateCode).css({ // target a specific marker and move it using jQuery
'left' : pointX,
'top': pointY
});
}
I've omitted the code for generating the array of angles and randomising that array - that's only needed for presentational purposes so the markers don't overlap.
I also do some weird things with the co-ordinates before I move the markers (again, this has been omitted) as I want the point to be at the bottom-centre of the marker rather than the top-left.