I am currently working on a 2D javascript game and I am doing the movement mechanics right now. I want players to be able to move forward and backward, towards or away from the mouse, while also having the ability to strafe.
I got the mouse following down pretty well but I am stuck on how to implement the strafing. I need my player to move along a dynamic circular path that changes sizes depending on how far away the player is from the mouse.
ex: If the mouse was the red X, I want to move the player along the green circular path.
This path of course will be changing size based on how far away the player is from the mouse.
I am updating the players position by moving whenever the movement keys are pressed so I am really looking for an equation to move the player in the correct circular path that can be implemented in a "position updated every second" sort of way.
I know that for a circular path, the coordinates can be found by:
x = centerX * radius * Math.cos(theta);
y = centerY * radius * Math.sin(theta);
But I am having trouble implementing. Here is some of my framework, but I am afraid all the solutions I have tried haven't even gotten me close so I will not post the broken math I have already deleted
Player.prototype.update = function(delta){
this.playerCenter = [this.x+this.width/2, this.y+this.height/2];
let dX = (GAME.mouse.position.x - this.playerCenter[0]),
dY = (GAME.mouse.position.y - this.playerCenter[1]);
radius = Math.sqrt(dX * dX + dY * dY);
// Movement Forward
if(GAME.keyDown[87] && radius >= 50){
this.x += (dX / radius) * this.movementSpeed * delta;
this.y += (dY / radius) * this.movementSpeed * delta;
}
// Movement Backward
if(GAME.keyDown[83]){
this.x -= (dX / radius) * this.movementSpeed * delta;
this.y -= (dY / radius) * this.movementSpeed * delta;
}
// Strafe left
if(GAME.keyDown[65]){
}
// Strafe right
if(GAME.keyDown[68]){
}
}
You almost have the solution.
You need to go at 90 deg to the forward vector. To rotate a vector 90cw you swap the x,and y and negate the new x.
EG
dx = ?; // forward direction
dy = ?;
// rotate 90 clockwise
dx1 = -dy;
dy1 = dx;
Thus you can update your code as follows
var dX = (GAME.mouse.position.x - this.playerCenter[0]);
var dY = (GAME.mouse.position.y - this.playerCenter[1]);
var radius = Math.sqrt(dX * dX + dY * dY);
//normalise
if(radius > 0){
dX = (dX / radius) * this.movementSpeed * delta;
dY = (dY / radius) * this.movementSpeed * delta;;
}else{
dX = dY = 0; // too close need to set this or you will get NaN propagating through your position variables.
}
if(GAME.keyDown[87] && radius >= 50){ // Movement Forward
this.x += dX;
this.y += dY;
}
if(GAME.keyDown[83]){ // Movement Backward
this.x -= dX;
this.y -= dY;
}
if(GAME.keyDown[65]){ // Strafe left
this.x += -dY; // swap x and y negate new x to rotate vector 90
this.y += dX;
}
if(GAME.keyDown[68]){ // Strafe right
this.x -= -dY; // swap x and y negate new x to rotate vector 90
this.y -= dX;
}
Related
I know this has been asked a lot, but personally, i couldn't find a suitable answer. Pretty much everywhere, the function looks something like:
function rccol(rect, circle){
var dx = Math.abs(circle.x - (rect.x + rect.width / 2));
var dy = Math.abs(circle.y - (rect.y + rect.height / 2));
if(dx > circle.radius + rect.width / 2) return false;
if(dy > circle.radius + rect.height / 2) return false;
if(dx <= rect.width) return true;
if(dy <= rect.height) return true;
var dx = dx - rect.width;
var dy = dy - rect.height
return((dx * dx + dy * dy) <= (circle.radius * circle.radius));
}
And that works perfectly. The issue is that I'm using it for collision detection in a game, where the circle is the player's collision box, and the square is let's say a wall. I need to be able to determine where the contact occurred so that i can actually prevent the "player" from going into the "wall" so the simple boolean that gets returned, doesn't really work in my use-case.
Having circle center coordinates (cx, cy), you can calculate squared distance from circle center to rectangle.
dx = Max(Abs(cx - rect.center.x) - rect.width / 2, 0)
dy = Max(Abs(cy - rect.center.y) - rect.height / 2, 0)
SquaredDistance = dx * dx + dy * dy
When circle is outside of rectangle initially, it is possible to remove Max call.
dx = Abs(cx - rect.center.x) - rect.width / 2
dy = Abs(cy - rect.center.y) - rect.height / 2
Also we can remove Abs for known initial position (note - upto moment of sign change!)
if cx >= rect.center.x:
dx = cx - rect.center.x - rect.width / 2
else:
dx = - cx + rect.center.x - rect.width / 2
To avoid a lot od different cases, we can virtually put player in the first quadrant relative to rectangle center and correspondingly change coordinates and velocity components
if cx0 < 0:
cx0 = - cx0
vx = -vx
if cy0 < 0:
cy0 = - cy0
vy = -vy
To register collision moment, you have to substitute coordinates with parametric equations using start point and velocity vector components (vx, vy)
cx = cx0 + vx * t
cy = cy0 + vy * t
and solve (quadratic) equation for t
SquaredDistance - Radius^2 = 0
(cx0 + vx * t - rect.center.x - rect.width/2)^2 +
(cy0 + vy * t - rect.center.y - rect.height/2)^2 -
Radius^2 = 0
Ater that you can get zero (no collision), one (touch event) or two roots (moment of collision and moment of exit).
I'm working on a game with HTML5 Canvas and JavaScript. It's a simple space shooting game with a cannon in the center of the screen. I can rotate the cannon and fire missiles in the same angle as the cannons direction.
But I have a problem. For the missiles X and Y starting point, I'm using the X and Y position of the cannon. This looks weird, because I want the missile to start outside of the cannon, like perhaps 50 pixels in the direction of the angle. How do I calculate that?
With this code I create Missile objects:
var dX = Math.cos(this.playerRotationAngle * Math.PI / 180);
var dY = Math.sin(this.playerRotationAngle * Math.PI / 180);
this.activeMissilesArray.push(new Missile(cannon.posX, cannon.posY, dX, dY));
And this is from the constructor function of the Missile object where I calculate the direction:
this.directionX = dX * this.speed;
this.directionY = dY * this.speed;
The Draw method:
Draw: function(context)
{
context.drawImage(this.missile, this.posX-20, this.posY-20);
}
The Update method:
Update: function()
{
this.posX += this.directionX;
this.posY += this.directionY;
}
Have you tried using your speed formula with a value of 50 to adjust the initial position?
// inside the Missile constructor
// instead of:
// this.posX = x;
// this.posY = y;
// do:
this.posX = x + 50 * dX;
this.posY = y + 50 * dY;
What I am aiming to do is arc the position of a circle towards the position of the mouse cursor, this all being relative to the world viewed through the canvas. To keep a handle on the speed at which the circle moves I decided to make a boundary larger than the circle, if the mouse is outside the boundary then the "position" of the mouse is brought to the boundary so that when I arc towards the coords, if they arent super far from the position of the circle it doesnt move at crazy speeds. I have this working and this is the code which does it:
dx = Game.controls.mouseX - (this.x - xView); // get the distance between the x coords
dy = Game.controls.mouseY - (this.y - yView); // get the distance between the y coords
radii = this.radius + 1; // +1 because the "radius" of the mouse is 1
if((dx * dx) + (dy * dy) > radii * radii) // is the mouse not over the player?
{
if((dx * dx) + (dy * dy) < 301 * 301)
{
this.x += ((Game.controls.mouseX - (this.x - xView)) * 2 / (this.mass)) + step;
this.y += ((Game.controls.mouseY - (this.y - yView)) * 2 / (this.mass)) + step;
}
else
{
mx = Game.controls.mouseX;
my = Game.controls.mouseY;
do
{
dx = mx - (this.x - xView);
dy = my - (this.y - yView);
mx += (((this.x - xView) - mx) * 2 / (this.mass)) + step;
my += (((this.y - yView) - my) * 2 / (this.mass)) + step;
} while((dx * dx) + (dy * dy) > 301 * 301)
this.x += ((mx - (this.x - xView)) * 2 / (this.mass)) + step;
this.y += ((my - (this.y - yView)) * 2 / (this.mass)) + step;
}
}
The magic for 'outside the boundary' lies withing the do while. This is the best fix I could come up with and I cant see this as being an elegant or fast solution and am wondering what the proper course of action should be.
Im no artist but hopefully this image helps to illustrate what I am trying to achieve. The Black dot is the mouse pos, the black circle is the circle and the red circle is the boundary I have specified. I want to get the coords marked by the X.
Your question is a special case of Circle line-segment collision detection algorithm?, in this case with B and C being the same points, so you can use your center point for both of them.
That solution is given in C, but it translates to JavaScript very easily, just replace float with var, use Math.sqrt() and so on...
Oh, and then there is a JvaScript version here: Calculate the point of intersection of circle and line through the center, that's more appropriate :-)
If the black circle is in the center of the red circle and you have the radius of the red circle
// c is circle center
// mouse is the mouse position. Should have properties x,y
// radius is the circle radius;
// returns the point on the line where the circle intercepts it else it returns undefined.
function findX(c, mouse, radius)
var v = {};
// get the vector to the mouse
v.x = mouse.x - c.x;
v.y = mouse.y - c.y;
var scale = radius / Math.hypot(v.x,v.y);
if(scale < 1){ // is it outside the circle
return {
x : c.x + v.x * scale,
y : c.y + v.y * scale
};
}
return;
}
And if the the line start is not the center then a general purpose line circle intercept function will solve the problem. If the line starts inside the circle the function will return just one point. If the line is not long enough it will return an empty array..
// p1,p2 are the start and end points of a line
// returns an array empty if no points found or one or two points depending on the number of intercepts found
// If two points found the first point in the array is the point closest to the line start (p1)
function circleLineIntercept(circle,radius,p1,p2){
var v1 = {};
var v2 = {};
var ret = [];
var u1,u2,b,c,d;
// line as vector
v1.x = p2.x - p1.x;
v1.y = p2.y - p1.y;
// vector to circle center
v2.x = p1.x - circle.x;
v2.y = p1.y - circle.y;
// dot of line and circle
b = (v1.x * v2.x + v1.y * v2.y) * -2;
// length of line squared * 2
c = 2 * (v1.x * v1.x + v1.y * v1.y);
// some math to solve the two triangles made by the intercept points, the circle center and the perpendicular line to the line.
d = Math.sqrt(b * b - 2 * c * (v2.x * v2.x + v2.y * v2.y - radius * radius));
// will give a NaN if no solution
if(isNaN(d)){ // no intercept
return ret;
}
// get the unit distance of each intercept to the line
u1 = (b - d) / c;
u2 = (b + d) / c;
// check the intercept is on the line segment
if(u1 <= 1 && u1 >= 0){
ret.push({x:line.p1.x + v1.x * u1, y : line.p1.y + v1.y * u1 });
}
// check the intercept is on the line segment
if(u2 <= 1 && u2 >= 0){
ret.push({x:line.p1.x + v1.x * u2, y : line.p1.y + v1.y * u2});
}
return ret;
}
So I am a bit confused on how I can make a shape animate to the center of a canvas. I can get the center value:
width = canvas.width = window.innerWidth,
height = canvas.height = window.innerHeight,
centerX = width / 2,
centerY = height / 2;
and a simple decrement or increment depending on whether the initial position is positive or negative can be done as well:
var x = 100;
var y = 100;
function fn (){
ctx.beginPath();
ctx.arc(x, y, 50, 0, 2 * Math.PI, false);
ctx.fillStyle = '#444';
ctx.fill();
ctx.closePath();
x -= 1;
y -= 1;
}
The animation would be done using:
requestAnimationFrame(fn)
Problem with all this is. I need to manually adjust the x and y everytime. How can I better simply make the x and y values random for the shape and make it animate to the center, no matter from what direction and if the initial position is negative or positive. I was thinking of atang2 but honestly im not entirely sure.
You're basically on the right track. Use Math.sqrt for the distance and Math.atan2 to find the direction. Then its just the matter of how fast (velocity) you want the object to move to the target (centre of the canvas).
var tx = centerX - x,
tx = centerY - y,
distance = Math.sqrt(tx * tx + ty * ty),
radius = Math.atan2(ty, tx),
angle = (radius / Math.PI) * 180;
// Ensure we don't divide by zero if distance is 0
if (distance !== 0)
{
velX = (tx / distance) * velocity;
velY = (ty / distance) * velocity;
x += velX;
y += velY;
}
The answer given is flawed as there is no check for divide by zero. This error can easily be overlooked and then crop up in production code making it very hard to find out what has gone wrong.
Should be
var tx = centre.x - x;
var ty = centre.y - y;
var dist = Math.sqrt(tx * tx + ty * ty);
// or
var dist = Math.sqrt(Math.pow(tx, 2) + Math.pow(ty, 2));
if(dist !== 0){ // must have this test or when the coords get to the centre
// you will get a divide by zero
tx /= dist; // Normalise direction vector
ty /= dist;
}
tx *= speed; // set the magnitude to required speed;
ty *= speed; // Note that if at the centre this will be zero
x += tx;
y += ty;
I think it's usual question, but I have some problems with displaying dots in canvas. The first thing I'd like to know is how to draw dot like this (please zoom it).
The second thing is, how to draw a shadow to each element of the grid of this dots, with the light source in the center.
What I have at this moment right here:
the part of my code:
context.fillStyle = "#ccc";
context.shadowColor = '#e92772';
context.shadowOffsetX = 15;
context.shadowOffsetY = 15;
while (--e >= 1) {
x -= z;
if(x < 0) {
x = z*w;
y -= z;
}
context.moveTo(x, y);
context.fillRect( x, y, 1, 1 );
outs = a[e];
}
Also, I've tried to use "context.arc();", but I think "context.fillRect();" is more easier. And one else moment, when I use "while (--e >= 0)" instead of "while (--e >= 1)" I have two more dots, on the top. Why?
If you know some articles or tutorials, would you give me the link to them. Preferably without the use of the frameworks. Thanks.
You can use some trigonometry to simulate 3D dots with a light source.
HERE IS AN ONLINE DEMO
This is one way you can do it, there are of course others (this was the first that came to mind):
Draw the grid with some dots on the main canvas
Render a radial gradient to an off-screen canvas
Change composition mode so anything is draw on already existing pixels
Calculate distance and angle to light source and draw the dot to each grid point offset with the angle/dist.
Here is some code from the demo that does this.
Draw the grid with dots
We skip one grid point as we will fill each dot later with the gradient dot which otherwise would paint over the neighbor dot.
/// draw a grid of dots:
for (y = 0; y < ez.width; y += gridSize * 2) {
for (x = 0; x < ez.height; x += gridSize * 2) {
ctx.beginPath();
ctx.arc(x + offset, y + offset, radius, 0, arcStop);
ctx.closePath();
ctx.fill();
}
}
Create a light "reflection"
Prepare the gradient dot to an off-screen canvas (dctx = dot-context). I am using easyCanvas for the setup and to give me an off-screen canvas with center point already calculated, but one can setup this manually too of course:
grd = dctx.createRadialGradient(dot.centerX, dot.centerY, 0,
dot.centerX, dot.centerY, gridSize);
grd.addColorStop(0, '#fff');
grd.addColorStop(0.2, '#777'); // thighten up
grd.addColorStop(1, '#000');
dctx.fillStyle = grd;
dctx.fillRect(0, 0, gridSize, gridSize);
Do the math
Then we do all the calculation and offsetting:
/// change composition mode
ctx.globalCompositeOperation = 'source-atop';
/// calc angle and distance to light source and draw each
/// dot gradient offset in relation to this
for (y = 0; y < ez.width; y += gridSize) {
for (x = 0; x < ez.height; x += gridSize) {
/// angle
angle = Math.atan2(lightY - y, lightX - x);
//if (angle < 0) angle += 2;
/// distance
dx = lightX - x;
dy = lightY - y;
dist = Math.sqrt(dx * dx + dy * dy);
/// map distance to our max offset
od = dist / maxLength * maxOffset * 2;
if (od > maxOffset * 2) od = maxOffset * 2;
/// now get new x and y position based on angle and offset
offsetX = x + od * Math.cos(angle) - maxOffset * 0.5;
offsetY = y + od * Math.sin(angle) - maxOffset * 0.5;
/// draw the gradient dot at offset
ctx.drawImage(dot.canvas, x + offsetX, y + offsetY);
}
}
Shadow
For the shadow you just inverse the offset while using the composition mode destination-over which will draw outside the already drawn pixels:
/// Shadow, same as offsetting light, but in opposite
/// direction and with a different composite mode
ctx.globalCompositeOperation = 'destination-over';
for (y = 0; y < ez.width; y += gridSize) {
for (x = 0; x < ez.height; x += gridSize) {
/// angle
angle = Math.atan2(lightY - y, lightX - x);
//if (angle < 0) angle += 2;
/// distance
dx = lightX - x;
dy = lightY - y;
dist = Math.sqrt(dx * dx + dy * dy);
/// map distance to our max offset
od = dist / maxLength * maxOffset * 2;
if (od > maxOffset * 4) od = maxOffset * 4;
/// now get new x and y position based on angle and offset
offsetX = x - od * Math.cos(angle) + gridSize * 0.5;
offsetY = y - od * Math.sin(angle) + gridSize * 0.5;
ctx.beginPath();
ctx.arc(x + offsetX, y + offsetY, radius, 0, arcStop);
ctx.fill();
}
}
This can all be optimized of-course into a single loop pair but for overview the code is separated.
Additional
In the demo I added mouse tracking so the mouse becomes the light-source and you can see the dot-reflection changes while you move the mouse. For best performance use Chrome.
To match your need just scale down the values I am using - or - draw to a big off-screen canvas and use drawImage to scale it down to a main canvas.