I have a function which gets the mouse position in world space, then checks to see if the mouse is over or near to the circle's line.
The added complication how ever is the circle is transformed at an angle so it's more of an ellipse. I can't see to get the code to detect that the mouse is near the border of circle and am unsure where I am going wrong.
This is my code:
function check(evt){
var x = (evt.offsetX - element.width/2) + camera.x; // world space
var y = (evt.offsetY - element.height/2) + camera.y; // world space
var threshold = 20/scale; //margin to edge of circle
for(var i = 0; i < obj.length;i++){
// var mainAngle is related to the transform
var x1 = Math.pow((x - obj[i].originX), 2) / Math.pow((obj[i].radius + threshold) * 1,2);
var y1 = Math.pow((y - obj[i].originY),2) / Math.pow((obj[i].radius + threshold) * mainAngle,2);
var x0 = Math.pow((x - obj[i].originX),2) / Math.pow((obj[i].radius - threshold) * 1, 2);
var y0 = Math.pow((y - obj[i].originY),2) / Math.pow((obj[i].radius - threshold) * mainAngle, 2);
if(x1 + y1 <= 1 && x0 + y0 >= 1){
output.innerHTML += '<br/>Over';
return false;
}
}
output.innerHTML += '<br/>out';
}
To understand it better, I have a fiddle here: http://jsfiddle.net/nczbmbxm/ you can move the mouse over the circle, it should say "Over" when you are within the threshold of being near the circle's perimeter. Currently it does not seem to work. And I can't work out what the maths needs to be check for this.
There is a typo on line 34 with orignX
var x1 = Math.pow((x - obj[i].orignX), 2) / Math.pow((obj[i].radius + threshold) * 1,2);
should be
var x1 = Math.pow((x - obj[i].originX), 2) / Math.pow((obj[i].radius + threshold) * 1,2);
now you're good to go!
EDIT: In regards to the scaling of the image and further rotation of the circle, I would set up variables for rotation about the x-axis and y-axis, such as
var xAngle;
var yAngle;
then as an ellipse can be written in the form
x^2 / a^2 + y^2 / b^2 = 1
such as in Euclidean Geometry,
then the semi-major and semi-minor axes would be determined by the rotation angles. If radius is the circles actual radius. then
var semiMajor = radius * cos( xAngle );
var semiMinor = radius;
or
var semiMajor = radius;
var semiMinor = radius * cos( yAngle );
you would still need to do some more transformations if you wanted an x and y angle.
so if (xMouseC, yMouseC) are the mouse coordinates relative to the circles centre, all you must do is check if that point satisfies the equation of the ellipse to within a certain tolerance, i.e. plug in
a = semiMajor;
b = semiMinor;
x = xMouseC;
y = yMouseC;
and see if it is sufficiently close to 1.
Hope that helps!
Related
I'm creating a raycasting engine on javascript using p5js and there is an issue with the line to line (raycast to wall) intersection.
I found a lot of line to line collision algorithms, including p5 collide library, but the problem appears on every one of them.
this.intersects = function (raycastStart, raycastEnd) {
var x1 = this.startPoint.x; //Start point is the first point of a line.
var y1 = this.startPoint.y;
var x2 = this.endPoint.x; //End point is the second point of a line.
var y2 = this.endPoint.y;
var x3 = raycastStart.x;
var y3 = raycastStart.y;
var x4 = raycastEnd.x;
var y4 = raycastEnd.y;
var a_dx = x2 - x1;
var a_dy = y2 - y1;
var b_dx = x4 - x3;
var b_dy = y4 - y3;
var s = (-a_dy * (x1 - x3) + a_dx * (y1 - y3)) / (-b_dx * a_dy + a_dx * b_dy);
var t = (+b_dx * (y1 - y3) - b_dy * (x1 - x3)) / (-b_dx * a_dy + a_dx * b_dy);
//Vector2 is simply class with two fields: x and y.
return (s >= 0 && s <= 1 && t >= 0 && t <= 1) ? new Vector2(x1 + t * a_dx, y1 + t * a_dy) : null;
}
The line to line collision works on one side properly, but on the other, it works incorrect, according to my y position.
this is my map.
on one side it works perfectly
but on the other, it checks collision for line segments, that are lower than my Y position
(I would comment, but don't have enough reputation to do so...)
It appears that your line collision algorithm is working. But what appears to be missing is a check to determine which raycaster-to-line intersection is closer. That is, in your working example the raycast never casts across two line segments, so there is no question about which line segment constrains your raycast. But in your non-working example, the raycaster hits 2 of your 4 segments, so you now need to determine which of the 2 intersection points is closer to the raycast start, in order to determine which line segment is closer.
I was trying to make something that told you the intersection points of two circles. Where I put in the centers of the circles and the radius. (I got the intersection function from stackoverflow: here). I am trying to add the user input but when ever I change the static number inside the code to a user input (either through prompt or html input), the function breaks and the alert sends me an unfinished answer and an Nan.
Here is the coding so far (without user input):
<html>
<button onclick="button()">Test</button>
<script>
var x0 = 3;
var y0 = 0;
var r0 = 3;
var x1 = -1;
var y1 = 0;
var r1 = 2;
function button() {
intersection(x0, y0, r0, x1, y1, r1)
function intersection(x0, y0, r0, x1, y1, r1) {
var a, dx, dy, d, h, rx, ry;
var x2, y2;
/* dx and dy are the vertical and horizontal distances between
* the circle centers.
*/
dx = x1 - x0;
dy = y1 - y0;
/* Determine the straight-line distance between the centers. */
d = Math.sqrt((dy*dy) + (dx*dx));
/* Check for solvability. */
if (d > (r0 + r1)) {
/* no solution. circles do not intersect. */
return false;
}
if (d < Math.abs(r0 - r1)) {
/* no solution. one circle is contained in the other */
return false;
}
/* 'point 2' is the point where the line through the circle
* intersection points crosses the line between the circle
* centers.
*/
/* Determine the distance from point 0 to point 2. */
a = ((r0*r0) - (r1*r1) + (d*d)) / (2.0 * d) ;
/* Determine the coordinates of point 2. */
x2 = x0 + (dx * a/d);
y2 = y0 + (dy * a/d);
/* Determine the distance from point 2 to either of the
* intersection points.
*/
h = Math.sqrt((r0*r0) - (a*a));
/* Now determine the offsets of the intersection points from
* point 2.
*/
rx = -dy * (h/d);
ry = dx * (h/d);
/* Determine the absolute intersection points. */
var xi = x2 + rx;
var xi_prime = x2 - rx;
var yi = y2 + ry;
var yi_prime = y2 - ry;
var list = "(" + xi + ", " + yi + ")" + "(" + xi_prime + ", " +
yi_prime + ")"
alert(list);
}
}
</script>
</html>
When I change anyone of the variables that apart of the circle into user input like:
var x0 = prompt("X cord of circle 1");
The alert comes up as: (3-2.6250, -1.4523687548277813)(NaN, 1.4523687548277813)
and without the user input (shown in the large code block) it comes out as: (0.375, -1.4523687548277813)(0.375, 1.4523687548277813). Which is the correct answer.
Can anyone tell me what I am doing wrong or what is going on?
Prompt will take the user input as a string. To convert it to an integer for math jazz, use parseInt.
var x0String = prompt("X cord of circle 1");
var x0 = parseInt(x0String);
JavaScript should "convert" numeric string to integer if you perform calculations on it since JS is weakly typed, but it is good practice and you can avoid some pitfalls by parsing the integer value from a string yourself.
Your prompt returns a string, but you can't do math on a string. Try converting it to a number:
var x0 = Number(prompt("X cord of circle 1"));
As Daniel pointed out it's always better to change the string to a number if you need it as a number. It seemed really confusing, why the program was not working, until I found that x0 is used twice.
The reason the program was returning NaN is because when using the + operator, the number is converted into a string not a number.
That happens here: x0 + (dx * a/d);
What happens then is that a negative number is added to the string creating something like: 2-2
As you might expect the value can no longer be converted into a number, thus returning NaN, when we try to minus it later.
Yes theres a few threads on this, but not many using angles and I'm really trying to figure it out this way,
I'm now stuck on setting the new velocity angles for the circles. I have been looking at:
http://www.hoomanr.com/Demos/Elastic2/
as a reference to it, but I'm stuck now.
Can anybody shed some light?
cx/cy/cx2/cy2 = center x/y for balls 1 and 2.
vx/vy/vx2/vy2 = velocities for x/y for balls 1 and 2
function checkCollision() {
var dx = cx2 - cx; //distance between x
var dy = cy2 - cy; // distance between y
var distance = Math.sqrt(dx * dx + dy * dy);
var ang = Math.atan2(cy - cy2, cx - cx2);
// was displaying these in a div to check
var d1 = Math.atan2(vx, vy); //ball 1 direction
var d2 = Math.atan2(vx2, vy2); //ball 2 direction
// this is where I am stuck, and i've worked out this is completely wrong now
// how do i set up the new velocities for
var newvx = vx * Math.cos(d1 - ang);
var newvy = vy * Math.sin(d1 - ang);
var newvx2 = vx2 * Math.cos(d2 - ang);
var newvy2 = vy2 * Math.sin(d2 - ang);
if (distance <= (radius1 + radius2)) {
//Set new velocity angles here at collision..
}
Heres a codepen link:
http://codepen.io/anon/pen/MwbMxX
A few directions :
• As mentioned in the comments, use only radians (no more *180/PI).
• atan2 takes y as first param, x as second param.
var d1 = Math.atan2(vy, vx); //ball 1 direction in angles
var d2 = Math.atan2(vy2, vx2); //ball 2 direction in angles
• to rotate a vector, compute first its norm, then only project it with the new angle :
var v1 = Math.sqrt(vx*vx+vy*vy);
var v2 = Math.sqrt(vx2*vx2+vy2*vy2);
var newvx = v1 * Math.cos(d1 - ang);
var newvy = v1 * Math.sin(d1 - ang);
var newvx2 = v2 * Math.cos(d2 - ang);
var newvy2 = v2 * Math.sin(d2 - ang);
• You are detecting the collision when it already happened, so both circles overlap, but you do NOT solve the collision, meaning the circles might still overlap on next iteration, leading to a new collision and a new direction taken, ... not solved, etc..
-->> You need to ensure both circles are not colliding any more after you solved the collision.
• Last issue, but not a small one, is how you compute the angle. No more time for you sorry, but it would be helpful both for you and us to build one (several) scheme showing how you compute the angles.
Updated (but not working) codepen here :
http://codepen.io/anon/pen/eNgmaY
Good luck.
Edit :
Your code at codepen.io/anon/pen/oXZvoe simplify to this :
var angle = Math.atan2(dy, dx),
spread = minDistance - distance,
ax = spread * Math.cos(angle),
ay = spread * Math.sin(angle);
vx -= ax;
vy -= ay;
vx2 += ax;
vy2 += ay;
You are substracting the gap between both circles from the speed. Since later you add the speed to the position, that will do the spatial separation (=> no more collision).
I think to understand what vx-=ax means, we have to remember newton : v = a*t, where a is the acceleration, so basically doing vx=-ax means applying a force having the direction between both centers as direction, and the amount by which both circle collided (spread) as intensity. That amount is obviously quite random, hence the numerical instability that you see : sometimes a small effect, sometimes a big one.
look here for a constant punch version :
http://codepen.io/anon/pen/WvpjeK
var angle = Math.atan2(dy, dx),
spread = minDistance - distance,
ax = spread * Math.cos(angle),
ay = spread * Math.sin(angle);
// solve collision (separation)
cx -= ax;
cy -= ay;
// give a punch to the speed
var punch = 2;
vx -= punch*Math.cos(angle);
vy -= punch*Math.sin(angle);
vx2 += punch*Math.cos(angle);
vy2 += punch*Math.sin(angle);
I'm developing a user-interface for positioning an image on a google map.
I started from : http://overlay-tiler.googlecode.com/svn/trunk/upload.html which is pretty close to what I want.
But instead of 3 contact points I want a rotate tool, a scale tool and a translate tool (the later exists).
I tried to add a rotate tool but it doesn't work as I expected :
I put a dot on the left bottom corner that control the rotation (around the center of the image). The mouse drag the control dot and I calculate the 3 others points.
My code is based on the mover object but I changed the onMouseMove function :
overlaytiler.Rotater.prototype.rotateDot_ = function(dot, theta, origin) {
dot.x = ((dot.x - origin.x) * Math.cos(theta) - (dot.y - origin.y) * Math.sin(theta)) + origin.x;
dot.y = ((dot.x - origin.x) * Math.sin(theta) + (dot.y - origin.y) * Math.cos(theta)) + origin.y;
dot.render();
};
overlaytiler.Rotater.prototype.onMouseMove_ = function(e) {
var dots = this.controlDots_;
var center = overlaytiler.Rotater.prototype.getCenter_(dots);
// Diagonal length
var r = Math.sqrt(Math.pow(this.x - center.x, 2) + Math.pow(this.y - center.y, 2));
var old = {
x: this.x,
y: this.y
};
// Real position
var newPos = {
x: this.x + e.clientX - this.cx,
y: this.y + e.clientY - this.cy
}
var newR = Math.sqrt(Math.pow(newPos.x - center.x, 2) + Math.pow(newPos.y - center.y, 2));
var theta = - Math.acos((2 * r * r - (Math.pow(newPos.x - old.x, 2) + Math.pow(newPos.y - old.y, 2))) / (2 * r * r));
// Fixed distance position
this.x = (newPos.x - center.x) * (r / newR) + center.x;
this.y = (newPos.y - center.y) * (r / newR) + center.y;
dots[1].x = center.x + (center.x - this.x);
dots[1].y = center.y + (center.y - this.y);
dots[1].render();
overlaytiler.Rotater.prototype.rotateDot_(dots[2], theta, center);
overlaytiler.Rotater.prototype.rotateDot_(dots[0], theta, center);
// Render
this.render();
this.cx = e.clientX;
this.cy = e.clientY;
};
Unfortunately there is a problem with precision and angle sign.
http://jsbin.com/iQEbIzo/4/
After a few rotations the image is highly distorted and rotation is supported only in one direction.
I wonder how I can achieve a great precision and without any distortion.
Maybe my approach is useless here (try to move the corners at the right coordinates), I tried to rotate the image with the canvas but my attempts were unsuccessful.
Edit : Full working version : http://jsbin.com/iQEbIzo/7/
Here is my version of it. #efux and #Ben answers are far more complete and well designed however the maps don't scale in/out when you zoom in/out. Overlays very likely need to do this since they are used to put a "second map" or photograph over the existing map.
Here is the JSFiddle: http://jsfiddle.net/adelriosantiago/3tzzwmsx/4/
The code that does the drawing is the following:
DebugOverlay.prototype.draw = function() {
var overlayProjection = this.getProjection();
var sw = overlayProjection.fromLatLngToDivPixel(this.bounds_.getSouthWest());
var ne = overlayProjection.fromLatLngToDivPixel(this.bounds_.getNorthEast());
var div = this.div_;
div.style.left = sw.x + 'px';
div.style.top = ne.y + 'px';
div.style.width = (ne.x - sw.x) + 'px';
div.style.height = (sw.y - ne.y) + 'px';
div.style.transform = 'rotate(' + rot + 'deg)';
};
For sure this code could be implemented on efux and Ben code if needed but I haven't tried yet.
Note that the box marker does not updates its position when the rotation marker moves...
rotation is supported only in one direction
This is due to how you calculate the angle between two vectors.
It always gives you the same vector no matter if the mouse is right of the dot or not. I've found a solution in a german math board (unfortunately I cant access the site without using the cache of Google : cached version).
Note that in this example the angle α is on both sides the same and not as you would expect -α in the second one. To find out if the vector a is always on "the same side" of vector b you can use this formula.
ax*by - ay*bx
This is either positive or negative. You you simply can change the sign of the angle to α * -1.
I modified some parts of your code.
overlaytiler.Rotater.prototype.rotateDot_ = function(dot, theta, origin) {
// translate to origin
dot.x -= origin.x ;
dot.y -= origin.y ;
// perform rotation
newPos = {
x: dot.x*Math.cos(theta) - dot.y*Math.sin(theta),
y: dot.x*Math.sin(theta) + dot.y*Math.cos(theta)
} ;
dot.x = newPos.x ;
dot.y = newPos.y ;
// translate back to center
dot.x += origin.x ;
dot.y += origin.y ;
dot.render();
};
If you want to know, how I rotate the points please reference to this site and this one.
overlaytiler.Rotater.prototype.onMouseMove_ = function(e) {
var dots = this.controlDots_;
var center = overlaytiler.Rotater.prototype.getCenter_(dots);
// get the location of the canvas relative to the screen
var rect = new Array() ;
rect[0] = dots[0].canvas_.getBoundingClientRect() ;
rect[1] = dots[1].canvas_.getBoundingClientRect() ;
rect[2] = dots[2].canvas_.getBoundingClientRect() ;
// calculate the relative center of the image
var relCenter = {
x: (rect[0].left + rect[2].left) / 2,
y: (rect[0].top + rect[2].top) / 2
} ;
// calculate a vector from the center to the bottom left of the image
dotCorner = {
x: rect[1].left - (rect[1].left - relCenter.x) * 2 - relCenter.x,
y: rect[1].top - (rect[1].top - relCenter.y) * 2 - relCenter.y
} ;
// calculate a vector from the center to the mouse position
mousePos = {
x: e.clientX - relCenter.x,
y: e.clientY - relCenter.y
} ;
// calculate the angle between the two vector
theta = calculateAngle(dotCorner, mousePos) ;
// is the mouse-vector left of the dot-vector -> refer to the german math board
if(dotCorner.y*mousePos.x - dotCorner.x*mousePos.y > 0) {
theta *= -1 ;
}
// calculate new position of the dots and render them
overlaytiler.Rotater.prototype.rotateDot_(dots[2], theta, center);
overlaytiler.Rotater.prototype.rotateDot_(dots[1], theta, center);
overlaytiler.Rotater.prototype.rotateDot_(dots[0], theta, center);
// Render
this.render();
this.cx = e.clientX;
this.cy = e.clientY;
};
You can see that I wrote some function for vector calculations (just to make the code more readable):
function calculateScalarProduct(v1,v2)
{
return (v1.x * v2.x + v1.y * v2.y) ;
}
function calculateLength(v1)
{
return (Math.sqrt(v1.x*v1.x + v1.y*v1.y)) ;
}
function calculateAngle(v1, v2)
{
return (Math.acos(calculateScalarProduct(v1,v2) / (calculateLength(v1)*calculateLength(v2)))) ;
}
This is my working solution. Comment if you don't understand something, so I can make my answer more comprehensive.
Working example: JSBin
Wow, this was a tough one.
I'm Having a Bezier Curve in Javascript built with a few bezier Curves.
I can move handles and they keep the symmetry. I'm doing that by first calculating
the distance between Handle and Point on Beziér. Then I compare the distances
of the two handles, calculate a multiplier and apply it to the not dragged
handle. This works for keeping Symmetry.
But I want to achieve that the length of the not dragged handle stays the same.
http://cl.ly/image/0c1z00131m2y (a little picture explaining what i mean).
The code, i currently use to calculate the movement is this:
dx = Math.abs(drag.x - point.p[(draggedItemIndex)/2].x);
dy = Math.abs(drag.y - point.p[(draggedItemIndex)/2].y);
dx2 = Math.abs(point.cp[draggedItemIndex-1].x - point.p[draggedItemIndex/2].x);
dy2 = Math.abs(point.cp[draggedItemIndex-1].y - point.p[draggedItemIndex/2].y);
dxdx = dx2/dx;
dydy = dy2/dy;
point.cp[draggedItemIndex-1].x -= dragX*dxdx;
point.cp[draggedItemIndex-1].y -= dragY*dydy;
Thank you for your answer.
I'm now doing it with ciruclar calculations.
//Circle Center Point
cx = point.p[(draggedItemIndex)/2].x;
cy = point.p[(draggedItemIndex)/2].y;
//Dragged Point Position (To Circle Origin)
x1 = drag.x - cx;
y1 = drag.y - cy;
//Mirrored Point Position (To Circle Origin)
x2 = point.cp[draggedItemIndex-1].x - cx;
y2 = point.cp[draggedItemIndex-1].y - cy;
//Angle Dragged Point
a1 = Math.atan2(-y1,x1)*(180/Math.PI);
//Mirrored Angle
a2 = (a1-180)*(Math.PI/180)*(-1);
//Mirrored Point Radius
r = Math.sqrt(Math.pow(x2, 2)+Math.pow(y2, 2));
//Apply new Position to Point
point.cp[draggedItemIndex-1].x = cx + r * Math.cos(a2);
point.cp[draggedItemIndex-1].y = cy + r * Math.sin(a2);