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Back to basic Sliding response in 2D

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I have made some simple collision detection and response in 2D.
i have made it like this.

move player
iterate all obstacles
push player out the amout it has penetrated
cut velocity with slide vector for each plane/line

it works with all sorts on angles, i still have to check which line that is closest for better result.
But it seems that when i set the new speed it overbounces on the lines.
If i go slow, i slide along the lines as long as i have push on the speed with my keybord but if i approach a line fast then the sphere bounces away.
i think that something is wrong with my slide vector...

vx -= nx * ((vx * nx) + (vy * ny));
vy -= ny * ((vx * nx) + (vy * ny));

vx = speed x
vy = speed y
nx = normal from spherePos - closestPoint on Lines
ny = normal from spherePos - closestPoint on Lines

i don´t know how the formula for 2D slide. In 3D i use v-= -n * dot(v.n) but how can i do this in 2D?

[source lang="java"]

var moveBall = function () {
pos_x += vx;
pos_y += vy;
//Iterate and find all lines/planes that are to close, then push player out. TODO: sort this and find closest first!
for (var i = 0; i < lines.length; i++) {
var closestpoint = new ClosetPointOnLine(lines.x, lines.y, lines.x2, lines.y2, pos_x, pos_y);
var l = lineLength(pos_x, pos_y, closestpoint.x, closestpoint.y)

ctx.fillText("length: " + l, 150, 60);
if (l < SPHERE_RADIUS) {
pos_x += ((pos_x - closestpoint.x) / l) * (SPHERE_RADIUS - l);
pos_y += ((pos_y - closestpoint.y) / l) * (SPHERE_RADIUS - l);
var nx = (pos_x - closestpoint.x) / l;
var ny = (pos_y - closestpoint.y) / l;
vx -= nx * ((vx * nx) + (vy * ny));
vy -= ny * ((vx * nx) + (vy * ny));

[/source] Edited by KurtO

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You should precompute ((vx * nx) + (vy * ny)) for two reasons. Firstly, your code will be faster and secondly (which is also where your bug is), when computing vy -= ny * ((vx * nx) + (vy * ny)), you are using the new value of vx, computed on the previous line!

So, just do this:
[source lang="java"]dot = ((vx * nx) + (vy * ny));
vx -= nx * dot;
vy -= ny * dot;[/source]
Basically, the 2D formula is the same as the 3D formula, but simplified because z = 0.

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Wow! i am impressed how you can see my bug so clearly! Of course now when i know i have to precompute! Sometimes i am just stupid! =)
And then i have to recalt my sliding vector AFTER i moved my sphere of course.
My little demo is now complete except one detail (of course as always)

The sliding pushes the sphere outside the lines in tight spaces. i think i need to solve time t of impace before movement or do the updates recursive with 6-8 times to solve this problem, but i really dont know how.

thanks again faelnor! Edited by KurtO

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Yeah, resolving collisions in tight spaces is not an easy problem. You can prevent some of the problems by avoiding acute angles between lines and a having a minimum distance between your lines of at least the diameter of the sphere. You may also pass through walls if your sphere is moving too fast. Good luck!

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