I have a 2D side scroller whose levels are stored as vectors (that is, a bunch of lines) which looks like this:
How would I detect that I'm colliding with one of these lines, and react accordingly (say, slide down the slope, or stand still on a flat platform)? We can assume the player uses an AABB.
You might want to use a physics engine that does the work for you. Even if you get the collision detection right, there is still the problem of the collision response that let's the character slide down a slope, which can be even harder than the actual collision detection.
Box2D can do it for you.
for each line (represented by ax+by+c = 0) and each object(which moved from x0,y0 to x1 y1) you have to check if the result of this product is negetive (a*x0+b*y0+c)*(a*x1+b*y1+c). negetive value means there is a collision somewhere(it may be after the both end of line) and the possitive value means there are no collisions. if there realy was a collision then you have to calculate collision point using these formulas and check if that's somewhere between two ends of your line.
we want to calculate the collision point of these 2 lines :
ax+bx+c = 0
(x1-x0)x+(y1-y0)y - (x1-x0)x0+(y1-y0)y0 = 0
so we set these 3 parameters for comuting ease:
a' = x1 - x0
b' = y1 - y0
c' = -(a' * x0 + b' * y0)
and now our problem is :
ax +by +c = 0;
a'x+b'y+c' = 0;
and then you can have x',y'(collision coordinates)
x' = -(c/b + c') /(a' + b'/b*a)
y' = -(c/a + c') /(b' + a'/a*b)
after that to check if it's inside the line fragment you have to check if (x0-x')*(x1-x')+(y0-y')*(y1-y') is a negetive value, if yes you have a real collision if not the object is past from sides of your line.
