I recently posted a small article on how to do simple radial collision detection in a way that makes you 'slide' around objects which can be modelled as a cylinder. I just adapted it for planar objects too. This little tutorial should explain the method for detecting and dealing smoothly with things like walls (the primary application) and also more complicated objects whose boundaries can be modelled as a series of consecutive barriers.

So, here's the situation. Your camera/object encounters a wall or surface which is intended to block its path. Instead of bringing the camera to a stop, you want the player to slide along the outside of the wall smoothly, until they come to the end of it, at which point they will continue walking normally. This picture explains it better:

As you can see, the player has walked into the wall's bounding thickness (the central solid line can be seen as the centre of the wall, and the dotted line represents a user-defined thickness which defines how close the player is allowed to get to the wall's centre). To put them back outside the wall, we need to find the closest perpendicular point from the camera to the wall, and add on a certain amount of this vector (vectorWallCentre) to the camera's position such that the distance of the camera from the wall now matches the bounding thickness.

Let's say that the start and end points of the wall are defined by the position vectors p1 and p2 (in 2D, since the wall can be considered to be infinite in the +y direction, above and below us). The difference between these vectors (p2-p1) describes the direction of our line. This vector will simply be called 'line':

line = p2 - p1;

We now need to calculate a secondary parameter which will allow us to determine the closest point on the wall to our camera's location inside the bounding thickness. We'll call it 't'. It is calculated as follows (note that this is pseudocode):

t = Dot((cam - p1), line) / Dot(line, line);

Note that 'cam' is the current 2D position of our camera in world space (again, we don't need to bother with the y vector). We need to impose some restrictions on this value of t. Since it's possible that the closest point to our current location is in fact one of the ends of the line, we should take this into account. It's as simple as this:

if (t < 0){t = 0;} if (t > 1){t = 1;}

Finally, you can return a vector in 2D containing the line between your camera and the closest point on the wall. This is pseudocode (since the y direction is the up/down direction, we don't need to take worry about this, so our resulting vector is in 2D):

closestPoint = p1 + t*line;

This method for calculating the closest point on a line to a given location is explained in 'Real time collision detection' by Christer Ericson. Now that we know the location of the closest point on our line to the camera's position, we can move the camera along the line between the two locations (marked on the diagram) until our player is outside of the wall's boundary. The first thing we need to do (every time the game updates, or every time the camera moves - it's your decision) is to actually determine if a collision has happened. This is simple (again, here is some pseudocode):

vectorWallCentre = closestPoint - cam; distanceToWall = Length(vectorWallCentre);

This just determines the length of the vector between the player and the wall. If this value is less than the user-defined thickness of the wall (which we will call 'thickness'), then a collison has happened. Simple! So how do we deal with the collision? Easy! In one line of code:

newPos = ((thickness/distanceToWall)-1)*vectorWallCentre;

Here, newPos is the position to which the camera has been moved to put it outside of the wall. All you need to do is add this vector to your camera position:

cam += newPos;

That's the basic premise! This can be adapted to handle more than one wall (by simply adding up the collision contributions of each wall) and it can be used to model the surfaces of multiple walls comprising a shape or building.

Perhaps the most elegant thing about this is that it allows you to define the collision boundaries of buildings, walls, etc... as a simple series of points. It is easy to recycle this algorithm using a for loop to handle many walls at once. It works for both sides of a wall, and there are no problems handling corners and edges of walls. It allows for simple handling of things like doors too - just leave a gap between your lines in at the location of your door. I can't think of a simpler way to do collision detection with wall-like objects than this, and it's great that it effectively allows you to build collision models for buildings both inside and outside using nothing more than a collection of nodes defining the start and end of each wall of the building.

Thanks for reading!