How to calculate bounce angle?

I played around with it for a while, but I simply can't figure it out.

I made a tank that fires missiles, and when the missiles hit the walls, I want them to bounce off, but I want them to bounce off to the right angle.

Right now I haven't got any obstacles, the missiles just bounce off when they get outside the viewportRectangle I made.

Is the solution I'm looking for quite advanced?

Is there a relativly simple way to do it?

You might think that because your walls are aligned with the coordinate axes that it makes sense to write special case code (for a vertical wall, negate the x-coordinate of the velocity; for a horizontal wall, negate the y-coordinate of the velocity). However, once you've got the game working well with vertical and horizontal walls, probably the next thing you'll think is, "what about walls at arbitrary angles?" So it's worth thinking about the general case from the beginning.

In the general case, suppose your missile has velocity v and hits a wall with surface normal n.

Split v into components u perpendicular to the wall and w parallel to it.

Where:

u = (v · n / n · n) n
w = v − u

Here, v · n is the dot product of the vectors v and n. See the link for an explanation of how to compute it. The dot product n · n evaluates to the square of the length of the normal vector; if you always keep your normals in the form of unit vectors then n · n = 1 and you can omit the division.

After bouncing, the component of motion parallel to the wall is affected by friction f, and the component perpendicular to the wall is affected by elasticity, which can be given in the form of a coefficient of restitution r.

So the velocity after the collision is v′ = f w − r u. In a perfectly elastic, frictionless collision, v′ = w − u; that is, the motion is reflected about the normal at the point of collision, as in the diagram given in Bill's answer.

This approach works just the same in three dimensions too.

(Obviously this is a very simplified notion of bouncing; it takes no account of angular momentum or deformation. But for many kinds of video games this kind of simplification is perfectly adequate.)

I think an easier way to do this is to use the velocity of the missile instead of calculating angles. Say you have a missile that has xVelocity and yVelocity to represent its movement horizontally and vertically. Those velocities can be positive or negative to represent left, right, up, or down.

• If a missile hits a top or bottom border reverse the sign of the yVelocity.
• If a missile hits a left or right border reverse the sign of the xVelocity.

This will keep the movement in the opposite axis the same.

Borrowing the image from ChrisF's answer, let's say the missile starts out at position I.

With the xVelocity and yVelocity both being positive (in 2D graphics right and down are typically positive) the missile will travel in the direction indicated. Let's just assign values of

xVelocity = 3
yVelocity = 4

When the missile hits the wall at position C, its xVelocity shouldn't change, but its yVelocity should be reversed to -4 so that it travels back in the up direction, but keeps going to the right.

The benefit to this method is that you only need to keep track of a missile's xPosition, yPosition, xVelocity, and yVelocity. Using just these four components and your game's update rate, the missile will always get redrawn at the correct position. Once you get into more complicated obstacles that are not at straight angles or are moving, it will be a lot easier to work with X and Y velocities than with angles.