#Vector 2d collision how to

The obstacle's closest boundary is a plane defined by the vectors and. Suppose you have already determined that a collision is about to happen in the next frame. Now suppose you're coding a modified 3D Pong game that has additional objects on the screen, and you want to model the collision of the ball with one of these obstacles. Example 13.3: Non-Axis-Aligned 3D Vector Reflection Two vectors define the plane, so the normal vector can be found using the cross-product of those two vectors, as discussed in Chapter 4. The only slight difference is that in 3D the object bounces off a plane rather than a 2D line. If you know the incoming velocity and the 3D plane about to be hit, you can calculate the final velocity using the same vector operations.

#Vector 2d collision how to

You might be wondering how to extend this to 3D. Sum all the vectors with the reversed object vector, and we have a non-axis aligned reflection. The reflection is determined to be twice the size of the length. We then determine the length component of the reflection by multiplying the projection by the boundary normal. Multiply the projection with the boundary normal. Then we determine the projection length by reversing the colliding object's vector and calculating the dot product. First, we normalize the vector that describes the boundary. This function follows right along with the solution to the previous example. To implement this form of reflection in code, we can use this function: vector2D axisAlignedCollision(vector2D vect, char b) Typically when you approach this scenario, you know the moving object's incoming velocity vector ( v i ), you know the boundary line of the stationary object it is about to bounce off of (B), and you're looking for the new resulting velocity vector ( v f ). Let's start with two dimensions and then extend the process to 3D. What if the stationary object is oriented in such a way that its edges are no longer parallel to the x- and y-axes? The angle of incidence must still equal the angle of reflection, but now it's more complicated than just reversing one component. Now that we've discussed axis-aligned vector reflection, let's tackle non-axis-aligned. Therefore, the final velocity vector must be. That means you must reverse the horizontal component of the velocity and leave the vertical component the same. In Pong, the ball goes back and forth across the screen, so when it hits the paddle, it collides with the vertical edge. If the ball is approaching the paddle with an incoming velocity of when it hits, what should its resulting velocity be? Solution Suppose you're coding a simple Pong game, and you want to model the collision of the ball with the paddle. Įxample 13.1: Axis-Aligned and Non-Axis-Aligned Vector Reflection If the stationary boundary is horizontal, v f = įor incoming velocity v i =. If the stationary boundary is vertical, v f = and Similarly, if the wall is horizontal, all you have to do is reverse the direction of the vertical component of the ball's velocity when it hits. If the bumper is vertical, all you have to do is reverse the horizontal component of the velocity when the ball hits, as shown in Figure 13.2. Hopefully, after working through Chapter 10, 'Motion in Two and Three Dimensions,' you're tracking the ball's velocity with a vector in component form: ball velocity =. For now, let's go back to the billiard ball about to hit the bumper. We'll tackle the non-axis-aligned case next. Likewise, if the stationary object is in an axis-aligned bounding box, which means that the sides of the box are perfectly horizontal and vertical, the vector reflection is simple to model.

This process is very simple to program if the wall is perfectly horizontal or perfectly vertical.

In other words, the angle of incidence (incoming) must equal the angle of reflection (outgoing), as shown in Figure 13.1. An interesting symmetry exists: The angle that the ball comes in at must equal the angle at which it leaves. This type of scenario can be modeled using vector reflection, which refers to the motion of the moving objectin this case, the ball. The bumper doesn't move, so you only need to model the resulting motion of one object, the ball. The simplest type of collision to model is one in which a moving object collides with a fixed stationary object, such as a billiard ball hitting the bumper.