Before Diagonal

After Diagonal

#### 90° in the Shade

The issue came up because I was trying to make some of my physics interactions behave different from how they do in reality. You would think that bending reality or completely changing how physics works should be possible in a computer simulation's implementation, but I found out that changing how things work quickly leads to unintended problems. I wonder if this says something about the necessity of how physics actually works in real life.If you look at the "Before Diagonal" image on the right, you see a white ball heading towards a collision with a blue diagonal. Then, in "After Diagonal", you can see the white ball after it has bounced off of the blue diagonal. For the purposes of my game the white ball must always be exactly halfway between a row or column of purple stars. Before the bounce it is travelling horizontally, and is halfway vertically in a row. After it bounces it is travelling vertically, and is halfway horizontally in a column. The problem is that in an actual 90° bounce like this, with a ball that has a non-zero radius, it would not bounce from halfway-vertical-in-row to halfway-horizontal-in-column like this. The lower part of leading edge of the ball would hit the diagonal first, before the halfway point, and then the ball would bounce upwards, but to the left of the halfway-horizontal-in-column point.

I initially tried to resolve this problem by simply

*teleporting*the ball from the one halfway point to the next halfway point when the bounce occurred. This looked fine, and seemed to work ok, until I added interactions between multiple balls. The problem was that if there was already another ball in the place to where the first ball is teleported, then they would become overlapped and not properly bounce off of one another.

I solved this problem by not doing the teleportation and having the ball bounce as if it has a zero radius. This works fine for my purposes, but has another small problem. For the skin shown in the images to the right, the ball is fuzzy and the diagonal is lightning-like, so having the ball overlap the diagonal when it bounces looks fine. For an alternative skin, though, where the ball is completely solid and the diagonal is more physical-looking, it will not look ok. My plan to solve this is to have the interaction calculation done as if the radius is zero, but have the rendering adjust the ball's visible position so it doesn't overlap the diagonal.

Before Collision

After Collision

Collision!

#### Billiards this is Not

After resolving the above issue I then started working on ball-to-ball collisions. When the two balls are on the same row or column this is easy. The issue is when they are moving perpendicular to one another.If you look an the "Before Collision" image to the right you can see that the tow balls are heading towards one another and will collide in the lower-left area of the image. If these were actual balls, like billiard balls, then the result of the collision is that the one moving down would head left and the one moving left would head down. The angle each ball changes to would depend on their speed and mass. My problem with implementing this type of collision is the same as that I described above related to bouncing off of diagonals. Basically, I want the balls to remain exactly in the halfway point between a row or a column. In this scenario, though, that would not happen.

For ball-to-ball collisions I could not use the same strategy I used above for diagonal collisions; calculating as if the ball had a zero radius. I actually initially tried this, and it worked ok for two balls, but once more than two were involved it became possible that all of the balls come to be in exactly the same position and could never resolve their collisions. Also, adjusting the rendering of the overlapped balls so that the don't appear to be overlapping is more difficult.

The solution I eventually came up with was to have the balls simply bounce and reverse directions entirely (see "After Collision" image). As I said, in real physics, that would not happen, and I wanted to make it look reasonable. To attempt do that I added a graphic element that is shown when the collision occurs, and implies that something more than just a normal real-life, ball-to-ball collision is happening. Currently I'm using the graphic shown in the "Collision!" image, but this is tentative, and also can be customized for each skin. Even though the physics of this collision isn't even close to real physics, it actually works pretty well in the game.

#### Summary

Resolving both of the problems described above took quite a while. I experimented with a number of different solutions before settling on the current one. I also tried to get things working in the early stages when I had the balls teleporting during a diagonal bounce. This seemed we work for some cases, but was never reliable. I find it interesting that even the small adjustment to physical rules I was trying to make in having the balls bounce and maintain their position halfway in a row or column caused problems that were basically impossible to solve. Of course the other side if this is that even my final solution goes against how physics works in real life.One other thing that makes me feel pretty comfortable with my current solution is that it ended up in much cleaner code. In other strategies I always had a number of special cases, that made the code messy. Once I changed to my current solution they went away.

Next time: More Optimizations.

Can the blue line bend on impact until the zero-radius of the object hitting it is the same as the mid point of the next column/row? Maybe even speed up the ball equivalent to the "bounce" as the line straightens up.

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