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Pinball Mechanics
Written by Mattijs van Delden (csg216@cs.rug.nl)
Pinball MechanicsThe only literature about pinball games was a really old issue of Sinclair User with a two page article called `How the hell did we design a pinball game?'. Well, it didn't quite explain that (especially the `hell' part), only a small bit about a method to model the ball and the sides of the table and that a good pinball game needs `quite a bit of physics'. This brings me to the three most important aspects of a pinball game:
Moving the ballIf you don't like physics or geometry, skip this section now! Let's face it physimaniacs, there is nothing like a good old Newtonian formula, is there? Basic movement of a stainless steel ball (forget the `silver' thing, silver is expensive so I don't think it's made out of silver) on a very smooth surface is just a matter of forces (and almost an ideal system). Gravity pulls the ball down, so if we put the ball on a tilted table (get it?), it will accellerate. The magnitude of this accelleration depends on the angle of the surface. I once played pinball on a real table with an angle of 45 degrees. I must say, that the game was really fast! The effect of gravity can be simulated by subtracting a specific number from the speed of the ball in the vertical direction. This number is larger for tables that are tilted more. Simple eh? The only tiny problem is finding a realistic looking value for the number and the game is almost finished. Stop! Don't start coding now, because there is more to a pinball game!At the moment, our ball is effectively moving on an `ideal' surface. This means that there is no friction. In the real world (i.e. the world that will crush you after you finished your education) there is always friction, even with a steel ball on a painted surface. Chance is, that this effect will be visible and if it is visible, we will have to model it. This means that when something is not visible, we don't model it, because it will just be a waste of time. We are not going to model the friction of the air and the ball, because you won't see it. Back to table friction: it's a force that always points directly opposite to the speed. The magnitude of the friction vector depends on the materials of the objects that move and their speeds. The more speed, the more friction. Thus, it is possible to model friction by changing the speedvector (making it smaller) depending on the material that is under the ball and the speed of the ball itself. Again, a piece of cake. There is another factor: spin of the ball. At the moment, I'm not modelling this, but if you think I should AND have a good reason why, say the word. Now we get to the difficult part: letting the ball bounce around a pinball table. When the ball `hits' an edge of the table, it has to `bounce' back. To start with the easy part, there is a nice formula that describes a point mass bouncing from a wall. You can specify the elasticity of the two objects to get bouncing objects from a rubber ball to a piece of clay. The only problem is that the formula is about a point mass. The famous silver ball is hardly a point mass, I hear you say. Wrong! It is, or to put it better: we will model it as if it was a point mass. This brings us to the hitting part. The Sinclair User article described a method to define the edges of the table using straight line segments. Curved sections of the table can be made out of a large number of small segments. The placement of the lines is something special. We don't place them above the edges of the tables, but move them one radius of the ball to the inside of the table. This means that when the point crosses the line segment, the (sprite of the) ball collides with the (drawn) edge. Now we have a point moving around a table and crashing into linesegments. When this happens, the point has to bounce back. Therefore, it is extremely important to have a reliable algorithm to detect when the point is crossing a segment. When this goes wrong, the ball will fall right through the table and out of the screen, destroying your memory (believe me, it happened quite a few times!) This is the moment where I drop the `we' stuff for a moment, because, I've got the algorithm and you haven't! It cost me quite a bit of time and energy to design and implement an absolutely reliable algorithm. But I did it (thanks go to Wilco Dijkstra for helping me enormously) and it is worth the blood, sweat and tears. The table consists of a background (for the human to use) and of a set of linesegments (for the computer to use). I am using !Draw to draw the linesegments over the sprite of the background. Bezier curves are used for the curved parts of the table. These curves are converted into a number of small straight linesegments (flattened) for use in the program.
Flipping aroundThis is quite a hard part of any pinball game. With the flippers, you can aim the ball very accurately at various targets (we are talking about principles of course) and generally smash the silver thing around the table. Therefore, the flippers in the game have to be really realistic or the gameplay will go down the drain. Fortunately, I have my own pinball table at home, so I can compare the program at each step with the real thing.The best method is to look at that real thing. If you saw your pinball table in two and look at the inside, you'll see that the flippers are operated by a strong relay (an electromagnet). Fork out some tape or glue and if you hit the right button (it's not too hard, there are just two buttons. If you can find only one, look at the other side of the table) the flipper is accellerated. The funny thing is that this accelleration does hardly depend on the ball being hit or not. I am currently trying a number of methods of whacking the ball. When I have found the method that works best (in my humble opinion, of course) I will add it here.
LevelsUnlike the simple tables that were `hot' in the sixties and seventies, modern pinball tables have lots of levels. Balls roll around over rails going everywhere and a second small playfield above or under the normal playfield is more the rule than an exception. So any decent game must have these things. Actually, modelling levels is quite easy. Instead of one set of segments for the playfield, there is a set for each level. A parameter of the ball is the current level that it is on. This number determines the set of segments to use. Simple. But there is a small catch: changing the level of the ball. When the ball rolls up a rail, at some point the level has to be changed from, say, 0 to 1. When this happens, the normal playfield set of segments will become inactive which means that the ball will fall right through any edges of this set. The set for level 1 has to take over at that point. The point where the ball changes level could be a line segment. When the ball crosses the segment, the level is changed, depending on the direction of the ball. Another possibility is to use a box. When the ball crosses the box, the heat is on.
...this page last updated: 2/5/95... |
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©Gareth Moore 1994-2001
Acorn Gaming is a completely independent publication and has no official connection with any company |
