Monday, November 2, 2009

Planet terrain collision

When I started my lunar lander project several years ago the planet was a smooth disc. Detecting landings and collisions involved a simple radius check. Recently I dusted off the project and made a more complex, randomly generated terrain, invalidating that collision model. After putting the kids down for quiet time yesterday, I brewed a pot of coffee and set to work adapting collision code I'd written previously for Abyss, my Ultima Underworld hacking experiment. I have something that basically works, now, which is exciting as it is a big step toward this being a playable game.

Unfortunately there isn't much to see in still images. The rocket is prevented from going into the ground, that's all. I've included a couple of random screenshots just to have something to look at. Here's a shot of the final approach for a landing. The dim blue line is the ballistic trajectory and the brighter line is the powered trajectory. It's important not to let the powered trajectory dip below ground level!

This is zoomed out a lot more and shows the chaotic nature of the terrain that I've got at the moment:

The terrain generator is very simple, and generates inaccessible pockets of air inside the planet as well as floating islands in the sky. The floating islands are kind of cool; the inaccessible caves are just taunting; I need to remove them in a post-process.

For physics purposes, the terrain is represented by a binary space partition; the BSP divides up space into about 20,000 convex polygons (depending on the random terrain), some of which are solid and some of which are air. I use sentinel values in the child pointer slots of a BSP split node to signal solid and empty leaves, so there is no storage allocated for the leaves themselves. Each split node costs 20 bytes: the three line equation coefficients and pointers to its two children.

The rocket is currently represented by a disc. (Yes, eventually it will be more complex.) To detect intersections between the BSP and this disc, I traverse the BSP tree depth-first, building a stack of the currently active splitting lines. If the disc straddles a split line, the branch not taken is saved on a stack to be visited later. Otherwise I just go down the side containing the disc.

When the recursion hits a solid leaf, the stack of active splitting lines implicitly defines the polygonal region for that leaf. I have a function that returns the smallest separating axis between this region and the disc. If it turns out that the disc and the leaf region are overlapping, I generate a contact constraint in the direction of the separating axis.

This week I also switched all the code to 32-bit floating point arithmetic; large portions of it used 64-bit precision as a holdover from my orrery project. I also was able to reduce the integration from fourth-order Runge Kutta to a second-order method (Heun's). The main place this shows differences is when orbiting under high time acceleration.

One of the remaining top priorities is coming up with an adequate camera control algorithm. I'd really like to minimize the amount of manual control necessary, so I have to figure out what is important to show. Making a more complex rocket model, with shock absorbing landing gear, is another.

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