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W/A/S/D control snake movement in 3D, ignoring 4th dimension. When camera rotates in 4D, two axes trade places and two remaining axes stay unchanged. When camera rotates in 3D, two axes trade places and the third axis stays fixed. Movement has the same nature in 3D and in 4D. So their real position may be significantly different from their apparent projected position. They are also shifted to/from snake head due to projection, Objects at the different W-level than the snake head have distinct blue or red tint. (or slightly red and blue simultaneously due to their non-zero size). Therefore, objects at the same W-level as the snake head are white The "vanishing point" for 4D-to-3D projection is located there too. The camera is attached to the center of the snake head. The directions along W axis are named red and blue according to their color tint. Objects with positive or negative offset in W coordinate have blue or red tint in their color. Objects with the same W coordinate as the camera have default colors (e.g. Objects are colored differently according to their positions. In order to make different positions along W axis more distinguishable, Second, commonly used 3D-to-2D perspective projection that folds Z axis too. In the end, 4D world is projected two times.įirst, custom 4D-to-3D projection that folds W axis. Gray dot is the vanishing point at W coordinate approaching infinity. It becomes bigger and runs away from the vanishing point in 3D.įigure 2: the set of parallel square frames along W axis from different points of view. When the 4D object moves away from the camera in the opposite direction along W axis, It becomes smaller and approaches the vanishing point in 3D. Therefore, when the 4D object moves away from the camera in one (arbitrarily picked) direction along W axis, There's no way to reasonably define "behind" for W axis. While 3D-to-2D projection usually makes the objects behind the camera invisible, it's not the case for 4D-to-3D projection. The only difference is that 4D-to-3D projection works in both directions. Its 3D projection also becomes smaller and smaller, approaching the vanishing point in 3D. The vanishing point is in 3D now, and as the object moves along W axis away from the camera, In order to project from 4D to 3D, W axis is also folded using similar algorithm. Gray dot is the vanishing point at Z coordinate approaching infinity. The vanishing point is 2D position on the screen, usually in the center.įigure 1: the set of parallel square frames along Z axis from different points of view. Its 2D projection becomes smaller and smaller, approaching the vanishing point. display), Z axis is folded by perspective projection.Īs the object moves along Z axis away from the camera, When 3D world is projected on 2D surface (e.g. W is the 4th axis that doesn't have specific direction in 3D world.īefore I explain 4D-to-3D projection, I want to say a few words about classic 3D-to-2D perspective projection. Z is the standard 3rd axis that goes "forward" from the eyes of the spectator into the screen. X goes left to right and Y goes bottom to top. X and Y are the standard 2D axes of the screen. ![]() I guess that's why 4D games aren't made that often.ĤD graphics mostly follows the same rules as 3D. I cannot play it beyond certain snake length. This game is not really designed to be playable by a human being. There's just no way one can nicely fit this much geometry on the screen. There may be up to 14640 (!) snake tail segments in the game world. Nothing to do here, 4D just have insanely big information density after projecting on 2D screen. Yes, the game becomes messy when the snake grows. So I skip common knowledge in this document. There are a lot of videos and articles written by people who are better at explaining things than me, I strongly recommend to have at least basic understanding of 4D geometry. Go to menu to try playing the game itself. ![]() ![]() When the game is started, it starts playing AI demo automatically. This app is closer to proof-of-the-concept for 4D gameplay, rendering and animation than to actual playable game. Snake4D is classic snake game in the mathematically correct 4D world. 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