I'm working on a new 4D game. The view into the game world is going to be two 3D slices. The top view will basically be x-forward, y-left, w-up. The bottom view will be basically x-forward, z-left, w-up.

The game is going to be really fast-moving.... ("Sonic with the good shoes"-type fast-moving). There will be obstacles in the game-field that you and your opponents will bounce off of at high speeds. More about the gameplay when I'm further ahead.

At the moment, I've got my first object rendered. To make many of my obstacles (and possibly some of the vehicles), I'm extruding three-dimensional objects into four-dimensions. I read in an extrusion profile that tells me how big to scale the three-dimensional object at different w-values.

For testing, I'm using... (0,0.75), (0.75,1.5), (3.0,0.0) where those pairs are (w,scale). For this particular thing extrusion profile, each vertex in my 3-d object gets turned into three vertexes in my four-dimensional object. So, if the original object has a three-dimensional vertex (1,1,0), that vertex becomes these four-dimensional vertexes (0.75,0.75,0,0), (1.5,1.5,0,0.75), and (0,0,0,3). Each triangular facet in the three-dimensional object then becomes two triangular prisms (technically, truncated triangular pyramids with parallel top and bottom cuts)... one to get from w=0 to w=0.75 and one to get from w=0.75 to w=3.0.

For my test object in 3-D, I've taken "Suzanne" the monkey from Blender 3D and cut her down to 202 vertexes.

If we view a 3-D slice that has constant w, we get the monkey scaled appropriately based on the scaling factor from the extrusion profile. More interesting is when the 3-D slice is not of constant w.... here the 3-D slice is perpendicular to the vector (1,0,0,1).

I'm not sure yet about the holes yet. I'm going to have to look into those (pun semi-intended). But, there you have it... The world's first extruded monkey.