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Following a spline path is a fairly trivial task algorithmically. The base concept consists of a series of nodes or points in 3D space. These points are then linked together sequentially so that an object may traverse them from point A to point B.
Of course, a character or object must be able to follow the path even if the total structure of the linkage isn't linear, like the curvy light rails in Dissidia.
There are numerous methods for spline path traversal. Dissidia Final Fantasy appears to use a very direct linear method. Although the rails in Dissidia are curved, the character is rigidly fixed to the path.
The motion of the character along the light rails is smooth because there are many nodes within the spline path.
There are other methods of spline path traversal but they are better suited to imprecise path traversal like one might see in a racing or free flight situation. Grinding on rails is about as linear as it gets and yet there are still several methods to accomplish this task.
For our example, we're going to create a spline path with 3DS Max, apply a renderable spline modifier, attach some bones, and export the result into Unity 3D where the algorithms will take over and allow our player character to grind on the rail.
The first step in 3DS Max is to select Create Shapes > Arc. Drag the shape until it appears like the screen shot below.
After creating the Arc the next step is to apply the Renderable Spline Modifier to it. You do this by selecting Modifiers > Patch/Spline Editing > Renderable Spline Modifier. It looks a little something like the screen below.
Once the Renderable Spline Modifier has been applied it's time to adjust its settings so it's visibly noticeable. Using the Modify Panel on the right side of the 3DS Max UI set the parameters of the Renderable Spline to match the snapshot below.
These settings create a square shaped rail out of the spline and also apply the texture mapping coordinates necessary to properly texture the spline. We won't be using Max's texturing tools beyond this. Instead we'll apply a texture and shader inside Unity.