Rolling Cube along a path in C4D using math and Xpresso

A couple of days ago I came across this video of Maxon Training Team (channel that I recommend you follow):

This tutorial shows techniques for rolling a cube along a path using XPresso and the new Nodes system. The result is good and in certain situations it can be fine, but it is not precise, it is an approximation. I tried to look if there was a mathematical solution to the problem but in my short search I found only these other methods of solving the problem:

This is another fast and effective approach that leverages the internal physics of C4D.

Here, on the other hand, a solution is offered to obtain a mathematically precise rolling, but it would probably be difficult, to deny me if I am wrong, to adapt it to make the cube follow a path other than the straight line.

So I thought I’d solve the problem mathematically so that the cube can follow a path along a spline. But first I want to show you a short example video where I used my own preset.

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The Italian Songbook – Realmagazine animation

The Italian Songbook project is a “Cultural Soundscape” conceived and created by Director Antonio (Tonino) Pappano Riccio.
The aim of The Italian Songbook project is to revitalise an older taste of our ancestors to celebrate the eternal and powerful aspects of song, within a context that suits our own modern sentiments. It is your guide and companion as you embrace the beauty of vocal and orchestral art.

It was a pleasure to create an animation for the Antonio Pappano’s project using my Realmagazine preset for Cinema 4D. Click the link below to visit the project page:

The Italian Songbook