Hi MV,

You're absolutely on the right track—your analogy between raster and vector graphics is a helpful comparison. Many CAD modelers are built on mathematical definitions for shapes, allowing for anything from rough approximations to extremely high precision. Engines like ACIS (developed by Spatial Technologies in the 1980s) exemplify how far this can go: they define geometry at a near-perfect level and are widely used in various industries.

The translation of those mathematically precise models into polygons is a critical step. It's where one must balance smoothness, performance, and data size. What works brilliantly in machine tooling, for example, can become impractical in character animation—context always matters.
Your mention of IK (and FK) brings this point home again. Here, FK is often underrated, and when people lean too heavily on automation, it's sometimes a sign they haven't fully mastered the manual approach. I speak from experience—while I have a full motion capture setup, for smaller tasks like animating just a finger, I always go manual. Starting the whole setup while knowing that cleaning up work is needed makes that an easy decision. It's quicker, more direct, and often gives me the control I need without the overhead.

The same principle applies to Dynamics and Simulation. I used the first Maxon Dynamics Module released around 2002, and while it opened new possibilities, it also changed the nature of the questions I received. Many artists hoped dynamics would replace the need to learn animation fundamentals. But dynamics has no understanding of artistic intent—it's physics, not storytelling. This became even clearer when the Bullet system replaced the earlier module. The ability to throw something into a simulation was seductive, but the results often needed art direction—and that's where limitations surfaced.

Cinema 4D is not a game engine in my book; it's built for artists. So, over the years, we developed tricks and workarounds to regain expression control over simulation results. Ironically, bending dynamics to follow an artistic vision can take longer than simply animating things manually. That trade-off between control and automation is always present.

So, thank you for bringing up the raster–vector analogy. Once precision is translated into polygons (with inherently straight edges), we rely on smoothing methods to hide the loss. But the process is rarely reversible—you can't easily turn polygons back into their original mathematical perfection that the formula had.

As for robot arms and advanced rigs, I've tested many versions over the years, including complex constraint-based systems. Our team even ran internal challenges to find the best approaches, and problems, some of which led to improvements in the software. Here's one example from that period:
https://www.youtube.com/watch?v=5dNmL-NpU_w

But challenges remain. For example, dynamic or simulation systems have no built-in understanding of problems like gimbal lock or Euler angle issues (see: https://en.wikipedia.org/wiki/Euler_angles). Connectors and joints work well to a point, but there are limitations.

That said, I won't discourage you. Quite the opposite—I'm glad you're exploring this. If anyone finds a novel solution, it might just be someone like you who's willing to dive deep into a problem others have walked past. Just keep asking: what's the actual goal? Is it a render, an animation system, or something else?

You might find useful insights in academic research—there are papers exploring joint systems with up to 20 degrees of freedom, sometimes even with shared code examples. For those cases, I'd recommend visiting the Developer Café, as our current forum doesn't support code sharing due to security policies.

Whatever direction you choose, I wish you the best. Choose your goals with care, and go deep. That's where the breakthroughs happen.

My best wishes

P.S.: CV4_2025_drs_25_CAsd_41.c4d
___ .CV4_2025_drs_25_CAsd_51.c4d