How to Derive the Equations of 3D Surfaces of Arbitrary Complexity and Model Them in Blender

3D surfaces can be defined parametrically, with three functions x(u, v), y(u, v) and z(u, v). While the parametric equations of simple surfaces such as a cylinder or sphere can be easily derived with just a pencil and paper, others, such as a spinning hypocycloid orbiting around a center which itself is rotating, seem impossibly complex.
This tutorial provides a system and method for deriving the equations of even the most complex of 3D surfaces using the multiplication of transformation matrices based on an online calculator we have developed.
The online calculator is available at www.otvinta.com....
For more tutorials and 3D models, visit www.otvinta.com

[@octavioaguayo5366]

This is one of the best videos I've ever seen regarding math. It made my understanding of topics that I saw from Linear Algebra and Vector Calculus be SO much better. I LOVE THIS 10/10

[@ArnaudMEURET]

What a gentle way to arrive at the mind-blowing last example ! You are legend! ❤

[@arirajuh]

The best explanation, for utilizing mathematics.

[@adamab9003]

Cool and interesting. I had no idea that such methods could be used to produce models like that.

[@shogga690]

Excellent 🎉. Would be nice to add hyperbolic functions

[@konradswart4069]

The video contains a mistake. The 2d rotation matrix is: cos a, -sin a sin a, cos a The rotation matrix in the video is a clockwise rotation. Oh! I see! You multiply a vetror with this matrix from the left! Then it is correct!

[@edinardovasconcelos5493]

Hi my name is Edinardo Araújo, i'm dong a extrem progress in modeling parametric surfaces 3D. But i'm using Geogebra that is very limited. There are a community about how make 3D models in Blender using equations? I would like to share my habilities and learn there. Thanks!!!!

[@taksinwatanabe9362]

Thank you very much for sharing! Very helpful!

[@bmariani52]

For the DONUT figure, this is a FASTER equation It has to be tilted in X,Y,Z space x=45 y = 30, z 0 degrees a = 3 for size for u = 0 to 2*PI Step Inc 2 for v = 0 to 2*PI Step Inc 2 x = (a + a*cos(v)) * cos(u) y = (a + a*cos(v)) * sin(u) z = a*sin(v)

[@ahamrtasmi]

Simply awesome!

[@fabiobiffcg4980]

Nice! That's interesting!

[@mogergog]

Cool! Thank you!

[@fewerjunkjunk8842]

The (Python) translated code doesn't work in Blender 4.2. The blend file in the reference link to the video is of the wrong blend file.

[@fewerjunkjunk8842]

Doesn't work in Blender 2.8 either.

[@fewerjunkjunk8842]

The blend file page on O.T.Vinta was last updated in 2019. In 2019, the most current version of Blender was 2.8.

[@mobinvaryan7196]

thank you

[@BLACK-hl4ic]

Make some Blender videos

[@Andy-ht2jb]

*Promo SM* 😢