Partial derivative of a parametric surface, part 2

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Taking the same example surface used in the last example, we now take a look at the partial derivative in the other direction.

[@IamFilter94]

2:34 that sound effect

[@chao.j]

that deserves a Grammy :-D

[@fishermanwithfishes2286]

what you hearing is a derivative of the actually effect

[@colemanchristy2770]

Turn on subtitles

[@goclbert]

Vroop doop doop will now be the noise I hear whenever I do a transformation

[@anonymous_4276]

Thanks a lot. This entire playlist needs more attention imo. It's extremely helpful.

[@shivammalviya3737]

"Vroop doop doop"

[@haroonq7876]

Well sir once you put that (s, t) plane on the (x, y) plane you make things easy to understand, infect it tell's us these things actually means, so you have done a wonderful job.

[@MayankGoel447]

Finally, understood parametric curves represent 1 input, basically a 1D line stretches and curves in 3D space. Similarly, Parametric surfaces correspond to 2 inputs, a plane which bends and curves in 3D space.
Is there a name for 3D input to 3D output transformation?

[@randomstuff9960]

Voiced zooming sounds...😅

[@Promixro]

thanks

[@Team-pj1nj]

does the gradient of vector V which can be written as [partial v partial s, partial v partial t] point to the steepest ascent? and if it is/isn't why?

[@xeooox]

My right ear can do math now

[@jeffgalef121]

You stated that dv is not small because it's scaled by a very small ds. But, isn't that always the case with derivatives? That is, isn't the denominator always really small? In other cases, you still only get a really small dv/ds value.

[@vergelimit8654]

Is it really cheating though? Wouldn't the T/S plane be exactly where you placed it in 3d space?

[@henitmandaliya]

He shows transformations like this one (2-D to 3-D) using this animation to show the points on the old T/S plane being mapped onto the new 3-D space and how any movement on the old plane corresponds to movement on the new surface illustrated by the function. So no, he's not actually cheating and the T/S plane doesn't move per say but the points on it are shown to move through the transformation.

[@adityaprasad465]

The 3D space is x/y/z. There's nowhere the t/s plane "would" be, other than on a completely separate graph.

[@gameblamerfan]

sick I'am still in trigonometry :(

[@desrucca]

Why dont just slice the plane like the earlier video?

[@amineaboutalib]

because those were bivariate functions with one value