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### Course: Multivariable calculus>Unit 1

Lesson 5: Transformations

# Transformations, part 3

Learn how you can think about a parametric surface as a certain kind of transformation.  Created by Grant Sanderson.

## Want to join the conversation?

• Is there a way to normalize the audio across videos? It's annoying to constantly switch between volumes across videos.
• hold up what is this im trying to study for a vague test. where am i
• here, the output of the function is a 3d vector. But what we see is a doughnut. How can I relate to points on the doughnut with 3d vectors?
• Take a point on the surface of the donut, and call it (x, y, z). The 3D vector is simply the vector from the origin to that point.
• What does the checkerboard pattern on the torus represent? Or is this just a fancy, non-boring way of coloring it?
• If you don't have a pattern on it, you won't be able to imagine it's shape. It would look like a 2-D disc
• The Surface Area of this donuts is 4*pi*pi
• Just a quick check, the output of the function is actually a plane of vectors right?
(1 vote)
• It's no longer a plane. Rather, the output is a surface. However, it's not a surface of vectors. It's a surface of points (A given input produces a vector in R3 which uniquely determines a point in space. Doing so with multiple vectors gives us the donut shape).
• I get the feeling that a similar math method is used in 3d texturing, like when using the UVW unwrap modifier in 3ds max (a 3d surface get sliced and put in a 2d plane then after coloring and painting it gets wrapped as 3d again). Is that correct?