Analyzing a parametric surface to get vector maps

Grasshopper
,
1

I am working on an assignment where we are creating parametric surfaces and then using the torsion + tangent vector, and curvature + normal vector, to create vector maps and therefore secondary surfaces based on the above.

My ranges are:
u: (0, 1)
v: (0, 1)

Parametric equations:
x(u,v): (4+sin(2πv))(sin(2πu))(sin(3πv))
y(u,v): (sin(2πv))(cos(2πu))+(8v)-4
z(u,v): (4+(sin(2πv)))(sin(2πu))(cos(3πv))

I have graphed these as a surface in GH and have also graphed the parametric curve using the same equations (with variable t).

Now, I am struggling to understand how to evaluate it to find three more surfaces (Vector Maps), this is as much as the assignment says so I’m not sure what steps to take next.

Here is the GH file. Any guidance is appreciated <3
Assignment 2 GH_12_10 Update.gh (37.0 KB)

2

FYI, 0 to 1 is the default domain for both Construct Domain and Range so you can delete all four Construct Domain components and get the same result. :roll_eyes:

3

Good to know! Any tips on the steps for how to analyze the surface?

4

You can use these components to evaluate surface Normal, Curvature …
I feed with same UV as input surface, so

image
image1262×804 134 KB

Then you can do whatever you want with Points, Vectors (that could be represented as points) … as they are associated with UV coordinates

Assignment 2 GH_12_10 Update LD.gh (13.2 KB)