Pillow-Surface

gwengler shared this question 2 years ago
Needs Answer

I want to create a Surface like this.

Do anyone know, how to implement?

Look at the ggb-attachement - there I've only the profilelines.

Comments (4)

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I see the following possibilities:

  1. Analytical: Use a analytical description and create the surfaces by analytical described parametrized surfaces.
  2. Design: Use bézier surfaces or NURBS surfaces those will lead to better manipulatable surfaces that are not exactly fit to those curves (might be not a exact globe surface).
  3. Interpolation: Use a coons patch description to create the top and down surfaces (will not lead to a globe surface) and a linear interpolation for the side surfaces.

I do not know what you want to do or how you want to implement it (aside from the fact that the GGb form and the JPG form differ quite a lot). Approach 1 and 3 are the easier ones.

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  1. see pillow1.ggb: side surfaces are linear interpolation of calculated grid line and top&down surface is surface of decentered globe (similar to solution of mathmatic)8657eaae1469d296d29048f3a79484fb
  2. see pillow2.ggb: the control points Aij allow manipulation of top surface the side surfaces are linear interpolation of side lines (further information on sources to bézier curves and surfaces) to modify the form drag the control points Aij -> by manipulating them and by defining the negative surface and the other side surfaces you can get quite easily the form of your picture0a810f48e77c1650114f06a940e950e4
  3. see pillow3.ggb: top&down surfaces interpolated with coons-surface definition (look at wikipedia formulation for coons surfaces) side surfaces are interpolated like 1. (note that for coons surfaces the curve definitions have to have the same direction and the surface form is determined by border curves)16d931473cafa1e52473cac13bfe05af

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https://www.geogebra.org/m/mqwp4x2y

for another proportions use some constant factors or scale zAxis

Files: foro.ggb
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