[MATLAB]: How would I mathematically and visually reproduce the 3D surface of the new “Western Hall” of the King of the Cross?

Question

Does anyone have any clues for me? I want to learn from this (i.e. I do not want to be lazy and ask someone to answer this for me).

I would like to develop my understanding of mathematical 3D surfaces. My own project is to create a three-dimensional surface / graph of the hall structure in MATLAB.

I found a link with good photos of my geometry here . I do not expect to get it 100% excellent, but I would like to come closer!

At the end of this exercise, I would like to get a mathematical definition of geometry, as well as a visual representation of the surface. This may include Cartesian equations, parametric equations, matrices, etc.

Any help would be greatly appreciated!

Answer 1

To give specific advice for MATLAB:

I would download the section image from the web page you linked and display it in the MATLAB shape window. Then you can try to draw lines on top until you find one that works well. So you can do something like:

A = imread('~/Desktop/1314019872-1244-n364-1000x707.jpg'); imshow(A) hold on axis on %# my guess at the function - obviously not a good fit x = [550:900]; plot(x, 0.0001*x.^2 + 300) 

Of course, you may need to move the position of the source or crop the image, etc.

As the best alternative to this trial and error method is possible, you can trace the section outline (for example, by clicking points with something like ginput ), and then use one of the MATLAB tools curve fitting (for example, fit ) to match the data function.

The last three-dimensional shape looks to me (in a casual look) a 3D inversion of the section shape around the central axis. Therefore, using > a cylindrical coordinate system might be a good idea.

The final construction of your 3D shape can be done using the surf or mesh function.

Answer 2

I would start by defining a function that determines for each x, y coordinate whether there is a point z, and if so, with what height.

The shape reminds me of a little log or square root.