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I want to calculate the surface area and the volume of an irregular bottle. Since the bottle is of an irregular shape, the volume and surface area cannot be calculated by simple solids of revolution integration technique. While reading a research paper, I found that I can take multiple images of the silhouette of my object from different angles, trace the silhouette, and then produce a wire-frame model of my object. Combining several crosssections, I can produce a wire-frame 3d model.

Can anyone suggest me where and how can I plot the silhouette of an object from an image? Like some graphing software or something. And how can I integrate multiple sets of plots of silhouettes to reconstruct a 3D model?

Images to trace the silhouette from would be like this.

And the final wire-frame model that I intend to create should look like this.

These two images are borrowed from this research paper. You can also get to know in detail about the method that I am referring to.

https://pdfs.semanticscholar.org/4788/dfa593ffacbec36c7dbb5800173715894029.pdf

Also, feel free to suggest if you have better methods for doing the same thing.

P.S. - the software that is used in the research paper is a paid one. Also, the paper was published in 2006, and so I am sure that there are better methods available.

Aditya Garg
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    I don't think this question is on-topic here. If you already had the 3D model and were looking for mathematical software that can determine the volume/surface area/etc., you may be able to make an argument that the question is on topic, but as it appears to me, you're looking for some software that will help you produce the model (which is not on topic here). – Clayton Aug 21 '19 at 12:24
  • I am sorry, I am new to the community. But won't a software that will help me plot a 3D model still be a math-software? – Aditya Garg Aug 21 '19 at 12:27
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    I'm voting to close this very interesting question because it's not really about mathematics. There will be mathematics in whatever software might do the job, but the hard part will be the software design. If you need this for just one bottle (so not a solution to the general problem) you could try building a wire frame model more or less by hand, correcting it incrementally. You could find the volume physically by displacing water. – Ethan Bolker Aug 21 '19 at 12:31
  • Can you fill the bottle then empty it into a measuring cup? – Randall Aug 21 '19 at 12:34

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