point-cloud-to-sac

C++ header-only library
Given a solid as a point-cloud, calculate it's sectional area

Dependencies

Standard Library

Current Capabilities

`SectionalAreaXwiseYsymmetrical()`

The given point cloud must lie on the bounding surface of the underlying solid. Further, the solid must align with certain assumptions:

must be symmetrical with respect to the XZ plane ${\bf P}(u,v) = (u,0,v)$ and all points in the point cloud must be in the same side of $\bf P$
it does not have to be convex, but it must be star-convex with respect to ${\bf P}$ in the sense that for every point ${\bf p}=(p_1,p_2,p_3)$ on the point cloud, the line between ${\bf p}$ and $(p_1,0,p_3)$ must be contained inside the solid

Usage

After creating a directory in your project foo, copy the following files from src

point-cloud-to-sac.hpp
on-surface-point-cloud-to-sac.hpp
on-surface-point-cloud-to-sac-utils.hpp

Then, in your script #include "foo/point-cloud-to-sac.hpp". The point cloud must be provided as a std::vector<std::vector<double>> pnts where pnts.at(i) refers to the $i^{th}$ point.

See doc/documentation.pdf and tests/test-1.cpp, tests/test-3.cpp for two examples: the former is on a solid for which we know the exact sectional area, while the latter for one which we do not.

Future

Add option to import point cloud as file
Access point cloud by reference
Accept general point cloud list
Implement SectionalAreaXwiseYsymmetrical() without the assumptions for the underlying solid: (1) Y-symmetry can be easily discarded (2) star-convexity can be discarded by orienting the parallelograms and establishing some order in the contour of the points (i.e. based on their distance?)
Implement SectionalAreaXwiseYsymmetrical() without the point-cloud having to lie on the bounding surface.