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.