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Fix docs
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JacquesOlivierLachaud committed Jul 13, 2024
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3 changes: 1 addition & 2 deletions examples/geometry/volumes/pConvexity-benchmark.cpp
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/**
This example compares the speed of computation of P-convexity wrt
to the computation of full convexity. Both definitions are
equivalent but P-convexity is faster to compute, especially when
increasing the dimension.
equivalent but P-convexity is faster to compute, especially in higher dimensions.
\verbatim
pConvexity-benchmark
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6 changes: 3 additions & 3 deletions src/DGtal/geometry/doc/moduleDigitalConvexity.dox
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- method PConvexity::convexityMeasure returns the convexity measure \f$ M_d(A) \f$ of the given range of digital points \a A,
- method PConvexity::fullConvexityMeasure returns the full convexity measure \f$ M_d^F(A) \f$ of the given range of digital points \a A.

The Figure below illustrates the links and the differences between the
The figure below illustrates the links and the differences between the
two convexity measures Md and MdF on simple 2D examples. As one can
see, the usual convexity measure may not detect disconnectedness, is
sensitive to specific alignments of pixels, while full convexity is
sensitive to specific alignments of pixels. On the contrary, full convexity is
globally more stable to perturbation and is never 1 when sets are
disconnected.

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</table>


All approaches follow more or less a quasi linear complexity \f$ O(n
All approaches follow more or less a linearithmic or subquadratic complexity \f$ O(n
\log n) \f$ (tests are limited to dimension lower or equal to
4). However, we can distinguish three cases:

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