From b0bc80eb32b59e026d97e94217a5fcd13b070a40 Mon Sep 17 00:00:00 2001 From: Jacques-Olivier Lachaud Date: Sat, 13 Jul 2024 11:53:04 +0200 Subject: [PATCH] Fix docs --- examples/geometry/volumes/pConvexity-benchmark.cpp | 3 +-- src/DGtal/geometry/doc/moduleDigitalConvexity.dox | 6 +++--- 2 files changed, 4 insertions(+), 5 deletions(-) diff --git a/examples/geometry/volumes/pConvexity-benchmark.cpp b/examples/geometry/volumes/pConvexity-benchmark.cpp index 2b81f2ee5d..1044934b3b 100644 --- a/examples/geometry/volumes/pConvexity-benchmark.cpp +++ b/examples/geometry/volumes/pConvexity-benchmark.cpp @@ -43,8 +43,7 @@ /** 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 diff --git a/src/DGtal/geometry/doc/moduleDigitalConvexity.dox b/src/DGtal/geometry/doc/moduleDigitalConvexity.dox index 0d783541ce..20ee07fa4b 100644 --- a/src/DGtal/geometry/doc/moduleDigitalConvexity.dox +++ b/src/DGtal/geometry/doc/moduleDigitalConvexity.dox @@ -468,10 +468,10 @@ starting from dimension 2, and is always less or equal to the convexity measure. - 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. @@ -610,7 +610,7 @@ so that they are either 0-convex or fully convex. -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: