struct
#include <diplib/chain_code.h>
Polygon A polygon with floatingpoint vertices.
Contents
 Reference
Public functions
 auto BoundingBox() const > BoundingBoxFloat
 Returns the bounding box of the polygon.
 auto IsClockWise() const > bool
 Determine the orientation of the polygon (if constructed from a chain code, should return true)
 auto Area() const > dfloat
 Computes the (signed) area of the polygon. Default, clockwise polygons have a positive area.
 auto Centroid() const > VertexFloat
 Computes the centroid of the polygon.

auto CovarianceMatrix(VertexFloat const& g) const > dip::
CovarianceMatrix  Returns the covariance matrix for the vertices of the polygon, using centroid
g
. 
auto CovarianceMatrix() const > dip::
CovarianceMatrix  Returns the covariance matrix for the vertices of the polygon.
 auto Length() const > dfloat
 Computes the length of the polygon (i.e. perimeter). If the polygon represents a pixelated object, this function will overestimate the object's perimeter. Use
dip::
instead.ChainCode:: Length  auto RadiusStatistics() const > RadiusValues
 Returns statistics on the radii of the polygon. The radii are the distances between the centroid and each of the vertices.
 auto RadiusStatistics(VertexFloat const& g) const > RadiusValues
 Returns statistics on the radii of the polygon. The radii are the distances between the given centroid and each of the vertices.
 auto EllipseVariance() const > dfloat
 Compares a polygon to the ellipse with the same covariance matrix, returning the coefficient of variation of the distance of vertices to the ellipse.

auto EllipseVariance(VertexFloat const& g,
dip::
CovarianceMatrix const& C) const > dfloat  Compares a polygon to the ellipse described by the given centroid and covariance matrix, returning the coefficient of variation of the distance of vertices to the ellipse.
 auto FractalDimension(dfloat length = 0) const > dfloat
 Computes the fractal dimension of a polygon.
 auto BendingEnergy() const > dfloat
 Computes the bending energy of a polygon.
 auto Simplify(dfloat tolerance = 0.5) > Polygon&
 Simplifies the polygon using the DouglasPeucker algorithm.
 auto Augment(dfloat distance = 1.0) > Polygon&
 Adds vertices along each edge of the polygon such that the distance between two consecutive vertices is never more than
distance
.  auto Smooth(dfloat sigma = 1.0) > Polygon&
 Locally averages the location of vertices of a polygon so it becomes smoother.

auto ConvexHull() const > dip::
ConvexHull  Returns the convex hull of the polygon.
Public variables
 Vertices vertices
 The vertices.
Function documentation
dfloat dip::Polygon:: EllipseVariance() const
Compares a polygon to the ellipse with the same covariance matrix, returning the coefficient of variation of the distance of vertices to the ellipse.
dfloat dip::Polygon:: FractalDimension(dfloat length = 0) const
Computes the fractal dimension of a polygon.
Fractal dimension is defined as the slope of the polygon length as a function of scale, in a loglog plot. Scale is obtained by smoothing the polygon using dip::
. Therefore, it is important that the polygon be densely sampled, use dip::
if necessary.
length
is the length of the polygon (see dip::
). It determines the range of scales used to compute the fractal dimension, so a rough estimate is sufficient. If zero is given as length (the default value), then it is computed.
dfloat dip::Polygon:: BendingEnergy() const
Computes the bending energy of a polygon.
The bending energy is the integral along the contour of the square of the curvature. We approximate curvature by, at each vertex, taking the difference in angle between the two edges, and dividing by half the length of the two edges (this is the portion of the boundary associated to the edge).
Note that this approximation is poor when the points are far apart. dip::
should be used to obtain a densely sampled polygon. It is also beneficial to sufficiently smooth the polygon so it better approximates a smooth curve around the object being measured, see dip::
.
Polygon& dip::Polygon:: Smooth(dfloat sigma = 1.0)
Locally averages the location of vertices of a polygon so it becomes smoother.
Uses a Gaussian filter with parameter sigma
, which is not interpreted as a physical distance between vertices, but as a distance in number of vertices. That is, the neighboring vertex is at a distance of 1, the next one over at a distance of 2, etc. Therefore, it is important that vertices are approximately equally spaced. dip::
modifies any polygon to satisfy that requirement.
A polygon derived from the chain code of an object without high curvature, when smoothed with a sigma
of 2, will fairly well approximate the original smooth boundary. For objects with higher curvature (including very small objects), choose a smaller sigma
.