Polygon struct
A polygon with floatingpoint vertices.
Contents
 Reference
Derived classes

struct dip::
ConvexHull  A convex hull is a convex polygon. It can be constructed from a simple
dip::Polygon
, and is guaranteed clockwise.
Aliases
 using Vertices = std::vector<VertexFloat>
 Type used to store the vertices.
Functions
 auto BoundingBox() const > dip::BoundingBoxFloat
 Returns the bounding box of the polygon.
 auto IsClockWise() const > bool
 Determine the orientation of the polygon.
 auto Area() const > dip::dfloat
 Computes the (signed) area of the polygon. The default, clockwise polygons have a positive area.
 auto Centroid() const > dip::VertexFloat
 Computes the centroid of the polygon.
 auto CovarianceMatrix(dip::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 > dip::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. In this case, use
dip::ChainCode::Length
instead.  auto Perimeter() const > dip::dfloat
 An alias for
dip::Polygon::Length
.  auto RadiusStatistics() const > dip::RadiusValues
 Returns statistics on the radii of the polygon. The radii are the distances between the centroid and each of the vertices.
 auto RadiusStatistics(dip::VertexFloat const& g) const > dip::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 > dip::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(dip::VertexFloat const& g, dip::CovarianceMatrix const& C) const > dip::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(dip::dfloat length = 0) const > dip::dfloat
 Computes the fractal dimension of a polygon.
 auto BendingEnergy() const > dip::dfloat
 Computes the bending energy of a polygon.
 auto Simplify(dip::dfloat tolerance = 0.5) > dip::Polygon&
 Simplifies the polygon using the DouglasPeucker algorithm.
 auto Augment(dip::dfloat distance = 1.0) > dip::Polygon&
 Adds vertices along each edge of the polygon such that the distance between two consecutive
vertices is never more than
distance
.  auto Smooth(dip::dfloat sigma = 1.0) > dip::Polygon&
 Locally averages the location of vertices of a polygon so it becomes smoother.
 auto Reverse() > dip::Polygon&
 Reverses the orientation of the polygon, converting a clockwise polygon into a counterclockwise one and vice versa.
 auto Rotate(dip::dfloat angle) > dip::Polygon&
 Rotates the polygon around the origin by
angle
, which is positive for clockwise rotation.  auto Scale(dip::dfloat scale) > dip::Polygon&
 Scales the polygon isotropically by multiplying each vertex coordinate by
scale
.  auto Scale(dip::dfloat scaleX, dip::dfloat scaleY) > dip::Polygon&
 Scales the polygon anisotropically by multiplying each vertex coordinate by
scaleX
andscaleY
.  auto Translate(dip::VertexFloat shift) > dip::Polygon&
 Translates the polygon by
shift
.  auto ConvexHull() const > dip::ConvexHull
 Returns the convex hull of the polygon. The polygon must be simple.
Variables
 dip::Polygon::Vertices vertices
 The vertices.
Function documentation
bool IsClockWise() const
Determine the orientation of the polygon.
This is a fast algorithm that assumes that the polygon is simple. Nonsimple polygons do not have a single orientation anyway.
If the polygon is constructed from a chain code, this function should always return true
.
dip::dfloat 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.
dip::dfloat FractalDimension(dip::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::Polygon::Smooth
. Therefore, it is important that
the polygon be densely sampled, use dip::Polygon::Augment
if necessary.
length
is the length of the polygon (see dip::Polygon::Length
). 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.
dip::dfloat 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::Polygon::Augment
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::Smooth
.
dip::Polygon& Simplify(dip::dfloat tolerance = 0.5)
Simplifies the polygon using the DouglasPeucker algorithm.
For a polygon derived from a chain code, setting tolerance to 0.5 leads to a maximumlength digital straight segment representation of the object.
dip::Polygon& Smooth(dip::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::Polygon::Augment
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
.