mirror of
https://github.com/qgis/QGIS.git
synced 2025-10-15 00:02:52 -04:00
561 lines
21 KiB
Plaintext
561 lines
21 KiB
Plaintext
/************************************************************************
|
|
* This file has been generated automatically from *
|
|
* *
|
|
* src/core/geometry/qgscircle.h *
|
|
* *
|
|
* Do not edit manually ! Edit header and run scripts/sipify.py again *
|
|
************************************************************************/
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
class QgsCircle : QgsEllipse
|
|
{
|
|
%Docstring(signature="appended")
|
|
Circle geometry type.
|
|
|
|
A circle is defined by a center point with a radius and an azimuth.
|
|
The azimuth is the north angle to the semi-major axis, in degrees. By default, the semi-major axis is oriented to the north (0 degrees).
|
|
%End
|
|
|
|
%TypeHeaderCode
|
|
#include "qgscircle.h"
|
|
%End
|
|
public:
|
|
QgsCircle();
|
|
|
|
QgsCircle( const QgsPoint ¢er, double radius, double azimuth = 0 ) /HoldGIL/;
|
|
%Docstring
|
|
Constructs a circle by defining all the members.
|
|
|
|
:param center: The center of the circle.
|
|
:param radius: The radius of the circle.
|
|
:param azimuth: Angle in degrees started from the North to the first quadrant.
|
|
%End
|
|
|
|
static QgsCircle from2Points( const QgsPoint &pt1, const QgsPoint &pt2 ) /HoldGIL/;
|
|
%Docstring
|
|
Constructs a circle by 2 points on the circle.
|
|
The center point can have m value which is the result from the midpoint
|
|
operation between ``pt1`` and ``pt2``. Z dimension is also supported and
|
|
is retrieved from the first 3D point amongst ``pt1`` and ``pt2``.
|
|
The radius is calculated from the 2D distance between ``pt1`` and ``pt2``.
|
|
The azimuth is the angle between ``pt1`` and ``pt2``.
|
|
|
|
:param pt1: First point.
|
|
:param pt2: Second point.
|
|
%End
|
|
|
|
static QgsCircle from3Points( const QgsPoint &pt1, const QgsPoint &pt2, const QgsPoint &pt3, double epsilon = 1E-8 ) /HoldGIL/;
|
|
%Docstring
|
|
Constructs a circle by 3 points on the circle.
|
|
M value is dropped for the center point.
|
|
Z dimension is supported and is retrieved from the first 3D point
|
|
amongst ``pt1``, ``pt2`` and ``pt3``.
|
|
The azimuth always takes the default value.
|
|
If the points are colinear an empty circle is returned.
|
|
|
|
:param pt1: First point.
|
|
:param pt2: Second point.
|
|
:param pt3: Third point.
|
|
:param epsilon: Value used to compare point.
|
|
%End
|
|
|
|
static QgsCircle fromCenterDiameter( const QgsPoint ¢er, double diameter, double azimuth = 0 ) /HoldGIL/;
|
|
%Docstring
|
|
Constructs a circle by a center point and a diameter.
|
|
The center point keeps z and m values from ``center``.
|
|
|
|
:param center: Center point.
|
|
:param diameter: Diameter of the circle.
|
|
:param azimuth: Azimuth of the circle.
|
|
%End
|
|
|
|
|
|
static QgsCircle fromCenterPoint( const QgsPoint ¢er, const QgsPoint &pt1 ) /HoldGIL/;
|
|
%Docstring
|
|
Constructs a circle by a center point and another point.
|
|
The center point keeps z and m values from ``center``.
|
|
Axes are calculated from the 2D distance between ``center`` and ``pt1``.
|
|
The azimuth is the angle between ``center`` and ``pt1``.
|
|
|
|
:param center: Center point.
|
|
:param pt1: A point on the circle.
|
|
%End
|
|
|
|
|
|
static QgsCircle from3Tangents( const QgsPoint &pt1_tg1, const QgsPoint &pt2_tg1, const QgsPoint &pt1_tg2, const QgsPoint &pt2_tg2, const QgsPoint &pt1_tg3, const QgsPoint &pt2_tg3, double epsilon = 1E-8, const QgsPoint &pos = QgsPoint() ) /HoldGIL/;
|
|
%Docstring
|
|
Constructs a circle by 3 tangents on the circle (aka inscribed circle of a triangle).
|
|
Z and m values are dropped for the center point.
|
|
The azimuth always takes the default value.
|
|
|
|
:param pt1_tg1: First point of the first tangent.
|
|
:param pt2_tg1: Second point of the first tangent.
|
|
:param pt1_tg2: First point of the second tangent.
|
|
:param pt2_tg2: Second point of the second tangent.
|
|
:param pt1_tg3: First point of the third tangent.
|
|
:param pt2_tg3: Second point of the third tangent.
|
|
:param epsilon: Value used to compare point.
|
|
:param pos: Point to determine which circle use in case of multi return.
|
|
If the solution is not unique and pos is an empty point, an empty circle is returned. -- This case happens only when two tangents are parallels. (since QGIS 3.18)
|
|
|
|
.. seealso:: :py:func:`from3TangentsMulti`
|
|
|
|
Example
|
|
-------------------------------------
|
|
|
|
.. code-block:: python
|
|
|
|
# [(0 0), (5 0)] and [(5 5), (10 5)] are parallels
|
|
QgsCircle.from3Tangents(QgsPoint(0, 0), QgsPoint(5, 0), QgsPoint(5, 5), QgsPoint(10, 5), QgsPoint(2.5, 0), QgsPoint(7.5, 5))
|
|
# <QgsCircle: Empty>
|
|
QgsCircle.from3Tangents(QgsPoint(0, 0), QgsPoint(5, 0), QgsPoint(5, 5), QgsPoint(10, 5), QgsPoint(2.5, 0), QgsPoint(7.5, 5), pos=QgsPoint(2, 0))
|
|
# <QgsCircle: Circle (Center: Point (1.46446609406726203 2.49999999999999911), Radius: 2.5, Azimuth: 0)>
|
|
QgsCircle.from3Tangents(QgsPoint(0, 0), QgsPoint(5, 0), QgsPoint(5, 5), QgsPoint(10, 5), QgsPoint(2.5, 0), QgsPoint(7.5, 5), pos=QgsPoint(3, 0))
|
|
# <QgsCircle: Circle (Center: Point (8.53553390593273775 2.5), Radius: 2.5, Azimuth: 0)>
|
|
%End
|
|
|
|
static QVector<QgsCircle> from3TangentsMulti( const QgsPoint &pt1_tg1, const QgsPoint &pt2_tg1, const QgsPoint &pt1_tg2, const QgsPoint &pt2_tg2, const QgsPoint &pt1_tg3, const QgsPoint &pt2_tg3, double epsilon = 1E-8, const QgsPoint &pos = QgsPoint() ) /HoldGIL/;
|
|
%Docstring
|
|
Returns an array of circle constructed by 3 tangents on the circle (aka inscribed circle of a triangle).
|
|
|
|
The vector can contain 0, 1 or 2 circles:
|
|
|
|
- 0: Impossible to construct a circle from 3 tangents (three parallel tangents)
|
|
- 1: The three tangents make a triangle or when two tangents are parallel there are two possible circles (see examples).
|
|
If pos is not an empty point, we use its coordinates to determine which circle will be returned.
|
|
More precisely the circle that will be returned will be the one whose center is on the same side as pos relative to the third tangent.
|
|
- 2: Returns both solutions when two tangents are parallel (this implies that pos is an empty point).
|
|
|
|
Z and m values are dropped for the center point.
|
|
The azimuth always takes the default value.
|
|
|
|
:param pt1_tg1: First point of the first tangent.
|
|
:param pt2_tg1: Second point of the first tangent.
|
|
:param pt1_tg2: First point of the second tangent.
|
|
:param pt2_tg2: Second point of the second tangent.
|
|
:param pt1_tg3: First point of the third tangent.
|
|
:param pt2_tg3: Second point of the third tangent.
|
|
:param epsilon: Value used to compare point.
|
|
:param pos: (optional) Point to determine which circle use in case of multi return.
|
|
|
|
.. seealso:: :py:func:`from3Tangents`
|
|
|
|
Example
|
|
-------------------------------------
|
|
|
|
.. code-block:: python
|
|
|
|
# [(0 0), (5 0)] and [(5 5), (10 5)] are parallels
|
|
QgsCircle.from3TangentsMulti(QgsPoint(0, 0), QgsPoint(5, 0), QgsPoint(5, 5), QgsPoint(10, 5), QgsPoint(2.5, 0), QgsPoint(7.5, 5))
|
|
# [<QgsCircle: Circle (Center: Point (8.53553390593273775 2.5), Radius: 2.5, Azimuth: 0)>, <QgsCircle: Circle (Center: Point (1.46446609406726203 2.49999999999999911), Radius: 2.5, Azimuth: 0)>]
|
|
QgsCircle.from3TangentsMulti(QgsPoint(0, 0), QgsPoint(5, 0), QgsPoint(5, 5), QgsPoint(10, 5), QgsPoint(2.5, 0), QgsPoint(7.5, 5), pos=QgsPoint(2, 0))
|
|
# [<QgsCircle: Circle (Center: Point (1.46446609406726203 2.49999999999999911), Radius: 2.5, Azimuth: 0)>]
|
|
QgsCircle.from3TangentsMulti(QgsPoint(0, 0), QgsPoint(5, 0), QgsPoint(5, 5), QgsPoint(10, 5), QgsPoint(2.5, 0), QgsPoint(7.5, 5), pos=QgsPoint(3, 0))
|
|
# [<QgsCircle: Circle (Center: Point (8.53553390593273775 2.5), Radius: 2.5, Azimuth: 0)>]
|
|
# [(0 0), (5 0)], [(5 5), (10 5)] and [(15 5), (20 5)] are parallels
|
|
QgsCircle.from3TangentsMulti(QgsPoint(0, 0), QgsPoint(5, 0), QgsPoint(5, 5), QgsPoint(10, 5), QgsPoint(15, 5), QgsPoint(20, 5))
|
|
# []
|
|
%End
|
|
|
|
static QgsCircle fromExtent( const QgsPoint &pt1, const QgsPoint &pt2 ) /HoldGIL/;
|
|
%Docstring
|
|
Constructs a circle by an extent (aka bounding box / :py:class:`QgsRectangle`).
|
|
The center point can have m value which is the result from the midpoint
|
|
operation between ``pt1`` and ``pt2``. Z dimension is also supported and
|
|
is retrieved from the first 3D point amongst ``pt1`` and ``pt2``.
|
|
Axes are calculated from the 2D distance between ``pt1`` and ``pt2``.
|
|
The azimuth always takes the default value.
|
|
|
|
:param pt1: First corner.
|
|
:param pt2: Second corner.
|
|
%End
|
|
|
|
static QgsCircle minimalCircleFrom3Points( const QgsPoint &pt1, const QgsPoint &pt2, const QgsPoint &pt3, double epsilon = 1E-8 ) /HoldGIL/;
|
|
%Docstring
|
|
Constructs the smallest circle from 3 points.
|
|
Z and m values are dropped for the center point.
|
|
The azimuth always takes the default value.
|
|
If the points are colinear an empty circle is returned.
|
|
|
|
:param pt1: First point.
|
|
:param pt2: Second point.
|
|
:param pt3: Third point.
|
|
:param epsilon: Value used to compare point.
|
|
%End
|
|
|
|
int intersections( const QgsCircle &other, QgsPoint &intersection1 /Out/, QgsPoint &intersection2 /Out/, bool useZ = false ) const;
|
|
%Docstring
|
|
Calculates the intersections points between this circle and an ``other`` circle.
|
|
|
|
If found, the intersection points will be stored in ``intersection1`` and ``intersection2``.
|
|
|
|
By default this method does not consider any z values and instead treats the circles as 2-dimensional.
|
|
If ``useZ`` is set to ``True``, then an intersection will only occur if the z values of both circles are
|
|
equal. In this case the points returned for ``intersection1`` and ``intersection2`` will contain
|
|
the z value of the circle intersections.
|
|
|
|
:return: number of intersection points found.
|
|
|
|
.. versionadded:: 3.2
|
|
%End
|
|
|
|
bool tangentToPoint( const QgsPointXY &p, QgsPointXY &pt1 /Out/, QgsPointXY &pt2 /Out/ ) const;
|
|
%Docstring
|
|
Calculates the tangent points between this circle and the point ``p``.
|
|
|
|
If found, the tangent points will be stored in ``pt1`` and ``pt2``.
|
|
|
|
.. note::
|
|
|
|
This method is 2D only and does not consider the z-value of the circle.
|
|
|
|
:return: ``True`` if tangent was found.
|
|
|
|
.. seealso:: :py:func:`outerTangents`
|
|
|
|
.. seealso:: :py:func:`innerTangents`
|
|
|
|
.. versionadded:: 3.2
|
|
%End
|
|
|
|
int outerTangents( const QgsCircle &other, QgsPointXY &line1P1 /Out/, QgsPointXY &line1P2 /Out/, QgsPointXY &line2P1 /Out/, QgsPointXY &line2P2 /Out/ ) const;
|
|
%Docstring
|
|
Calculates the outer tangent points between this circle
|
|
and an ``other`` circle.
|
|
|
|
The outer tangent points correspond to the points at which the two lines
|
|
which are drawn so that they are tangential to both circles touch
|
|
the circles.
|
|
|
|
The first tangent line is described by the points
|
|
stored in ``line1P1`` and ``line1P2``,
|
|
and the second line is described by the points stored in ``line2P1``
|
|
and ``line2P2``.
|
|
|
|
Returns the number of tangents (either 0 or 2).
|
|
|
|
.. note::
|
|
|
|
This method is 2D only and does not consider the z-value of the circle.
|
|
|
|
.. seealso:: :py:func:`tangentToPoint`
|
|
|
|
.. seealso:: :py:func:`innerTangents`
|
|
|
|
.. versionadded:: 3.2
|
|
%End
|
|
|
|
int innerTangents( const QgsCircle &other, QgsPointXY &line1P1 /Out/, QgsPointXY &line1P2 /Out/, QgsPointXY &line2P1 /Out/, QgsPointXY &line2P2 /Out/ ) const;
|
|
%Docstring
|
|
Calculates the inner tangent points between this circle
|
|
and an ``other`` circle.
|
|
|
|
The inner tangent points correspond to the points at which the two lines
|
|
which are drawn so that they are tangential to both circles but on
|
|
different sides, touching the circles and crossing each other.
|
|
|
|
The first tangent line is described by the points
|
|
stored in ``line1P1`` and ``line1P2``,
|
|
and the second line is described by the points stored in ``line2P1``
|
|
and ``line2P2``.
|
|
|
|
Returns the number of tangents (either 0 or 2).
|
|
|
|
.. note::
|
|
|
|
This method is 2D only and does not consider the z-value of the circle.
|
|
|
|
.. seealso:: :py:func:`tangentToPoint`
|
|
|
|
.. seealso:: :py:func:`outerTangents`
|
|
|
|
.. versionadded:: 3.6
|
|
%End
|
|
|
|
virtual double area() const /HoldGIL/;
|
|
|
|
virtual double perimeter() const /HoldGIL/;
|
|
|
|
|
|
|
|
|
|
virtual void setSemiMajorAxis( double semiMajorAxis ) /HoldGIL/;
|
|
|
|
%Docstring
|
|
Inherited method. Use :py:func:`~QgsCircle.setRadius` instead.
|
|
|
|
.. seealso:: :py:func:`radius`
|
|
|
|
.. seealso:: :py:func:`setRadius`
|
|
%End
|
|
|
|
virtual void setSemiMinorAxis( double semiMinorAxis ) /HoldGIL/;
|
|
|
|
%Docstring
|
|
Inherited method. Use :py:func:`~QgsCircle.setRadius` instead.
|
|
|
|
.. seealso:: :py:func:`radius`
|
|
|
|
.. seealso:: :py:func:`setRadius`
|
|
%End
|
|
|
|
double radius() const /HoldGIL/;
|
|
%Docstring
|
|
Returns the radius of the circle
|
|
%End
|
|
void setRadius( double radius ) /HoldGIL/;
|
|
%Docstring
|
|
Sets the radius of the circle
|
|
%End
|
|
|
|
QVector<QgsPoint> northQuadrant() const /Factory/;
|
|
%Docstring
|
|
The four quadrants of the ellipse.
|
|
They are oriented and started from North.
|
|
|
|
:return: quadrants defined by four points.
|
|
|
|
.. seealso:: :py:func:`quadrant`
|
|
%End
|
|
|
|
QgsCircularString *toCircularString( bool oriented = false ) const;
|
|
%Docstring
|
|
Returns a circular string from the circle.
|
|
|
|
:param oriented: If oriented is ``True`` the start point is from azimuth instead from north.
|
|
%End
|
|
|
|
bool contains( const QgsPoint &point, double epsilon = 1E-8 ) const;
|
|
%Docstring
|
|
Returns ``True`` if the circle contains the ``point``.
|
|
%End
|
|
|
|
virtual QgsRectangle boundingBox() const;
|
|
|
|
|
|
virtual QString toString( int pointPrecision = 17, int radiusPrecision = 17, int azimuthPrecision = 2 ) const;
|
|
|
|
|
|
QDomElement asGml2( QDomDocument &doc, int precision = 17, const QString &ns = "gml", QgsAbstractGeometry::AxisOrder axisOrder = QgsAbstractGeometry::AxisOrder::XY ) const;
|
|
%Docstring
|
|
Returns a GML2 representation of the geometry.
|
|
Since GML2 does not supports curve, it will be converted to a LineString.
|
|
|
|
:param doc: DOM document
|
|
:param precision: number of decimal places for coordinates
|
|
:param ns: XML namespace
|
|
:param axisOrder: Axis order for generated GML
|
|
|
|
.. seealso:: :py:func:`asGml3`
|
|
%End
|
|
|
|
QDomElement asGml3( QDomDocument &doc, int precision = 17, const QString &ns = "gml", QgsAbstractGeometry::AxisOrder axisOrder = QgsAbstractGeometry::AxisOrder::XY ) const;
|
|
%Docstring
|
|
Returns a GML3 representation of the geometry.
|
|
|
|
From the GML3 description:
|
|
A Circle is an arc whose ends coincide to form a simple closed loop.
|
|
The three control points shall be distinct non-co-linear points for
|
|
the circle to be unambiguously defined. The arc is simply extended
|
|
past the third control point until the first control point is encountered.
|
|
|
|
Coordinates are taken from quadrant North, East and South.
|
|
|
|
:param doc: DOM document
|
|
:param precision: number of decimal places for coordinates
|
|
:param ns: XML namespace
|
|
:param axisOrder: Axis order for generated GML
|
|
|
|
.. seealso:: :py:func:`asGml2`
|
|
%End
|
|
|
|
static int calculateSegments( double radius, double parameter, int minSegments, Qgis::SegmentCalculationMethod method );
|
|
%Docstring
|
|
Calculates the number of segments needed to approximate a circle.
|
|
|
|
:param radius: Circle radius. Must be positive; if <= 0, `minSegments` is returned.
|
|
:param parameter: Maximum tolerance allowed for the deviation between the circle and its approximation,
|
|
except for the ConstantDensity method where it is a constant. If <= 0, a default value of 0.01 is used.
|
|
:param minSegments: Minimum number of segments to use. If < 3, it is set to 3.
|
|
:param method: Calculation method to use.
|
|
|
|
:return: Number of segments needed for the approximation.
|
|
|
|
\pre `radius` must be strictly positive; otherwise, the function returns `minSegments`.
|
|
\pre `parameter` should be positive; if not, it defaults to 0.01.
|
|
\pre `minSegments` should be at least 3; if less, it is clamped to 3.
|
|
|
|
.. versionadded:: 3.44
|
|
%End
|
|
|
|
|
|
SIP_PYOBJECT __repr__();
|
|
%MethodCode
|
|
QString str
|
|
= QStringLiteral( "<QgsCircle: %1>" ).arg( sipCpp->toString() );
|
|
sipRes = PyUnicode_FromString( str.toUtf8().constData() );
|
|
%End
|
|
|
|
private :
|
|
|
|
static int calculateSegmentsStandard( double radius, double tolerance, int minSegments );
|
|
%Docstring
|
|
Calculate the number of segments needed to approximate a circle within a given tolerance.
|
|
|
|
This function uses the sagitta (geometric chord height) to determine the number of segments
|
|
required to approximate a circle such that the maximum deviation between the circle and its
|
|
polygonal approximation is less than the specified tolerance.
|
|
|
|
Mathematical approach:
|
|
1. Using the sagitta formula: s = r(1 - cos(θ/2))
|
|
where s is the sagitta, r is the radius, and θ is the segment angle
|
|
2. Substituting tolerance for s:
|
|
tolerance = radius(1 - cos(θ/2))
|
|
3. Solving for θ:
|
|
tolerance/radius = 1 - cos(θ/2)
|
|
cos(θ/2) = 1 - tolerance/radius
|
|
θ/2 = arccos(1 - tolerance/radius)
|
|
θ = 2 * arccos(1 - tolerance/radius)
|
|
4. Number of segments = ceil(2π / θ)
|
|
= ceil(π / arccos(1 - tolerance/radius))
|
|
|
|
:param radius: The radius of the circle to approximate
|
|
:param tolerance: Maximum allowed deviation between the circle and its polygonal approximation
|
|
:param minSegments: Minimum number of segments to use, regardless of the calculated value
|
|
|
|
:return: The number of segments needed
|
|
|
|
.. note::
|
|
|
|
This is a private helper method
|
|
%End
|
|
|
|
static int calculateSegmentsAdaptive( double radius, double tolerance, int minSegments );
|
|
%Docstring
|
|
Calculate the number of segments with adaptive tolerance based on radius.
|
|
|
|
This method extends :py:func:`~QgsCircle.calculateSegments` by using an adaptive tolerance that scales
|
|
with the radius to maintain better visual quality. While :py:func:`~QgsCircle.calculateSegments` uses
|
|
a fixed tolerance, this version adjusts the tolerance based on the radius size.
|
|
|
|
Mathematical approach:
|
|
1. Compute adaptive tolerance that varies with radius:
|
|
adaptive_tolerance = base_tolerance * sqrt(radius) / log10(radius + 1)
|
|
|
|
For small radii: tolerance decreases → more segments for better detail
|
|
For large radii: tolerance increases gradually → fewer segments needed
|
|
sqrt(radius) provides basic scaling
|
|
log10(radius + 1) dampens the scaling for large radii
|
|
|
|
2. Apply sagitta-based calculation:
|
|
|
|
Calculate angle = 2 * arccos(1 - adaptive_tolerance/radius)
|
|
Number of segments = ceil(2π/angle)
|
|
|
|
This adaptation ensures:
|
|
|
|
Small circles get more segments for better visual quality
|
|
Large circles don't get excessive segments
|
|
Smooth transition between different scales
|
|
|
|
:param radius: The radius of the circle to approximate
|
|
:param tolerance: Base tolerance value that will be scaled
|
|
:param minSegments: Minimum number of segments to use
|
|
|
|
:return: The number of segments needed
|
|
|
|
.. note::
|
|
|
|
This is a private helper method
|
|
%End
|
|
|
|
static int calculateSegmentsByAreaError( double radius, double baseTolerance, int minSegments );
|
|
%Docstring
|
|
Calculate the number of segments based on the maximum allowed area error.
|
|
|
|
This function computes the minimum number of segments needed to approximate
|
|
a circle with a regular polygon such that the relative area error between
|
|
the polygonal approximation and the actual circle is less than the specified tolerance.
|
|
|
|
Mathematical derivation:
|
|
1. Area ratio between a regular n-sided polygon and a circle:
|
|
Circle area: Ac = πr²
|
|
Regular polygon area: Ap = (nr²/2) * sin(2π/n)
|
|
Ratio = Ap / Ac = (n / 2π) * sin(2π/n)
|
|
|
|
2. For relative error E:
|
|
E = |1 - Ap / Ac| = |1 - (n / 2π) * sin(2π/n)|
|
|
|
|
3. Using Taylor series approximation for sin(x) when x is small:
|
|
sin(x) ≈ x - x³ / 6
|
|
With x = 2π / n:
|
|
sin(2π / n) ≈ (2π / n) - (2π / n)³ / 6
|
|
|
|
4. Substituting and simplifying:
|
|
E ≈ |1 - (n / 2π) * ((2π / n) - (2π / n)³ / 6)|
|
|
E ≈ |1 - (1 - (2π² / 3n²))|
|
|
E ≈ 2π² / 3n²
|
|
|
|
5. Rearranging to find the minimum n for a given tolerance:
|
|
Start with the inequality: E ≤ tolerance
|
|
Substitute the expression for E:
|
|
2π² / 3n² ≤ tolerance
|
|
Rearrange to isolate n²:
|
|
n² ≥ 2π² / (3 * tolerance)
|
|
Taking the square root:
|
|
n ≥ π * sqrt(2 / (3 * tolerance))
|
|
|
|
:param radius: The radius of the circle to approximate
|
|
:param baseTolerance: Maximum acceptable area error in percentage
|
|
:param minSegments: The minimum number of segments to use
|
|
|
|
:return: The number of segments needed
|
|
|
|
.. note::
|
|
|
|
This is a private helper method
|
|
%End
|
|
|
|
static int calculateSegmentsByConstant( double radius, double constant, int minSegments );
|
|
%Docstring
|
|
Calculate the number of segments using a simple linear relationship with radius.
|
|
|
|
This function implements the simplest approach to circle discretization by using
|
|
a direct linear relationship between the radius and the number of segments.
|
|
While not mathematically precise for error control, it provides a quick and
|
|
intuitive approximation that can be useful when exact error bounds aren't required.
|
|
|
|
Mathematical approach:
|
|
1. Linear scaling: segments = constant * radius
|
|
|
|
Larger constant = more segments = better approximation
|
|
Smaller constant = fewer segments = coarser approximation
|
|
|
|
:param radius: The radius of the circle to approximate
|
|
:param constant: Multiplier that determines the density of segments
|
|
:param minSegments: The minimum number of segments to use
|
|
|
|
:return: The number of segments needed
|
|
|
|
.. note::
|
|
|
|
This is a private helper method
|
|
%End
|
|
};
|
|
|
|
/************************************************************************
|
|
* This file has been generated automatically from *
|
|
* *
|
|
* src/core/geometry/qgscircle.h *
|
|
* *
|
|
* Do not edit manually ! Edit header and run scripts/sipify.py again *
|
|
************************************************************************/
|