Index of the geometry_complex module
-
m
base.geometry_complex
...
- objects connected with the geometry of complex numbers
-
m
zplane
...
- objects of the complex plane
-
m
zpoints
...
- objects representing a point of the complex plane
-
m
z_points
...
- points of the complex plane with fixed or dependant position
-
f
zPoint
...
- factory' function returns instance of a class representing a point of the
complex plane with position fixed or dependant on its arguments
-
C
u_to_zPoint
...
- complex point (stereographically) projected from the given point of
the Riemann sphere
-
C
zPowerPoint
...
- complex point of intersection of the radical axis of the given 2 circles
and the line of the circles' centers
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C
zRotation
...
- complex point determined by stereographic projection of the rotation of
the second complex point argument, with the projection of the first complex point
argument as the rotation axis, by the given angle.
-
C
zCircumPoint
...
- complex point on the given complex circle rotated by the given
angle (in radians)
-
C
zPolarPoint
...
- complex point fixed at given 'angle' and 'dist' polar coordinates
-
C
zInversePoint
...
- complex point inverse to the given complex point with respect to
the given complex circle
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C
zFixedPoint
...
- complex point fixed at given (real, imaginary) coordinates
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C
zOrthoPoint
...
- complex point orthogonal to the given complex point, i.e. antipodal
to it's stereographic projection onto the Riemann sphere.
-
C
zHarmonic
...
- complex point harmonic conjugate to the 3rd given complex point with
the respect to the 1st and 2nd given complex points
-
C
zConjugate
...
- complex point conjugate of the given complex point
-
C
z_uRotation
...
- complex point determined by stereographic projection of the rotation of
the complex point argument, with the given point of the Riemann sphere
as the rotation axis, by the given angle.
-
m
z_mobpoints
...
- points of the complex plane with position determined in connection with
a defined Moebius transformation
-
f
mobPoint
...
- factory' function returns instance of a class representing the Mobius transoformation of
a given point
-
C
mobFixed
...
- complex point representing one of the points fixed of the given
Mobius transformation
-
C
mobInversePole
...
- complex point to which the point at infinity is transformed under the given
Mobius transformation
-
C
mobPole
...
- complex point which is transformed to the point at infinity under the given
Mobius transformation
-
m
z_sliders
...
- points of the complex plane which can be picked and moved
-
f
zSlider
...
- factory' function returns instance of a class representing a point of the
complex plane which can be picked and moved
-
C
zLineSlider
...
- complex point on the given complex line which can be picked, with movement constrained to
the given line and with initial position determined by the 'ratio' keyword.
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C
zCircleSlider
...
- complex point on the given complex circle which can be picked, with movement constrained to
the given circle and with initial position determined by the 'angle' keyword.
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C
zFreePoint
...
- complex point intially at given (real,imaginary) coordinates that can be picked and
moved freely on the complex plane
-
m
z_anipoints
...
- points of the complex plane which change position at each update cycle
-
f
zAniPoint
...
- factory function returns instance of a class representing a point of the
complex plane which moves along a given object or defined path at each update cycle
-
C
zSlidingPoint
...
- complex point which moves along the given complex line, at a rate
determined by the 'rate' keyword
-
C
zCirclingPoint
...
- complex point which moves along the given complex circle, at a rate
determined by the 'rate' keyword, and initial position determined by
the 'angle' keyword.
-
C
zRotatingPoint
...
- complex point which moves the 2nd given complex point along the path induced by the
rotation of the unit sphere, with the stereographic projection of the first complex point
argmuent as axis of rotation, and initial position determined by the 'angle' keyword.
-
m
z_lines
...
- lines of the complex plane (i.e. circles of infinite radius)
-
f
zLine
...
- factory function returns instance of a class representing a line
(circle of infinite radius) of the complex plane
-
C
zBiChord
...
- line of the complex plane determined as the radical axis
of the given 2 the complex circles arguments
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C
zLineFromPoints
...
- line of the complex plane through the given 2 complex point arguments
-
m
z_circles
...
- circles of the complex plane
-
f
zCircle
...
- factory' function returns instance of a class representing the locus
of points equidistant from a given point of the complex plane
-
C
zFundamentalCircle
...
- complex circle by which the first zcircle argument is tranformed to
second zcircle argument by inversion . required 'alt=FUNDAMENTAL' keyword
-
C
u_to_zCircle
...
- complex circle as the stereographic projection of the given spheric section
of the Riemann sphere to the complex plane
-
C
zOrthoCircle_Circum
...
- complex circle orthogonal to the given complex circle,
and through the given 2 zpoint arguments.
-
C
zInverseCircle
...
- complex circle inverse to the second given zcircle argument with respect
to the first given zcircle
-
C
zUnitCircle
...
- "
complex circle with center at origin center and unit radius
-
C
zOrthoCircle
...
- complex circle orthogonal to the given complex circle , with
given zpoint as center
-
C
zCircleFromPoints
...
- complex circle with the first given zpoint as center
and the second given zpoint on the circumference
-
C
zCircumCircle
...
- complex circle through the given 3 zpoints
-
m
z_pointarrays
...
- array of points of the complex plane
-
f
zPointArray
...
- factory' function returns instance of a class representing an array of points
of the complex plane
-
C
zLinePoints
...
- array of complex points equidistant on a given line of the complex plane
-
C
zCirclePoints
...
- array of complex points equidistant on thecircumference of the given complex circle
-
m
z_linearrays
...
- array of lines on the complex plane
-
f
zLineArray
...
- factory function returns instance a class representing an array of
lines (i.e. circles of infinite radius) on the complex plane
-
C
zLinePencil
...
- array of lines on the complex plane and through the given complex point
-
m
z_circlepencils
...
- array of circles of the complex plane
-
f
zCirclePencil
...
- factory' function returns instance of a class representing an array of circles
on the complex plane
-
C
u_to_zCirclePencil
...
- array of complex circles generated by the stereographic projection
of a pencil of spheric sections of the Riemann sphere
-
C
zCircles
...
- array of complex circles generated by the given 2 complex circles
-
m
z_transforms
...
- geometric objects of the complex plane as transformed by a given Moebius
tranformation
-
f
mobTransform
...
- factory function returns instance of a class representing a given list of objects
transformed by a Moebius tranformation
-
C
mobReciprocate
...
- Mobius transformation reciprocating the given list of objects
of the complex plane
-
C
mobInverse
...
- Mobius transformation applied to the given list of objects of the complex plane
defined by the matrix inverse of matrix representing the given Mobius transformation
-
C
mobMapCircles
...
- Mobius transformation applied to the given list of objects of the complex plane mapping
the interior of the first given complex circle to the exterior of the second
given complex circle,
-
C
mobUnitCircle
...
- Mobius transformation applied to the given list of objects of the complex plane
mapping the given complex circle to the unit circle.
-
C
mobTranslate
...
- Mobius transformation translating the given list of objects of the complex plane
in the direction of the given complex point
-
C
mobMultiply
...
- Mobius transformation multiplying the given list of objects of the complex plane
by the given complex point
-
C
mobPointSets
...
- Mobius transformation applied to the given list of objects of the complex plane
mapping the 3 (ordered) complex points of the first point set
to the 3 (ordered) complex points of the second point set.
-
C
mobRotate
...
- Mobius transformation applied to the given list of objects of the complex plane
induced by the rotation of the Riemann sphere, with the stereographic projection of the
given complex point as axis, by the given numeric angle (in radians)
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C
mobFromFixed
...
- Mobius transformation applied to the given list of objects of the complex plane
with the given 2 complex points as fixed points, and the given numerical
value as the transformation mulitplier
-
m
z_plane
...
- the complex plane, as drawing reference to
-
C
zPlane
...
-
plane for drawing reference to the complex plane
and taking no arguments
-
m
usphere
...
- objects of the Riemann (origin centered unit) sphere
-
m
upoints
...
- objects representing a point on the (origin centered unit) Riemann sphere
-
m
u_points
...
- points fixed or determined on the Riemann sphere
-
f
uPoint
...
- factory function returns instance of a class
representing fixed or determmined points of the Riemann sphere
-
C
uAntiPodal
...
- point of the Riemann sphere antipodal to the given point of the sphere
-
C
z_to_uPoint
...
- point of the Riemann sphere stereographically projected
from the given point of the complex plane
-
C
uInversePoint
...
- point of the Riemann sphere inverse to the given point of the sphere with
respect to the given spheric section of the sphere
-
C
uCircumPoint
...
- point of a spheric section of the Riemann sphere
-
C
uPolarPoint
...
- point of the Riemann sphere at the given spherical
coordinates, in radians
-
m
u_sliders
...
- points pickable and movable constrained to the Riemann sphere or an object
on the sphere
-
f
uSlider
...
- factory function returns instance of a class representing points of the Riemann sphere
that can be picked and moved on the sphere or constrained to an object on the sphere.
-
C
uSphereSlider
...
- point of the Riemann sphere that can be picked and moved
constrained to the sphere and with initial position at the given
spherical coordinates, in radians
-
C
uCircleSlider
...
- point of the given spheric section of the Riemann sphere that can
be picked and moved constrained to the spheric section , with its initial position
determined by optinal float argument, in radians
-
m
u_anipoints
...
- points which move on the Riemann sphere or an object on the sphere
at each update cycle
-
f
uAniPoint
...
- factory function returns instance of a class represetning a point which moves in relation
to a given geometric object of the Riemann sphere at each update cyle
-
C
uSpiral
...
- point of the Riemann sphere that moves as a spiral on the sphere from
its initial point to its antipodal point, with the initial point determined
by given polar coordinates, in radians
-
C
uCirclingPoint
...
- point of the given spheric section of the Riemann sphere that moves
along the spheric section at each update, with its initial position
determined by optinal float argument, in radians
-
m
u_circles
...
- spheric section of the Riemann sphere
-
f
uCircle
...
- factory function returns instance of a class representing a spheric
section of the Riemann sphere
-
C
uPolarCircle
...
- spheric section of Riemann sphere cut by the plane
polar to the given point with respect to Riemann sphere
-
C
uSphereSlice
...
- spheric section of Riemann sphere cut by the plane
polar to the given point with respect to Riemann sphere
-
C
z_to_uCircle
...
- spheric section of the Riemann sphere stereographically projected from the
given circle of the complex plane
-
C
uCircumCircle
...
- spheric section of the Riemann sphere through 3 given points on the sphere
-
C
uCircleFromNormal
...
- spheric section of the Riemann sphere cut by the plane
at the initial point argument and normal to the direction determined
by the given 2 point
-
m
u_circlepencils
...
- array of spheric sections of the Riemann sphere
-
f
uCirclePencil
...
- factory' function returns instance of a class representing an
array of spheric sections of the Riemann sphere
-
C
z_to_uCirclePencil
...
- array of spheric sections of the Riemann sphere formed by the stereographic projection
to the sphere of an array of circles of the complex plane
-
C
uSphereSlices
...
- array of spheric sections of the Riemann sphere formed by the intersection of
planes of the given plane array with the Riemann sphere
-
m
u_transforms
...
- projection to the Riemann sphere of objects of the complex plane
-
f
uTransform
...
- factory function returns instance of a class representing a projection
from the complex plane to the Riemann sphere
-
C
uStereoProject
...
- stereographic projection to the Riemann sphere of given list of objects of the complex plane
-
m
u_spheres
...
- sphere objects for reference drawing in connection with complex plane
projection and inversion
-
C
uSphere
...
- the origin centered sphere of unit radius representing the Riemann sphere
-
C
kSphere
...
- a sphere of radius sqrt(2) centered at vector(0,0,1)
-
m
r_points
...
- points of real 3d space with drawing defaults scaled to work with Riemann
sphere constructions
-
C
rFreePoint
...
- point of 3d space at initial x,y,z which can picked and moved
freely in space with default drawing size scaled to work
with Riemann sphere
-
C
rPoint
...
- point of 3d space at fixed x,y,z coordinates with default drawing size scaled
to work with Riemann sphere
-
C
rPole
...
- point determined as pole of the plane of the given spheric section of Riemann sphere
with respect to the Riemann sphere
-
m
r_lines
...
- lines of real 3d space with drawing defaults scaled to work with Riemann
sphere constructions
-
C
rLine
...
- line of 3d space through given two points, with drawing scaled to work with
Riemann sphere