The library documents itself · Geo & cartography

stzGeoProjection

53 own methods · 17 forms written with extensions, listed under their method

the source: base/geo/stzGeoProjection.ring(opens in a new tab) · All classes · The area reference: Geo & cartography

Under each method, its extensions (Q CS XT Z ZZ IB W U): bold and ticked, it exists; struck, it does not. The extensions and what they mean

Examples: 0 come from the library's tests; 20 were composed from each method's signature and run for this page, on a fresh object, for example o1 = new stzGeoProjection(:CylindricalEqualArea). 33 methods have none yet. Examples run on 2026-10-03 12:54 inside the library at commit 0e72e2e2c.

Method

Explanation, as the source carries it

init

(no comment in the source: the name reads as a sentence) initno extension

Name

(no comment in the source: the name reads as a sentence) name

composed example

o1 = new stzGeoProjection(:CylindricalEqualArea)
? o1.Name()
#--> CylindricalEqualArea

composed from the signature, run for this page

no extension

KindNumber

(no comment in the source: the name reads as a sentence) kind number

composed example

o1 = new stzGeoProjection(:CylindricalEqualArea)
? o1.KindNumber()
#--> 3

composed from the signature, run for this page

no extension

Params

THE ELEVEN NUMBERS, the shape the engine reads

composed example

o1 = new stzGeoProjection(:CylindricalEqualArea)
? @@( o1.Params() )
#--> [ 3, 0, 0, 0, 0, 0, 150, 480, 250, 0, 0.70 ]

composed from the signature, run for this page

no extension

DistortionAt

:h the scale along the MERIDIAN, 1 meaning true :k the scale along the PARALLEL :a, :b the semi-axes of Tissot's indicatrix -- the greatest and least scale in ANY direction. They are NOT h and k: those are the scales along two particular directions, which need not be the extremes, and confusing the pairs is the classic error in this subject. :areal the area scale. 1 everywhere on an equal-area projection. :angular the largest angle this place bends, degrees. 0 everywhere on a conformal one. :crossing the angle the meridian and parallel cross at on paper.

composed example

o1 = new stzGeoProjection(:CylindricalEqualArea)
? @@( o1.DistortionAt(2, 5) )
#--> [ [ "h", 1.00 ], [ "k", 1.00 ], [ "a", 1.00 ], [ "b", 1.00 ], [ "areal", 1.00 ], [ "angular", 0.44 ], [ "crossing", 90 ] ]

composed from the signature, run for this page

no extension

ArealScaleAt

HOW MUCH BIGGER OR SMALLER THIS PLACE IS DRAWN than it really is. On a Mercator at 70 degrees it is 8.5, which is the whole Greenland argument in one number.

composed example

o1 = new stzGeoProjection(:CylindricalEqualArea)
? o1.ArealScaleAt(2, 5)
#--> 1.00

composed from the signature, run for this page

no extension

AngularDistortionAt

(no comment in the source: the name reads as a sentence) angular distortion at

composed example

o1 = new stzGeoProjection(:CylindricalEqualArea)
? o1.AngularDistortionAt(2, 5)
#--> 0.44

composed from the signature, run for this page

no extension

Distortion

The means are weighted by GROUND -- cos(latitude) per cell -- because an unweighted average over a latitude grid counts the polar rows, which are slivers, as heavily as the equatorial ones, which are not. That flatters exactly the projections that are worst at the poles, which are the ones a reader most needs warning about.

composed example

o1 = new stzGeoProjection(:CylindricalEqualArea)
? @@( o1.Distortion() )
#--> [ [ "arealmin", 1.00 ], [ "arealmax", 1.00 ], [ "arealmean", 1.00 ], [ "angularmax", 170.01 ], [ "angularmean", 30.93 ], [ "sampled", 2592 ] ]

composed from the signature, run for this page

QCSXTZZZIBWU

HoldsItsClaim

DOES THIS PROJECTION KEEP ITS OWN PROMISE, measured rather than declared? An equal-area projection whose areal scale is not 1 everywhere has a wrong formula, and so does a conformal one that bends an angle. It is the check that caught two real defects the day this gallery was written -- a Mollweide half with the wrong normalisation, and a symmetry claim made for a projection that is a triangle.

composed example

o1 = new stzGeoProjection(:CylindricalEqualArea)
? o1.HoldsItsClaim()
#--> 1

composed from the signature, run for this page

no extension

IndicatrixAt

It is built by PROJECTING A SMALL CIRCLE rather than by drawing the ellipse the numbers above describe. The two agree in the limit and the first is the honest one: it shows what the projection actually does to a circle of that size, including the bending an ellipse cannot represent -- which at a radius anybody can see is not nothing.QCSXTZZZIBWU

IsEqualArea

what kind of lie this projection tells

composed example

o1 = new stzGeoProjection(:CylindricalEqualArea)
? o1.IsEqualArea()
#--> 1

composed from the signature, run for this page

no extension

IsConformal

(no comment in the source: the name reads as a sentence) is conformal

composed example

o1 = new stzGeoProjection(:CylindricalEqualArea)
? o1.IsConformal()
#--> 0

composed from the signature, run for this page

no extension

IsAzimuthal

(no comment in the source: the name reads as a sentence) is azimuthal

composed example

o1 = new stzGeoProjection(:CylindricalEqualArea)
? o1.IsAzimuthal()
#--> 0

composed from the signature, run for this page

no extension

IsConic

(no comment in the source: the name reads as a sentence) is conic

composed example

o1 = new stzGeoProjection(:CylindricalEqualArea)
? o1.IsConic()
#--> 0

composed from the signature, run for this page

no extension

Rotate

the parameters ------------------------------------------------------ yaw, pitch, roll in degrees: d3's [lambda, phi, gamma]. To centre a globe on a place at (lon, lat), rotate by [-lon, -lat, 0].QCSXTZZZIBWU

CenterOn

(no comment in the source: the name reads as a sentence) center onQCSXTZZZIBWU

Parallels

(no comment in the source: the name reads as a sentence) parallelsQCSXTZZZIBWU

Scale

(no comment in the source: the name reads as a sentence) scaleQCSXTZZZIBWU

Translate

(no comment in the source: the name reads as a sentence) translateQCSXTZZZIBWU

ClipAngle

(no comment in the source: the name reads as a sentence) clip angleQCSXTZZZIBWU

Precision

(no comment in the source: the name reads as a sentence) precisionQCSXTZZZIBWU

ScaleOf

(no comment in the source: the name reads as a sentence) scale of

composed example

o1 = new stzGeoProjection(:CylindricalEqualArea)
? o1.ScaleOf()
#--> 150

composed from the signature, run for this page

no extension

TranslateOf

(no comment in the source: the name reads as a sentence) translate of

composed example

o1 = new stzGeoProjection(:CylindricalEqualArea)
? @@( o1.TranslateOf() )
#--> [ 480, 250 ]

composed from the signature, run for this page

no extension

RotationOf

(no comment in the source: the name reads as a sentence) rotation of

composed example

o1 = new stzGeoProjection(:CylindricalEqualArea)
? @@( o1.RotationOf() )
#--> [ 0, 0, 0 ]

composed from the signature, run for this page

no extension

FitToSphere

fitting ------------------------------------------------------------- scale and place so the WHOLE sphere fills a w x h box with pad px of air: what a world map asks forQCSXTZZZIBWU

FitSphereIn

the same for a box [x0, y0, x1, y1] on a larger sheetQCSXTZZZIBWU

FitToPoints

scale and place so these points fill the box: what a map of one country asks forQCSXTZZZIBWU

FitFeaturesIn

scale and place so ALL the features fill the box. This is what "draw Tunisia" means, and it is NOT FitToSphere -- which fits the whole globe and leaves a country a speck in the middle of it. The first sheet of the three countries was drawn that way and came out as three clusters of labels over nothing at all.QCSXTZZZIBWU

FitPointsIn

It exists because the first bloc sheet reached for FitToPoints and then Translate, and Translate REPLACES the translation the fit just computed rather than offsetting it -- so the map left the paper. A fit that takes its box is the method that was missing.QCSXTZZZIBWU

FitToFeatures

(no comment in the source: the name reads as a sentence) fit to featuresQCSXTZZZIBWU

FitToFeature

scale and place so ONE feature fills the box: what "zoom to Tunisia" means, and what a caller does before drawing its governoratesQCSXTZZZIBWU

FitFeatureIn

(no comment in the source: the name reads as a sentence) fit feature inQCSXTZZZIBWU

Project

the two questions --------------------------------------------------- where a place goes: [x, y] in pixels, or [] when it is behind the globe or has no image on this projection

composed example

o1 = new stzGeoProjection(:CylindricalEqualArea)
? @@( o1.Project(2, 5) )
#--> [ 485.24, 236.93 ]

composed from the signature, run for this page

no extension

Invert

what place a pixel is: [lon, lat], or [] off the sphereno extension

Line

Each answers PIECES: a list of flat [x1, y1, x2, y2, ...] polylines, one per visible stretch. A line that goes behind a globe or crosses the seam of a flat map comes back in two, cut exactly at the edge.

composed example

o1 = new stzGeoProjection(:CylindricalEqualArea)
? @@( o1.Line([ 2, 3 ]) )
#--> [ [ 485.24, 242.15 ] ]

composed from the signature, run for this page

no extension

Ring

a ring as the LINES it is: pieces, cut where the map cuts themno extension

FilledRing

a ring as the POLYGONS it is (GE0c): the same pieces, rejoined along the map's own edge so each one closes and can be filled. A country across the antimeridian comes back as two polygons that meet the two seams; a continent around the pole comes back as one that runs along the bottom of the map.no extension

Graticule

(no comment in the source: the name reads as a sentence) graticuleno extension

Outline

(no comment in the source: the name reads as a sentence) outlineno extension

Arc

the great circle between two places, as piecesno extension

DrawSphereOn

The sphere's fill, the graticule and the outline: what every map stands on. Colours are the caller's; the shapes are the engine's.no extension

DrawGraticuleOn

(no comment in the source: the name reads as a sentence) draw graticule onno extension

DrawOutlineOn

(no comment in the source: the name reads as a sentence) draw outline onno extension

DrawLineOn

(no comment in the source: the name reads as a sentence) draw line onno extension

DrawRingOn

a ring, FILLED where it came back whole and stroked where the seam or the horizon cut it in two -- a cut piece is not a polygon and filling it would draw a shape the sphere does not have A HARO, FILLED -- every piece of it. Since GE0c a cut ring comes back closed along the map's edge, so there is no longer a case where a region can only be outlined.no extension

FilledPolygon

A POLYGON -- an outer ring and its HOLES (GE1) -- closed on the paper. paRings[1] is the outer edge; every ring after it is a hole, bridged into it so a lake inside a country is not filled in as land.no extension

HolesDropped

how many holes the last FilledPolygon could not give: a hole whose outer ring the map cut cannot carry a bridge, and it is counted

composed example

o1 = new stzGeoProjection(:CylindricalEqualArea)
? o1.HolesDropped()
#--> 0

composed from the signature, run for this page

no extension

DrawRingOutlineOn

...and the same ring as an outline only, uncut and unfilledno extension

DrawFeatureOn

a whole feature, from a boundary file (GE1) ------------------------- every part of it, each with its holes -- the islands DN24b's reader dropped and the lakes it filled inno extension

DrawFeaturesOn

(no comment in the source: the name reads as a sentence) draw features onno extension

DrawTissotOn

fit the paper to everything a file holds TISSOT'S INDICATRIX: circles of one true size all over the sphere, projected. Where they stay round the projection keeps shapes; where they stay the same size it keeps areas; where they do neither it says so. The honest way to show what a projection does, and it needs no atlas at all.no extension

Center

the place at the middle of the paper: what the rotation put there

composed example

o1 = new stzGeoProjection(:CylindricalEqualArea)
? @@( o1.Center() )
#--> [ 0, 0 ]

composed from the signature, run for this page

no extension

Caption

the projection, named on the picture: a map that does not say how it was flattened is asserting what it cannot check

composed example

o1 = new stzGeoProjection(:CylindricalEqualArea)
? o1.Caption()
#--> CylindricalEqualArea

composed from the signature, run for this page

no extension