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I underestimated the pointiness of triangles

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As it turns out, they are quite pointy. And creating an authagraphic
tetrahedral projection that has to shove landmasses into the pointy
corners doesn't work very well. Oh, well. I did some fun calculus to
make it work. I don't know how AuthaGraph does it. Probably by not being
authagraphic and lying to its followers. I'll probably make something
interrupted now.
This commit is contained in:
Justin Kunimune 2017-11-21 19:23:11 -05:00
parent 223342cd16
commit 0082af3ff5
7 changed files with 67 additions and 86 deletions
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output/graph - plotter.png
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6
src/apps/MapAnalyzer.java
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@ -97,9 +97,9 @@ public class MapAnalyzer extends MapApplication {
Cylindrical.BEHRMANN, Cylindrical.LAMBERT, Cylindrical.EQUAL_AREA, Cylindrical.GALL,
Azimuthal.STEREOGRAPHIC, Azimuthal.POLAR, Azimuthal.EQUAL_AREA, Azimuthal.GNOMONIC,
Azimuthal.ORTHOGRAPHIC, Azimuthal.PERSPECTIVE, Conic.LAMBERT, Conic.EQUIDISTANT,
Conic.ALBERS, Tetrahedral.LEE, Tetrahedral.TETRAGRAPH, Pseudocylindrical.SINUSOIDAL,
Pseudocylindrical.MOLLWEIDE, Tobler.TOBLER, Misc.HAMMER, Misc.AITOFF,
Misc.VAN_DER_GRINTEN, Robinson.ROBINSON, WinkelTripel.WINKEL_TRIPEL,
Conic.ALBERS, Tetrahedral.LEE, Tetrahedral.TETRAGRAPH, Tetrahedral.ACTAAUTHAGRAPH,
Pseudocylindrical.SINUSOIDAL, Pseudocylindrical.MOLLWEIDE, Tobler.TOBLER, Misc.HAMMER,
Misc.AITOFF, Misc.VAN_DER_GRINTEN, Robinson.ROBINSON, WinkelTripel.WINKEL_TRIPEL,
Misc.PEIRCE_QUINCUNCIAL, Misc.TWO_POINT_EQUIDISTANT, Misc.HAMMER_RETROAZIMUTHAL,
Pseudocylindrical.LEMONS, MyProjections.EXPERIMENT, MyProjections.PSEUDOSTEREOGRAPHIC,
MyProjections.HYPERELLIPOWER, Tetrahedral.TETRAPOWER, Tetrahedral.TETRAFILLET,

2
src/apps/MapDesignerRaster.java
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@ -87,7 +87,7 @@ public class MapDesignerRaster extends MapApplication {
Cylindrical.EQUIRECTANGULAR, Cylindrical.EQUAL_AREA, Cylindrical.GALL,
Azimuthal.STEREOGRAPHIC, Azimuthal.POLAR, Azimuthal.EQUAL_AREA, Azimuthal.GNOMONIC,
Azimuthal.PERSPECTIVE, Conic.LAMBERT, Conic.EQUIDISTANT, Conic.ALBERS, Tetrahedral.LEE,
Tetrahedral.TETRAGRAPH, Tetrahedral.AUTHAGRAPH, Pseudocylindrical.SINUSOIDAL,
Tetrahedral.TETRAGRAPH, Tetrahedral.ACTAAUTHAGRAPH, Pseudocylindrical.SINUSOIDAL,
Pseudocylindrical.MOLLWEIDE, Tobler.TOBLER, Misc.AITOFF, Misc.VAN_DER_GRINTEN,
Robinson.ROBINSON, WinkelTripel.WINKEL_TRIPEL, Misc.PEIRCE_QUINCUNCIAL,
Misc.TWO_POINT_EQUIDISTANT, Misc.HAMMER_RETROAZIMUTHAL, Pseudocylindrical.LEMONS,

13
src/apps/MapDesignerVector.java
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@ -82,12 +82,13 @@ public class MapDesignerVector extends MapApplication {
Cylindrical.EQUIRECTANGULAR, Cylindrical.EQUAL_AREA, Cylindrical.GALL,
Azimuthal.STEREOGRAPHIC, Azimuthal.POLAR, Azimuthal.EQUAL_AREA, Azimuthal.GNOMONIC,
Azimuthal.PERSPECTIVE, Conic.LAMBERT, Conic.EQUIDISTANT, Conic.ALBERS, Tetrahedral.LEE,
Tetrahedral.TETRAGRAPH, Pseudocylindrical.SINUSOIDAL, Pseudocylindrical.MOLLWEIDE,
Tobler.TOBLER, Misc.AITOFF, Misc.VAN_DER_GRINTEN, Robinson.ROBINSON,
WinkelTripel.WINKEL_TRIPEL, Misc.PEIRCE_QUINCUNCIAL, Misc.TWO_POINT_EQUIDISTANT,
Misc.HAMMER_RETROAZIMUTHAL, Pseudocylindrical.LEMONS, MyProjections.EXPERIMENT,
MyProjections.PSEUDOSTEREOGRAPHIC, MyProjections.HYPERELLIPOWER, Tetrahedral.TETRAPOWER,
Tetrahedral.TETRAFILLET, MyProjections.TWO_POINT_EQUALIZED };
Tetrahedral.TETRAGRAPH, Tetrahedral.ACTAAUTHAGRAPH, Pseudocylindrical.SINUSOIDAL,
Pseudocylindrical.MOLLWEIDE, Tobler.TOBLER, Misc.AITOFF, Misc.VAN_DER_GRINTEN,
Robinson.ROBINSON, WinkelTripel.WINKEL_TRIPEL, Misc.PEIRCE_QUINCUNCIAL,
Misc.TWO_POINT_EQUIDISTANT, Misc.HAMMER_RETROAZIMUTHAL, Pseudocylindrical.LEMONS,
MyProjections.EXPERIMENT, MyProjections.PSEUDOSTEREOGRAPHIC,
MyProjections.HYPERELLIPOWER, Tetrahedral.TETRAPOWER, Tetrahedral.TETRAFILLET,
MyProjections.TWO_POINT_EQUALIZED };
private static final int DEF_MAX_VTX = 5000;
private static final int FAST_MAX_VTX = 2000;

2
src/apps/MapExplainer.java
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@ -61,7 +61,7 @@ public class MapExplainer {
Azimuthal.POLAR.transverse(), Azimuthal.EQUAL_AREA.transverse(),
Azimuthal.GNOMONIC.transverse(), Azimuthal.ORTHOGRAPHIC.transverse(),
Conic.LAMBERT, Conic.EQUIDISTANT, Conic.ALBERS, Tetrahedral.LEE,
Tetrahedral.TETRAGRAPH, Tetrahedral.AUTHAGRAPH, Pseudocylindrical.SINUSOIDAL,
Tetrahedral.TETRAGRAPH, Tetrahedral.ACTAAUTHAGRAPH, Pseudocylindrical.SINUSOIDAL,
Pseudocylindrical.MOLLWEIDE, Tobler.TOBLER, Misc.HAMMER, Misc.AITOFF,
Misc.VAN_DER_GRINTEN, Robinson.ROBINSON, WinkelTripel.WINKEL_TRIPEL,
Misc.PEIRCE_QUINCUNCIAL.transverse(), Misc.TWO_POINT_EQUIDISTANT,

45
src/apps/MapPlotter.java
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@ -51,6 +51,7 @@ import maps.Cylindrical;
import maps.Misc;
import maps.MyProjections;
import maps.Projection;
import maps.Pseudocylindrical;
import maps.Robinson;
import maps.Tetrahedral;
import maps.Tobler;
@ -65,15 +66,28 @@ public class MapPlotter extends Application {
private static final double GLOBE_RES = .002;
private static final Projection[] COMMON = { Azimuthal.STEREOGRAPHIC, Cylindrical.MERCATOR,
Azimuthal.POLAR, Cylindrical.PLATE_CARREE, Azimuthal.EQUAL_AREA,
Cylindrical.GALL_PETERS, Cylindrical.GALL, Misc.VAN_DER_GRINTEN, Robinson.ROBINSON,
WinkelTripel.WINKEL_TRIPEL, Azimuthal.ORTHOGRAPHIC };
private static final Projection[] UNCOMMON = { Misc.PEIRCE_QUINCUNCIAL, Tetrahedral.LEE,
Tobler.TOBLER, Cylindrical.BEHRMANN, Misc.AITOFF };
private static final Projection[] INVENTED = { MyProjections.PSEUDOSTEREOGRAPHIC,
MyProjections.HYPERELLIPOWER, Tetrahedral.TETRAPOWER, Tetrahedral.TETRAFILLET,
MyProjections.TWO_POINT_EQUALIZED };
private static final Projection[] CYLINDRICAL = { Cylindrical.MERCATOR,
Cylindrical.PLATE_CARREE, Cylindrical.BEHRMANN, Cylindrical.GALL };
private static final Projection[] AZIMUTHAL = { Azimuthal.STEREOGRAPHIC, Azimuthal.POLAR,
Azimuthal.EQUAL_AREA };
private static final Projection[] PSEUDOCYL = { Pseudocylindrical.MOLLWEIDE,
Robinson.ROBINSON, Tobler.TOBLER, MyProjections.HYPERELLIPOWER };
private static final Projection[] PSEUDOAZM = { Misc.AITOFF,
MyProjections.PSEUDOSTEREOGRAPHIC };
private static final Projection[] TETRAHEDRAL = { Tetrahedral.LEE, Tetrahedral.TETRAGRAPH,
Tetrahedral.ACTAAUTHAGRAPH, Tetrahedral.TETRAPOWER };
private static final Projection[] OTHER = { Misc.VAN_DER_GRINTEN, WinkelTripel.WINKEL_TRIPEL,
Misc.PEIRCE_QUINCUNCIAL };
// private static final Projection[] COMMON = { Azimuthal.STEREOGRAPHIC, Cylindrical.MERCATOR,
// Azimuthal.POLAR, Cylindrical.PLATE_CARREE, Azimuthal.EQUAL_AREA,
// Cylindrical.GALL_PETERS, Cylindrical.GALL, Misc.VAN_DER_GRINTEN, Robinson.ROBINSON,
// WinkelTripel.WINKEL_TRIPEL, Azimuthal.ORTHOGRAPHIC };
// private static final Projection[] UNCOMMON = { Misc.PEIRCE_QUINCUNCIAL, Tetrahedral.LEE,
// Tobler.TOBLER, Cylindrical.BEHRMANN, Misc.AITOFF };
// private static final Projection[] INVENTED = { MyProjections.PSEUDOSTEREOGRAPHIC,
// MyProjections.HYPERELLIPOWER, Tetrahedral.ACTAAUTHAGRAPH, Tetrahedral.TETRAPOWER,
// Tetrahedral.TETRAFILLET, MyProjections.TWO_POINT_EQUALIZED };
private StackPane stack;
@ -98,9 +112,16 @@ public class MapPlotter extends Application {
final List<Data<Number,Number>> data = new LinkedList<Data<Number,Number>>();
final double[][][] points = Projection.globe(GLOBE_RES);
plotProjections(plot, overlay, labels, data, COMMON, "Common", points);
plotProjections(plot, overlay, labels, data, UNCOMMON, "Hipster", points);
plotProjections(plot, overlay, labels, data, INVENTED, "Mine", points);
plotProjections(plot, overlay, labels, data, CYLINDRICAL, "Cylindrical", points);
plotProjections(plot, overlay, labels, data, AZIMUTHAL, "Azimuthal", points);
plotProjections(plot, overlay, labels, data, PSEUDOCYL, "Pseudocylindrical", points);
plotProjections(plot, overlay, labels, data, PSEUDOAZM, "Pseudoazimuthal", points);
plotProjections(plot, overlay, labels, data, TETRAHEDRAL, "Tetrahedral", points);
plotProjections(plot, overlay, labels, data, OTHER, "Other", points);
// plotProjections(plot, overlay, labels, data, COMMON, "Common", points);
// plotProjections(plot, overlay, labels, data, UNCOMMON, "Hipster", points);
// plotProjections(plot, overlay, labels, data, INVENTED, "Mine", points);
final ChangeListener<Number> listener = new ChangeListener<Number>() {
final Timer timer = new Timer();

85
src/maps/Tetrahedral.java
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@ -76,6 +76,28 @@ public class Tetrahedral {
};
public static final Projection ACTAAUTHAGRAPH =
new TetrahedralProjection(
"Equahedral", 0b1011, Property.EQUAL_AREA, null, "to put AuthaGraph to shame.") {
public double[] innerProject(double lat, double lon) {
final double Lam = Math.floor(lon/(2*Math.PI/3))*(2*Math.PI/3) + Math.PI/3;
final double lam = lon - Lam;
final double tht = Math.atan((lam - Math.asin(Math.sin(lam)/Math.sqrt(3)))/Math.PI*Math.sqrt(108));
return new double[] {
Math.sqrt((1 - Math.sin(lat))/(1 - 1/Math.sqrt(1+2/Math.cos(lam))))/Math.cos(tht),
// (Math.PI/2-lat)/Math.atan(Math.sqrt(2)/Math.cos(lam))/Math.cos(tht),
Lam + tht };
}
public double[] innerInverse(double x, double y) {
// TODO: Implement this
return null;
}
};
public static final Projection TETRAPOWER =
new TetrahedralProjection(
"TetraPower", "A parameterised tetrahedral projection that I invented.",
@ -204,69 +226,6 @@ public class Tetrahedral {
};
public static final Projection AUTHAGRAPH =
new TetrahedralProjection("AuthaGraph",
"A hip new Japanese map that is almost authagraphic (this is an approximation; they won't give me their actual equations).",
0b1001, Property.COMPROMISE) {
public double[] project(double lat, double lon) {
return null; //TODO Can I live with myself if I never implement this?
}
public double[] innerProject(double lat, double lon) {
return null;
}
public double[] inverse(double x, double y) {
final double[] faceCenter;
final double dt, xp, yp;
if (y-1 < 4*x && y-1 < -4*x) {
faceCenter = new double[] { Math.PI/2-Math.asin(Math.sqrt(8)/3), 0, 0};
dt = 0;
xp = 4/Math.sqrt(3)*x;
yp = y+1/3.0;
}
else if (y-1 < -4*(x+1)) {
faceCenter = new double[] { -Math.PI/2, Math.PI, 0 };
dt = 0;
xp = 4/Math.sqrt(3)*(x+1);
yp = y+1/3.0;
}
else if (y-1 < 4*(x-1)) {
faceCenter = new double[] { -Math.PI/2, Math.PI, 0 };
dt = 0;
xp = 4/Math.sqrt(3)*(x-1);
yp = y+1/3.0;
}
else if (x < 0) {
faceCenter = new double[] { Math.PI/2-Math.asin(Math.sqrt(8)/3), 4*Math.PI/3, 0 };
dt = Math.PI/3;
xp = 4/Math.sqrt(3)*(x+0.5);
yp = y-1/3.0;
}
else {
faceCenter = new double[] { Math.PI/2-Math.asin(Math.sqrt(8)/3), 2*Math.PI/3, 0 };
dt = -Math.PI/3;
xp = 4/Math.sqrt(3)*(x-0.5);
yp = y-1/3.0;
}
return obliquifyPlnr(
innerInverse(Math.hypot(xp, yp), Math.atan2(yp, xp)+dt), faceCenter);
}
protected double[] innerInverse(double r, double tht) {
final double t0 = Math.floor((tht+Math.PI/2)/(2*Math.PI/3)+0.5)*(2*Math.PI/3) - Math.PI/2;
final double dt = tht-t0;
final double z = 2.49*r*Math.cos(dt);
final double g = 0.03575*z*z*z + 0.0219*z*z + 0.4441*z;
return new double[] {
Math.PI/2 - Math.atan(Math.tan(g)/Math.cos(dt)),
Math.PI/2 + t0 + dt };
}
};
/**
* A base for tetrahedral projections