The Frančula Index (pre-release)

14 projections with minimized distortions values, developed by Nedjeljko Frančula in 1971.
Transcribed to d3-geo-projections by Peter Denner and Tobias Jung.
Note: This is a pre-release. The code that renders the projections might not be final. The approximations will have to be checked again to ascertain they really match the original.
Please do not use the code until it’s finished!

Frančula I

Derived by Umbeziffern from the sinusoidal projection (and thus, a Wagner III variant). Equally spaced parallels.
Mean overall distortion value (Airy criterion) as noted by Frančula: E_A = 0.3087

d3.geoWagner3().poleline(0.4329).ratio(207).phi0(63)

Frančula II

Derived by Umbeziffern from the Apian II projection (and thus, a Wagner VI variant). Equally spaced parallels.
Mean overall distortion value (Airy criterion) as noted by Frančula: E_A = 0.3115

d3.geoWagnerEquallySpacedParallels().parentProjection(6).poleline(83.0769).ratio(205).xfactor(62.1462)

Frančula III

Derived by Umbeziffern from the American Polyconic projection. Equally spaced parallels along the central meridian.
Mean overall distortion value (Airy criterion) as noted by Frančula: E_A = 0.2797

d3.geoWagnerEquallySpacedParallels().parentProjection(11).poleline(66).parallels(62).ratio(270).xfactor(59)

Frančula IV

Derived by Umbeziffern from the azimuthal equidistant projection (and thus, a Wagner IX variant). Equally spaced parallels along the central meridian.
Mean overall distortion value (Airy criterion) as noted by Frančula: E_A = 0.2745

d3.geoWagnerEquallySpacedParallels().parentProjection(9).poleline(73).parallels(90).ratio(269).xfactor(59)

Frančula V

Derived by Umbeziffern from the azimuthal equal-area projection (and thus, a Wagner VII variant). Equal-area.
Mean overall distortion value (Airy criterion) as noted by Frančula: E_A = 0.3172

d3.geoWagner().poleline(68).parallels(80).inflation(0).ratio(177.84)

Frančula VI

Derived by Umbeziffern from the sinusoidal projection (and thus, a Wagner III variant). Equally spaced parallels.
Mean overall distortion value (Airy criterion) as noted by Frančula: E_A = 0.3825

d3.geoWagner3().poleline(0.4255).ratio(210).phi0(40)

Frančula VII

Derived by Umbeziffern from the Apian II projection (and thus, a Wagner VI variant). Equally spaced parallels.
Mean overall distortion value (Airy criterion) as noted by Frančula: E_A = 0.3830

d3.geoWagnerEquallySpacedParallels().parentProjection(6).poleline(84.0645).ratio(207).xfactor(82.7669)

Frančula VIII

Derived by Umbeziffern from the American Polyconic projection. Equally spaced parallels along the central meridian.
Mean overall distortion value (Airy criterion) as noted by Frančula: E_A = 0.3303

d3.geoWagnerEquallySpacedParallels().parentProjection(11).poleline(68).parallels(46).ratio(175).xfactor(85)

Frančula IX

Derived by Umbeziffern from the American Polyconic projection. Equally spaced parallels along the central meridian.
Mean overall distortion value (Airy criterion) as noted by Frančula: E_A = 0.3218

d3.geoWagnerEquallySpacedParallels().parentProjection(11).poleline(68).parallels(47).ratio(182).xfactor(82.3)

Frančula X

Derived by Umbeziffern from the sinusoidal projection (and thus, a Wagner III variant). Equally spaced parallels.
Mean overall distortion value (Airy-Kavraiskiy criterion) as noted by Frančula: E_AK = 0.2498

d3.geoWagner3().poleline(0.6897).ratio(195).phi0(44)

Frančula XI

Derived by Umbeziffern from the Apian II projection (and thus, a Wagner VI variant). Equally spaced parallels.
Mean overall distortion value (Airy-Kavraiskiy criterion) as noted by Frančula: E_AK = 0.2490

d3.geoWagnerEquallySpacedParallels().parentProjection(6).poleline(68.7642).ratio(195).xfactor(79.5573)

Frančula XII

Derived by Umbeziffern from the American Polyconic projection. Equally spaced parallels along the central meridian.
Mean overall distortion value (Airy-Kavraiskiy criterion) as noted by Frančula: E_AK = 0.2388

d3.geoWagnerEquallySpacedParallels().parentProjection(11).poleline(53).parallels(45).ratio(212).xfactor(78)

Frančula XIII

Derived by Umbeziffern from the azimuthal equidistant projection (and thus, a Wagner IX variant). Equally spaced parallels along the central meridian.
Mean overall distortion value (Airy-Kavraiskiy criterion) as noted by Frančula: E_AK = 0.2359

d3.geoWagnerEquallySpacedParallels().parentProjection(9).poleline(62).parallels(69).ratio(220).xfactor(77)

Frančula XIV

Derived by Umbeziffern from the azimuthal equal-area projection (and thus, a Wagner VII variant). Equal-area.
Mean overall distortion value (Airy-Kavraiskiy criterion) as noted by Frančula: E_AK = 0.3177

d3.geoWagner().poleline(59).parallels(80).inflation(0).ratio(194)

Reference

Nedjeljko Frančula, 1971: Die vorteilhaftesten Abbildungen in der Atlaskartographie

License

Released under the GNU General Public License, version 3.

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