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CONIC MAP PROJECTIONS # Cylindrical projections are used primarily for complete world maps, or for maps along narrow strips of a great circle arc, such as the Equator, a meridian, or an oblique great circle.

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Numerical Examples for Eckert VI Projection # SPHERE # Forward Equations # Given Radius of sphere: $R=\;\;$ unit Central meridian: $\lambda_0=\;$° Point: $\phi=\;$° $\lambda=\;$° Find $x, y$.

Numerical Examples for Eckert IV Projection # SPHERE # Forward Equations # Given Radius of sphere: $R=\;\;$ unit Central meridian: $\lambda_0=\;$° Point: $\phi=\;$° $\lambda=\;$° Find $x, y$.

Numerical Examples for Mollweide Projection # SPHERE # Forward Equations # Given Radius of sphere: $R=\;\;$ unit Central meridian: $\lambda_0=\;$° Point: $\phi=\;$° $\lambda=\;$° Find $x, y$.

Numerical Examples for Sinusoidal Projection # SPHERE # Forward Equations # Given Radius of sphere: $R=\;\;$ unit Central meridian: $\lambda_0=\;$° Point: $\phi=\;$° $\lambda=\;$° Find $x, y, h, k, \theta', \omega$.

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References # Abramowitz, Milton, and Stegun, I.A., 1964, Handbook of mathematical functions: Washington, National Bureau of Standards.

Numerical Examples for Van der Grinten Projection # SPHERE # Forward Equations # Given Radius of sphere: $R=\;\;$ unit Central meridian: $\lambda_0=\;$° Point: $\phi=\;$° $\lambda=\;$° Find $x, y$.

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Numerical Examples for Modified Stereographic Conformal Projection # SPHERE # Forward Equations # Given1 Radius of sphere: $R=\;\;$ unit Order of equation: $m=\;\;6$ Center: $\phi_1=\;64.0^\circ$ $\lambda_0=\;-152.0^\circ$ Constants $A_1-A_m$ $B_1-B_m$ See

Numerical Examples for Azimuthal Equidistant Projection # SPHERE # Forward Equations # Given Radius of sphere: $R=\;\;$ unit Center: $\phi_1=\;$° $\lambda_0=\;$° Point: $\phi=\;$° $\lambda=\;$° Find $x, y$ Using equations (5-3) and (25-2), $$ \eqalign{ \c…

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Numerical Examples for Lambert Azimuthal Equal-Area # SPHERE # Forward Equations # Radius of sphere: $R=\;\;$ units Center: $\phi_1=\;$ ° $\lambda_0=\;$ ° Point: $\phi=\;$ ° $\lambda=\;$ ° Find $x, y$ Using equation (24 -2), $$ \eqalign{ k' &= \{2/[1+\sin…

Numerical Examples for Gnomonic Projection # SPHERE # Forward Equations # Radius of sphere: $R=\;\;$ units Center: $\phi_1=\;$ ° $\lambda_0=\;$ ° Point: $\phi=\;$ ° $\lambda=\;$ ° Find $x, y$ Using equation (5-3), $$ \eqalign{ \cos c &= \sin 40^\circ \sin…

Numerical Examples for Stereographic Projection # SPHERE # Forward Equations # Given Radius of sphere: $R=\;\;$ units Center: $\phi_1=\;$ ° $\lambda_0=\;$ ° Central scale factor: $k_0=\;$ Point: $\phi=\;$ ° $\lambda=\;$ ° Find $x, y, k$ Using equations (2…

Numerical Examples for Orthographic Projection # SPHERE # Forward Equations # Given Radius of sphere: $R=\;\;$ units Center: $\phi_1=\;$ ° $\lambda_0=\;$ ° Point: $\phi=\;$ ° $\lambda=\;$ ° Find $x, y$ In general calculations, to determine whether this po…

Numerical Examples for Bonne Projection # SPHERE # Forward Equations # Given Radius of sphere: $R=\;\;$ units Standard parallel: $\phi_1=\;$ ° Central meridian: $\lambda_0=\;$ ° Point: $\phi=\;$ ° $\lambda=\;$ ° Find $x, y$ Using equations (19-1) through…

Numerical Examples for Polyconic Projection # SPHERE # Forward Equations # Given Radius of sphere: $R=\;\;$ units Origin: $\phi_0=\;$ ° $\lambda_0=\;$ ° Point: $\phi=\;$ ° $\lambda=\;$ ° Find $x, y, h$ From equations (18-2) through (18-4), $$ \eqalign{ E…

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Numerical Examples for Bipolar Oblique Conic Conformal Projection # SPHERE # Forward Equations # This example will illustrate equations (17-14) through (17-23), assuming prior calculation of the constants from equations (17-1) through (17-13).

Numerical Examples for Equidistant Conic Projection # SPHERE # Forward Equations # Given Radius of sphere: $R=\;\;$ unit Standard parallels: $\phi_1=\;$° $\phi_2=\;$° Origin: $\phi_0=\;$° $\lambda_0=\;$° Point: $\phi=\;$° $\lambda=\;$° Find $\rho, \theta,…

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Numerical Examples for Lambert Conformal Conical Projection # SPHERE # Forward Equations # Given Radius of sphere: $R=\;\;$ unit Standard parallels: $\phi_1=\;$° $\phi_2=\;$° Origin: $\phi_0=\;$° $\lambda_0=\;$° Point: $\phi=\;$° $\lambda=\;$° Find $\rho,…

Numerical Examples for Cassini Projection # SPHERE # Forward Equations # Given Radius of sphere: $R=\;\;$ unit Origin: $\phi_0=\;$° $\lambda_0=\;$° Point: $\phi=\;$° $\lambda=\;$° Find $x, y$ Using equations (8-5), and (13-1) through (13-3) in order, $$ \…

Numerical Examples for Miller Cylindrical Projection # SPHERE # Forward Equations # Given Radius of sphere: $R=\;\;$ unit Central meridian: $\lambda_0=\;$° Point: $\phi=\;$° $\lambda=\;$° Find $x, y, h, k$ Using equations (11-1) through (11-5) in order $$…

How to calculate Fourier coefficients for Oblique Cylindrical Equal-Area projection.

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Numerical Examples for Cylindrical Equal-Area Projection # SPHERE # Normal aspect # Forward Equations # Given Radius of sphere: $R=\;\;$ unit Central meridian: $\lambda_0=\;$° Standard parallel: $\phi_s=\;$° Point: $\phi=\;$° $\lambda=\;$° Find $x, y$ Usi…

Symbols # If a symbol is not listed here, it is used only briefly and identified near the formulas in which it is given.

Editorial Notes # Transformation of Map Graticules # Note 1: Snyder text refers to $\phi_1$ although the figure (Figure 5) shows $\phi_0$↩︎ Auxiliary latitudes # Note 1: Snyder shows value $39.762435^\circ$.↩︎ Oblique Mercator # Note 1: Snyder repeats sph…

Numerical Examples for Oblique Mercator Projection # SPHERE # Forward Equations # Given Radius of sphere: $R=\;\;$ unit Central scale factor: $k_0=\;$° Central line through: $\phi_1=\;$° $\lambda_1=\;$° $\phi_2=\;$° $\lambda_2=\;$° Point: $\phi=\;$° $\lam…

Numerical Examples for Albers Equal-Area Conic Projection # SPHERE # Forward Equations # Given Radius of sphere: $R=\;\;$ unit Standard parallels: $\phi_1=\;$° $\phi_2=\;$° Origin: $\phi_0=\;$° $\lambda_0=\;$° Point: $\phi=\;$° $\lambda=\;$° Find $\rho, \…

Numerical Examples for Transverse Mercator Projection # SPHERE # Forward Equations # Given Radius of sphere: $R=\;\;$ unit Origin: $\phi_0=\;$° $\lambda_0=\;$° Central scale factor: $k_0=\;$ Point: $\phi=\;$° $\lambda=\;$° Find $x, y, k$ Using equations (…

Numerical Examples for Mercator Projection # SPHERE # Forward Equations # Given Radius of sphere: $R=\;\;$ unit Central meridian: $\lambda_0=\;$° Point: $\phi=\;$° $\lambda=\;$° Find $x, y, k$ Using equations (7-1) , (7-2), and (7-3), $$ \eqalign { x &= \…

Numerical Examples for Auxiliary Latitudes # For all examples under this heading, the Clarke 1866 WGS-84 ellipsoid will be used.