The 3D Printer Revival Project
Bringing back to life an old 3D printer
Introduction on Eu, Mircea
Recent content in Introduction on Eu, Mircea
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A Neat Debugging Trick
Debugging Raspberry Pi Pico interrupts
EEPROM Programming with Raspberry Pi
A step by step guide to programming 24Cxx EEPROMs using a Raspberry Pi
Adding `traffic-advice` File to Apache2 Server
How to add a global traffic advice file to Apache2 web server
Maru' lu' Catalin
Măru’ lu’ Cătălin # Cel mai bun timp sa plantezi un copac este acum 20 de ani. Al doilea cel mai bun timp este acum. (Anonim) Acum aproape 30 de ani, fostul nostru coleg de liceu Cătălin Stoichița, a venit în vizită la Montreal și a sunat la ușă cu un mic băț cu trei ramuri în vârf. Mi-a zis: “M-am gândit ce să-ți aduc și mi-am zis că cel mai bine ar fi să-ți aduc un măr. O…
Conic Map Projections
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. To show a region for which the greatest extent is from east to west in the temperate zones, conic projections are usually preferable to cylindrical projections. Normal conic projections are…
The Dan Numbers
Programming a solution to a math puzzle
NVIDIA Quatro RTX 4000 Support Passthrough on Windows 11 Pro Hyper-V
A friend found this solution
GoAccess - Apache2 Log Analyzer
Use GoAccess to generate web server log reports
A Small, Inconsequential, Mystery
Questions the choice of initial value for inverse authalic latitude function
Learning on the Job: Using D3.js
I’m trying to learn D3.js
Working With Angles in C++
How to represent angles in C++.
Numerical Examples - Eckert VI Projection
Numerical Examples for Eckert VI Projection # SPHERE # Forward Equations # Given Radius of sphere: $R=\;\;$ unit Central meridian: $\lambda_0=\;$ ° Point: $\phi=\;$ ° $\lambda=\;$ ° Find $x, y$. From equation (32-8) , using $\phi$ or or $ -50^\circ $ as the first trial $\theta$ $$ \eqalign{ \Delta\theta =& -[(-50^\circ)\times\pi/180^\circ+\sin(-50^\circ)-(1+\pi/2)\sin(-50^\circ)]/ \cr…
Numerical Examples - Eckert IV Projection
Numerical Examples for Eckert IV Projection # SPHERE # Forward Equations # Given Radius of sphere: $R=\;\;$ unit Central meridian: $\lambda_0=\;$ ° Point: $\phi=\;$ ° $\lambda=\;$ ° Find $x, y$. From equation (32-4) , using $(\phi/2)$ or $ -25^\circ $ as the first trial $\theta$ $$ \eqalign{ \Delta\theta =&…
Numerical Examples - Mollweide Projection
Numerical Examples for Mollweide Projection # SPHERE # Forward Equations # Given Radius of sphere: $R=\;\;$ unit Central meridian: $\lambda_0=\;$ ° Point: $\phi=\;$ ° $\lambda=\;$ ° Find $x, y$. From equation (31-4) , using $\phi$ or $ -50^\circ $ as the first trial $\theta’$, $$ \eqalign{ \Delta\theta' =& -[(-50^\circ)+\sin(-50^\circ)-\pi\sin(-50^\circ)]/ \cr &…
Multithreading with SQLite
Examines the performance of SQLite in multithreading applications
Numerical Examples - Sinusoidal Projection
Numerical Examples for Sinusoidal Projection # SPHERE # Forward Equations # Given Radius of sphere: $R=\;\;$ unit Central meridian: $\lambda_0=\;$ ° Point: $\phi=\;$ ° $\lambda=\;$ ° Find $x, y, h, k, \theta', \omega$. From equations (30-1) through (30-5) in order, $$ \eqalign{ x &= 1.0\times[-75^\circ-(-90^\circ)]\cos(-50^\circ) \cr &= 0.1682814\text{ units} } $$ $$ \eqalign{ y &=…
References
References # Abramowitz, Milton, and Stegun, I.A., 1964, Handbook of mathematical functions : Washington, National Bureau of Standards. (Reprinted by Dover publications, Inc., New York, 1972). Adams, O.S., 1918, Lambert projection tables for the United States : U.S. Coast and Geodetic Survey Spec. Pub. 52. Adams, O.S., 1919, General theory of Polyconic projections : U.S. Coast and Geodetic Survey…
Numerical Examples - Van der Grinten Projection
Numerical Examples for Van der Grinten Projection # SPHERE # Forward Equations # Given Radius of sphere: $R=\;\;$ unit Central meridian: $\lambda_0=\;$ ° Point: $\phi=\;$ ° $\lambda=\;$ ° Find $x, y$. From equations (29-6) , (29-3) , (29-4) , (29-5) , and (29-6a) in order, $$ \eqalign{ \theta &= \arcsin |2\times(-50^\circ)/180^\circ| \cr &= 33.7489886^\circ } $$ $$ \eqalign{ A &=…
Numerical Examples - Modified Stereographic Conformal Projection
Numerical Examples for Modified Stereographic Conformal Projection # SPHERE # Forward Equations # Given 1 Radius of sphere: $R=\;\;$ unit Order of equation: $m=\;\;6$ Center: $\phi_1=\;64.0^\circ$ $\lambda_0=\;-152.0^\circ$ Constants $A_1-A_m$ $B_1-B_m$ See Table 33 , using constants for sphere. Point: $\phi=\;$ ° $\lambda=\;$ ° Find $x, y, k$ Using equations (26-1) through (26-3) in…
Knuth Algorithm for Polynomial Evaluation
Discussing the algorithm used by Snyder for Modified Stereographic Conformal projection
Numerical Examples - Azimuthal Equidistant Projection
Numerical Examples for Azimuthal Equidistant Projection # SPHERE # Forward Equations # Given Radius of sphere: $R=\;\;$ unit Center: $\phi_1=\;$ ° $\lambda_0=\;$ ° Point: $\phi=\;$ ° $\lambda=\;$ ° Find $x, y$ Using equations (5-3) and (25-2) , $$ \eqalign{ \cos c &= \sin40^\circ\sin(-20^\circ) + \cos 40^\circ\cos(-20^\circ)\cos (100^\circ - (-100^\circ))\cr &= -0.8962806 } $$ $$ c…
Build and Install PROJ on a new Ubuntu 22.04 LTS system
Step-by-step instructions to build and install PROJ - the coordinate transformation software.
Numerical Examples - Lambert Azimuthal Equal-Area
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) , $$ \eqalign{ k' &= \{2/[1+\sin40^\circ\sin(-20^\circ)+\cos40^\circ\cos(-20^\circ)\cos(100^\circ-(-100^\circ))] \}^{1/2} \cr &= 4.3912175 } $$ Using equations…
Numerical Examples - Gnomonic Projection
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) , $$ \eqalign{ \cos c &= \sin 40^\circ \sin 30^\circ + \cos 40^\circ \cos 30^\circ \cos [-110^\circ-(-100^\circ)] \cr &= 0.9747290 } $$ Since $\cos c$ is zero or negative,…
Numerical Examples - Stereographic Projection
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 (21-4) , (21-2) , and (21-3) in order, $$ \eqalign { k &= 2\times…
Numerical Examples - Bonne Projection
Numerical Examples for Bonne Projection # SPHERE # Forward Equations # Given Radius of sphere: $R=\;\;$ units Standard parallel: $\phi_1=\;$ ° Central meridian: $\lambda_0=\;$ ° Point: $\phi=\;$ ° $\lambda=\;$ ° Find $x, y$ Using equations (19-1) through (19-4) in order, $$ \eqalign{ \rho &= 1.0\times[\cot 40^\circ +(40^\circ - 30^\circ)\times \pi/180^\circ] \cr &=…
Numerical Examples - Orthographic Projection
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 point is beyond viewing, using equation (5-3) , $$ \eqalign{ \cos c &= \sin 40^\circ\sin30^\circ+\cos 40^\circ\cos…
Numerical Examples - Polyconic Projection
Numerical Examples for Polyconic Projection # SPHERE # Forward Equations # Given Radius of sphere: $R=\;\;$ units Origin: $\phi_0=\;$ ° $\lambda_0=\;$ ° Point: $\phi=\;$ ° $\lambda=\;$ ° Find $x, y, h$ From equations (18-2) through (18-4) , $$ \eqalign{ E &= (-75^\circ - (-96^\circ))\sin 40^\circ \cr &= 13.4985398^\circ } $$ From equations (7-1) and (18-2) , $$ \eqalign{ x &=…
Code Layout and Management - Q&A
Questions and answers about code layout and dependencies management
Allow Users to Create Symbolic Links in Windows
How to allow regular users to create symbolic links in Windows
23. General Perspective projection
23. GENERAL PERSPECTIVE PROJECTION # SUMMARY # Often used to show the Earth or other planets and satellites as seen from space. Orthographic, Stereographic, and Gnomonic projections are special forms of the Vertical Perspective. Vertical Perspective projections are azimuthal; Tilted Perspectives are not. Central meridian and a particular parallel (if shown) are straight lines. Other meridians and…
22. Gnomonic projection
22. GNOMONIC PROJECTION # SUMMARY # Azimuthal and perspective. All meridians and the Equator are straight lines. All parallels except the Equator and poles are ellipses, parabolas, or hyperbolas. Neither conformal nor equal-area. All great circles are shown as straight lines. Less than one hemisphere may be shown around a given center. No distortion at the center only. Distortion and scale rapidly…
Numerical Examples - Bipolar Oblique Conic Conformal Projection
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) . Given Radius of sphere: $R=\;\;$ m Point: $\phi=\;$ ° $\lambda=\;$ ° Find $x, y, k$ $$ $$ From equations (17-14) and (17-15) $$ \eqalign{ z_B &=…
The Third Cultural Revolution
The economics of knowledge distribution.
Numerical Examples - Equidistant Conic Projection
Numerical Examples for Equidistant Conic Projection # SPHERE # Forward Equations # Given Radius of sphere: $R=\;\;$ unit Standard parallels: $\phi_1=\;$ ° $\phi_2=\;$ ° Origin: $\phi_0=\;$ ° $\lambda_0=\;$ ° Point: $\phi=\;$ ° $\lambda=\;$ ° Find $\rho, \theta, x, y, k$ From equations (16-4) , (16-3) , (16-2) , (16-1) , and (14-4) in order $$ \eqalign{ n &=…
Allow Users to Change Time in Windows 10 and Windows 11
Programs can change system time without messing with UAC
Numerical Examples - Lambert Conformal Conical Projection
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 $\rho, \theta, x, y, k$ From equations (15-3) , (15-2) , and (15-1a) in order $$ \eqalign{ n &=…
Numerical Examples - Cassini Projection
Numerical Examples for Cassini Projection # SPHERE # Forward Equations # Given Radius of sphere: $R=\;\;$ unit Origin: $\phi_0=\;$ ° $\lambda_0=\;$ ° Point: $\phi=\;$ ° $\lambda=\;$ ° Find $x, y$ Using equations (8-5) , and (13-1) through (13-3) in order, $$ \eqalign{ B &= \cos25^\circ\sin[(-90^\circ)-(-75^\circ)] \cr &= -0.2345697 } $$ $$ \eqalign{ x &= 1.0\times…
Numerical Examples - Miller Cylindrical Projection
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 $$ \DeclareMathOperator{\arcsinh}{arcsinh} $$ $$ \eqalign{ x &= 1.0\times[-75^\circ-0^\circ]\times\pi/180^\circ \cr &=…
Cylindrical Equal-Area Projection
How to calculate Fourier coefficients for Oblique Cylindrical Equal-Area projection.
Uniform C Code Layout
A C/C++ code layout proposal similar to “pitchfork layout” that uses symbolic links to integrate multiple projects.
Symbols and Acronyms
Symbols # If a symbol is not listed here, it is used only briefly and identified near the formulas in which it is given. Symbol Description $Az$ azimuth, as an angle measured clockwise from the north. $a$ equatorial radius or semimajor axis of the ellipsoid of reference. $b$ polar radius or semiminor axis of the ellipsoid of reference. $ b = a(1 - f) = a(1 - e^2)^{1/2}$ $c$ great circle distance,…
Numerical Examples - Cylindrical Equal-Area Projection
Numerical Examples for Cylindrical Equal-Area Projection # SPHERE # Normal aspect # Forward Equations # Given Radius of sphere: $R=\;\;$ unit Central meridian: $\lambda_0=\;$ ° Standard parallel: $\phi_s=\;$ ° Point: $\phi=\;$ ° $\lambda=\;$ ° Find $x, y$ Using equations (10-1) and (10-2) , $$ x = 1\times[80^\circ-(-75^\circ)]\times\cos 30^\circ = 2.3428242\;\text{units} $$ $$ y =…
Notes
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 sphere radius and central scale factor, although they are not needed for these formulas. Also, seems latitude of central point is arbitrarily…
Numerical Examples - Oblique Mercator Projection
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: $\phi=\;$ ° $\lambda=\;$ ° Find $x, y, k$ Using equation (9-1) , $$ \begin{align} \lambda_p =&…
Numerical Examples - Albers Equal-Area Conic Projection
Numerical Examples for Albers Equal-Area Conic Projection # SPHERE # Forward Equations # Given Radius of sphere: $R=\;\;$ unit Standard parallels: $\phi_1=\;$ ° $\phi_2=\;$ ° Origin: $\phi_0=\;$ ° $\lambda_0=\;$ ° Point: $\phi=\;$ ° $\lambda=\;$ ° Find $\rho, \theta, x, y, k, h, \omega$ From equations (14-6) , (14-5) , (14-3) , (14-3a) , and (14-4) in order $$ \eqalign { n…
Numerical Examples - Transverse Mercator Projection
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 (8-5) , (8-1) , (8-3) , and (8-4) in order $$ \eqalign { B &= \cos 40.5^\circ \sin[(-73.5^\circ)-(-75.0^\circ)] \cr &= \cos…
Auxiliary Latitudes
Numerical Examples for Auxiliary Latitudes # For all examples under this heading, the Clarke 1866 WGS-84 ellipsoid will be used. $a=6378206.4\,\text{m}$ a is not needed here $e^2=0.00676866$ or: $e=0.0822719$ Auxiliary latitudes will be calculated for geodetic latitude $\phi =$ ° Conformal latitude # Using closed equation (3-1) : $$ \eqalign{ \chi =& 2\arctan\{\tan{(45^\circ +…
Numerical Examples - Mercator Projection
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) , $$ \eqalign { x &= \pi\times1.0\times[(-75.0^\circ) - (-180.0^\circ)]/180^\circ \cr &= 1.8325957\;\text{units} } $$ $$ \eqalign { y &=…