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How to inverse Y axis

How to inverse Y axis


I have a SQLlite database containing cached tiles with X,Y,Z fields and I want to use it in MapCache. My Y field is appearing upside down in Google tile index but I want to inverse it like this:

http://www.maptiler.org/google-maps-coordinates-tile-bounds-projection/

I'm searching for a way to use my databse in Mapcache or inverse Y field in database to adapt tile indexes with mapcache tile index.


I solve my problem with editing database and inverse Y field :

  1. create 2 copy of original table(contain personal data).
  2. sort 1st copy of table with Z,X,Y ACE and add a newID.
  3. sort 2nd copy of table with Z,X ACE and Y DESC and add a newID.
  4. update Y filed of 1st table with Y of 2nd table where newID=newID.

now i have a table (1st copy) same as original table with inversed Y value.

  1. finally delete rows of Table created by mapcache and update that with my data.

Note : this database works with mapcache with correct position of tiles but tils load slowly and zooming does not work properly(Zooms on area with distance of clicked area). I use mapcache demo as client.


4 Answers 4

I think I found the answer to this. 1. Select Chart Editor 2. Select Vertical axis Should be an option there for Reverse axis order

This may not be a direct help since i think you also need an offset, not just a reversal, but for people who just need to reverse the whole axis, this may work

It's a ridiculous workaround.

Make a new column, make it equal to zero minus your data column for the vertical axis

Replace the data column address in the chart with this new column

Click format>number>more formats>custom number format

Change the number format to -## this will label your positives as negatives, and negatives as positives

Since you have already got the negative of your figures, the chart draws them upside down.

Since the default number format of the data for the vertical axis is "from data", sheets will obligingly label your chart in the correct order.

Change the format to match the format you want, just remember to add a - to the format before the semicolon and delete the - from the format after the semicolon.


Contents

In 1687 Isaac Newton published the Principia in which he included a proof that a rotating self-gravitating fluid body in equilibrium takes the form of a flattened ("oblate") ellipsoid of revolution, generated by an ellipse rotated around its minor diameter a shape which he termed an oblate spheroid. [1] [2]

In geophysics, geodesy, and related areas, the word 'ellipsoid' is understood to mean 'oblate ellipsoid of revolution', and the older term 'oblate spheroid' is hardly used. [3] [4] For bodies that cannot be well approximated by an ellipsoid of revolution a triaxial (or scalene) ellipsoid is used.

The shape of an ellipsoid of revolution is determined by the shape parameters of that ellipse. The semi-major axis of the ellipse, a , becomes the equatorial radius of the ellipsoid: the semi-minor axis of the ellipse, b , becomes the distance from the centre to either pole. These two lengths completely specify the shape of the ellipsoid.

In geodesy publications, however, it is common to specify the semi-major axis (equatorial radius) a and the flattening f , defined as:

That is, f is the amount of flattening at each pole, relative to the radius at the equator. This is often expressed as a fraction 1/ m m = 1/f then being the "inverse flattening". A great many other ellipse parameters are used in geodesy but they can all be related to one or two of the set a , b and f .

A great many ellipsoids have been used to model the Earth in the past, with different assumed values of a and b as well as different assumed positions of the center and different axis orientations relative to the solid Earth. Starting in the late twentieth century, improved measurements of satellite orbits and star positions have provided extremely accurate determinations of the earth's center of mass and of its axis of revolution and those parameters have been adopted also for all modern reference ellipsoids.

The ellipsoid WGS-84, widely used for mapping and satellite navigation has f close to 1/300 (more precisely, 1/298.257223563, by definition), corresponding to a difference of the major and minor semi-axes of approximately 21 km (13 miles) (more precisely, 21.3846858 km). For comparison, Earth's Moon is even less elliptical, with a flattening of less than 1/825, while Jupiter is visibly oblate at about 1/15 and one of Saturn's triaxial moons, Telesto, is highly flattened, with f between 1/3 to 1/2 (meaning that the polar diameter is between 50% and 67% of the equatorial.

A primary use of reference ellipsoids is to serve as a basis for a coordinate system of latitude (north/south), longitude (east/west), and ellipsoidal height.

For this purpose it is necessary to identify a zero meridian, which for Earth is usually the Prime Meridian. For other bodies a fixed surface feature is usually referenced, which for Mars is the meridian passing through the crater Airy-0. It is possible for many different coordinate systems to be defined upon the same reference ellipsoid.

The longitude measures the rotational angle between the zero meridian and the measured point. By convention for the Earth, Moon, and Sun it is expressed in degrees ranging from −180° to +180° For other bodies a range of 0° to 360° is used.

The latitude measures how close to the poles or equator a point is along a meridian, and is represented as an angle from −90° to +90°, where 0° is the equator. The common or geodetic latitude is the angle between the equatorial plane and a line that is normal to the reference ellipsoid. Depending on the flattening, it may be slightly different from the geocentric (geographic) latitude, which is the angle between the equatorial plane and a line from the center of the ellipsoid. For non-Earth bodies the terms planetographic and planetocentric are used instead.

The coordinates of a geodetic point are customarily stated as geodetic latitude ϕ and longitude λ (both specifying the direction in space of the geodetic normal containing the point), and the ellipsoidal height h of the point above or below the reference ellipsoid along its normal. If these coordinates are given, one can compute the geocentric rectangular coordinates of the point as follows: [5]

and a and b are the equatorial radius (semi-major axis) and the polar radius (semi-minor axis), respectively. N is the radius of curvature in the prime vertical.

In contrast, extracting ϕ , λ and h from the rectangular coordinates usually requires iteration. A straightforward method is given in an OSGB publication [6] and also in web notes. [7] More sophisticated methods are outlined in geodetic system.

Currently the most common reference ellipsoid used, and that used in the context of the Global Positioning System, is the one defined by WGS 84.


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Unfortunately Minecraft Pi Edition's Python API is rather limited. Per the documentation there are only three fields to set via world.setting() or player.setting() , and you can confirm this by running strings minecraft-pi and inspecting the output.

You may have considered using xinput list and xinput set-prop . Whether this works could depend on your particular mouse hardware, but from what I can tell changing the coordinate transform matrix would only affect the 2D cursor position, not mouse look (controlled instead by delta movements).

Update: There's Phirel's patch to enable Survival Mode. It also happens to enable basic options in the GUI, including "Invert X-axis" (confusing terminology: invert Y direction

You can read below for my other approach using SDL.

One way to effectively mod this closed-source executable is to intercept SDL function calls with your own modified SDL.

To invert the mouse Y, find the part of the library where it normally sends the deltaY value and invert it!

then build and inject your modified library to test:

Or if you have enabled full OpenGL with KMS, you may have to avoid the script at /usr/bin/minecraft-pi overriding with its own LD_PRELOAD setting. More complicated, but you can inject the Mesa wrapper alongside like so:

One cool perk of this approach is that because mouse look uses relative movements while you're leaving the absolute Y position untouched, cursor movement still functions as before.

If you wish to make further modifications or need to debug your changes, add printf() statements, rebuild, and rerun.

Thanks for reading. If you reached this point, you either missed the key text above recommending a simpler approach of using the Survival Mode patch, or you're using this as a tutorial for a further input modding. If the latter, you may find some useful troubleshooting steps in the followup question.


I eventually find out that we need not use InverseFunction at all, just use the NDSolve since we can rewrite the equation as

Assuming you mean roll as in the way a circle rolls across the floor, you need a unit speed arc-length parameterization of the curve $(t^2,t)$ . Why? Becuase the key behavior of rolling is no slippage. If a point $(t_0^2,t_0)$ is tangent to the $y$ -axis at $(0,l(t_0))$ , then the arc length from $(0,0)$ to $(t_0^2,t_0)$ along the curve should be equal to $l(t_0)$ .

There's no closed form* for the curve $(gamma(t)^2,gamma(t))$ such that $ig(frac

ig)^2+ig(frac
ig)^2=1$ (unit speed). We can still write it symbolically though

We get $gamma$ is the inverse function of $frac14sinh^<-1>(2t)+frac t2sqrt<1+4t^2>$ . The angle of $(gamma(t)^2,gamma(t))$ is

We get $ an^<-1>(2gamma(t))$ . All Manipulate needs to do is translate and rotate the curve $(gamma(t)^2,gamma(t))$ so that $(gamma(t_0)^2,gamma(t_0))$ is tangent to $(0,t_0)$ .


Presentation Transcript

Geographic Communication Today Harvard Extension School ISMT-E155 Jeff Blossom, Instructor [email protected] Week 1 January 27 2014 5:30 - 5:45 Why Geographic Communication? Why me? 5:45 - 6:00 Why you? - Introduce name, what you do, why you're taking the class, and any special mapping interests you may have. 6:00 - 6:40 Review the syllabus 6:40 – 6:50 5 minute paper and break 6:50 – 7:20 Lecture: The origins of mapping. Modeling the Earth.

Geographic: geo – “the earth” graphos – “to write” Geography – To describe or write about the Earth. Communication – a process whereby meaning is shared between two living organisms. Why “Geographic Communication”?

Where is the Wal-Mart in Bellingham, MA? • ½ mile South of Maple St. on Hartford Ave. • 250 Hartford Ave Bellingham, MA 02019 • Highway 126 & Hartford Ave. • 42.116912,-71.464605 • “Just past the power lines before you get to 495” • “Where the old service station used to be on Route 126”

Where is the Wal-Mart in Bellingham, MA? Maps are the means by which geographic information is communicated visually.

-34.86,-56.17 Montevideo, Uruguay

Map of India (general reference map) Population density map (thematic map) darker color = higher population density

Geographic Communication Today Harvard Extension School ISMT-E155 Jeff Blossom, Instructor [email protected] Week 1 January 27 2014 5:30 - 5:45 Why Geographic Communication? Why me? 5:45 - 6:00 Why you? - Introduce name, what you do, why you're taking the class, and any special mapping interests you may have. 6:00 - 6:40 Review the syllabus 6:40 – 6:50 5 minute paper and break 6:50 – 7:20 Lecture: The origins of mapping. Modeling the Earth.

IntroductionsTeaching assistant: Stacy [email protected] Why you?- Introduce name- what you do- why you're taking the class- special mapping interests you may have

Geographic Communication Today Harvard Extension School ISMT-E155 Jeff Blossom, Instructor [email protected] Week 1 January 27 2014 5:30 - 5:45 Why Geographic Communication? Why me? 5:45 - 6:00 Why you? - Introduce name, what you do, why you're taking the class, and any special mapping interests you may have. 6:00 - 6:40 Review the syllabus (handout) 6:40 – 6:50 5 minute paper and break 6:50 – 7:20 Lecture: The origins of mapping. Modeling the Earth.

Lab assignment requirements • Answer questions in a Word or text file. • Export maps in PDF or PNG format. • Map data into KML format. • Upload the Word, PDF, and KML files to the course website drop box • If having problems with the Dropbox, submitting labs via email is fine. • Labe are due 9 days after assignment (the following Friday at midnight) • Need clarification or having trouble? Email anytime, come to office hours before and after class.

An 8 GB USB flash drive • Access to a PC with internet connection • and installation privileges • At least 5 hours a week commitment • Lecture slides will be available on the class website, prior to class. What you will need for this class

Geographic Communication Today Harvard Extension School ISMT-E155 Jeff Blossom, Instructor [email protected] Week 1 January 27 2014 5:30 - 5:45 Why Geographic Communication? Why me? 5:45 - 6:00 Why you? - Introduce name, what you do, why you're taking the class, and any special mapping interests you may have. 6:00 - 6:40 Review the syllabus (handout) 6:40 – 6:50 5 minute paper and break 6:50 – 7:20 Lecture: The origins of mapping. Modeling the Earth.

Geographic Communication Today Harvard Extension School ISMT-E155 Jeff Blossom, Instructor [email protected] Week 1 January 27 2014 5:30 - 5:45 Why Geographic Communication? Why me? 5:45 - 6:00 Why you? - Introduce name, what you do, why you're taking the class, and any special mapping interests you may have. 6:00 - 6:40 Review the syllabus (handout) 6:40 – 6:50 5 minute paper and break 6:50 – 7:20 Lecture: The origins of mapping. Modeling the Earth.

The origins of mapping and modeling the Earth A map is a visual representation of an area. Nearly all maps depict something on Earth, and are thus geographic in nature.

Map of the human brain 3d map of space matter

The first map 16,500 BC - Star maps on cave walls (France)

12,000 BC -Map engraved on a mammoth tusk (Ukraine)

The first maps - Babalonians Babylonian world map preserved on a clay tablet.

Mapping advancements – Ancient Greece Aristotle (384-322 B.C.E.) Proved the Earth is round, evidenced by: • The lunar eclipse is always circular • Ships seem to sink as they move away from view and pass the horizon • Some stars can be seen only from certain parts of the Earth. These observations led to modeling the Earth as a sphere

Mapping advancements – Ancient Greece Sphere – a perfectly round object in 3 dimensional space, with all points on the surface lying the same distance from the center. HeraclidesPonticus (390-310 B.C.) – Proposed the Earth rotates on its axis, east to west, once every 24 hours.

Spherical geometry: Great circles, hemisphere Great circle - the circular intersection of a sphere and a plane which passes through the center point of the sphere. • All lines of longitude and the Equator are great circles • Two hemisphere’s (half of a sphere) are created on either side of the plane

Spherical geometry: Small circles Small circle - the intersection of the sphere and a plane which does not pass through the center point of the sphere. All lines of latitude except for the Equator are small circles. Lines of latitude (small circles) great circle (Equator)

Mapping advancements – Ancient Greece Eratosthenes (275–195 B.C.E.) • First used the word “Geography” • Approximated the circumference of the Earth. • Wrote “On the Measurement of the Earth” • Put forth that accurate mapping depends on accurate linear measurement. • Proposed using meridians and parallels to base accurate measurements on.

Meridian – an imaginary line running north to south. Parallel - an imaginary line running east to west. Allowed for the description of places on Earth in as referenced to parallels and meridians

Meridian – an imaginary line running from the north pole to the south pole connecting all points along the same longitude. Parallel - an imaginary line circling the globe running due east to west, connecting all points along the same latitude angle.

Coordinate systems • Coordinate system – a system which uses one or more numbers to uniquely determine the position of a point. • Two axes (X and Y) on a horizontal plane • Equally spaced linear units

0,0 (origin) X axis Y axis

Geographic coordinate system • A geographic coordinate system is a coordinate system that enables every location on the Earth to be specified by a pair of numbers. • Commonly uses values of longitude and latitude to represent horizontal positions on Earth. For example -71.10, 42.37 (longitude, latitude) represents a point in Cambridge, MA.

Mapping advancements – Ancient Greece Euclid (323-283 B.C.E.) – the father of Geometry • Geometry – “Earth measuring” • A branch of mathematics concerned with shape, size, and relative positions of figures. • Two fundamental types of measurements: distances and angles A B For example: the distance from A to B equals 1 stadia Distance – a numerical description of how far apart objects are, using a common reference unit.

Euclidian Geometry - Angle Angle – a figure formed by two rays sharing a common end point: Ray – a line that is finite in one direction, but infinite in the other. ray 2 ray 1 endpoint

Euclidian Geometry - angle The magnitude of an angle is the amount of rotation that separates the two rays: axis of rotation more magnitude less magnitude

Euclidian Geometry - degree A degree, denoted by a small superscript circle (°), is 1/360 of a full circle. One full circle is 360° 360° 0° 270° 90° 90° angle 180°

Longitude: An angular distance east or west of a point on the Earth’s surface, measured from the center of the Earth.

Measuring longitude • Prime Meridian—The meridian of longitude 0 degrees, used as the origin for the measurement of longitude. • Longitude at a point may be determined by calculating the time difference between that at its location and the time at the prime meridian. • Since there are 24 hours in a day and 360 degrees in a circle, the sun moves across the sky at a rate of 15 degrees per hour (360°/24 hours = 15° per hour). • So if local time (where a person is) is four hours ahead of time at the prime meridian, then that person is at 60° longitude (4 hours × 15° per hour = 60°).

Latitude: An angular distance north or south of the Equator measured from the center of the Earth.

Latitudinal references Polaris • The north pole and south pole mark the opposite positions on the axis around which the earth rotates. • The Equator is a great circle located halfway between the poles, and is used as the origin reference for latitude. • Polaris (the north star) is a located directly above the north pole, and is visible as a fixed position in the sky about which the Earth rotates. Equator axis

Measuring latitude Polaris 45° Horizon • Measure the angle from the horizon to Polaris (or Sigma Octantis in the Southern Hemisphere) • using an astrolabe, cross staff, sextant, or other tool. This is your latitude.


Checks if this SRS can be changed to another SRS without causing computational incompatibilities.

This means checking that all values in the two SRSs that affect computations are the same. The syntax of the SRS definitions may still vary, e.g., by using different names or by having different authority codes.

In some cases, e.g., unknown projection methods, we don't know how to compare the two SRSs. In that case, we fail by saying that the SRSs are not the same.

The operation is not commutative. The SRS parameter is allowed to have a TOWGS84 specification even though this object doesn't. The opposite is not necessarily true. If this object lacks TOWGS84 information, transformation operations are forbidden on this SRS. Adding that possibility changes what computations are available, but it doesn't change the result of any computation that can currently be done.

An SRS that is currently identified as WGS 84 may both add and remove TOWGS84 information as long as the parameters are all 0. Adding a non-all-zero TOWGS84 clause to a WGS 84 SRS is not allowed.


Checks if this SRS can be changed to another SRS without causing computational incompatibilities.

This means checking that all values in the two SRSs that affect computations are the same. The syntax of the SRS definitions may still vary, e.g., by using different names or by having different authority codes.

In some cases, e.g., unknown projection methods, we don't know how to compare the two SRSs. In that case, we fail by saying that the SRSs are not the same.

The operation is not commutative. The SRS parameter is allowed to have a TOWGS84 specification even though this object doesn't. The opposite is not necessarily true. If this object lacks TOWGS84 information, transformation operations are forbidden on this SRS. Adding that possibility changes what computations are available, but it doesn't change the result of any computation that can currently be done.

An SRS that is currently identified as WGS 84 may both add and remove TOWGS84 information as long as the parameters are all 0. Adding a non-all-zero TOWGS84 clause to a WGS 84 SRS is not allowed.