# How to measure correct distances in a project with OpenLayers background?

I have 3 lat/long points as follows:

`A = {35.257246,139.721256} B = {35.256541,139.721491} C = {35.256326,139.7203271}`

1) Measurement result by Movable Type Scripts:

By using the distance calculation method at Movable Type Scripts, the distance results are:

`distance(A,B)= 80.88745771063131(m) distance(B,C)= 101.58773310547808(m)`

I believe these results are correct.

2) Measurement result by QGIS measure line tool:

The QGIS desktop 2.0.1 and the Projection CRS is set to`[+proj=longlat +datum=WGS84 +no_defs]`

. I use the Plugins/OpenLayers plugin/Add Google Satelite and import 3 lat/long points into QGIS.

The results are:

`distance(A,B) = 100.374(m) distance(B,C) = 135.114(m)`

I need to generate a map from a large set of lat/long points as above and Google Satellite background on QGIS.

Could you show me how to solve this problem?

The first source you mention remarks:

All these formulæ are for calculations on the basis of a spherical earth (ignoring ellipsoidal effects)

so you should not rely on the results.

If you use the openlayers plugin, **project** CRS should be set to EPSG:3857. As Erica points out, that is not suitable for measurements.

For measuring, delete the openlayers background, and set the project CRS to the UTM zone of your part of the world instead, or what is used by your local surveying authority.

If you need the openlayers background for measuring, take a screenshot with "Save as image", add that to the canvas with layer CRS EPSG:3857, then delete the openlayers background and change CRS.

I think this is a projection-related issue. WGS84 is not intended for accurate measurement anywhere but the equator, so the measure line tool (or a scale bar, if you were making a map) would be off. The Haversine calculation is independent of projection and so its results are reliable.

Refer to this question: Using scale bar units in QGIS composer?

Try projecting to a coordinate system that is appropriate for your area of interest (I'm not familiar with the best ones for Japan, so can't advise there; I usually default to UTM, however) and then you should be able to get accurate measurements.

Based on your comments, the problem is solved. In summary:

1-Using the excel tool, here, Excel tool for converting LatLong to UTM. In the Batch Convert LatLong to UTM sheet, paste the LatLong coordinates into collumn L, M then, the UTM coordinates are automatically calculated and save in AE,AF collumn. Saving the UTM coordinates to a file. (This step also can be done by using GIS softwares, such as Global Mapper,etc… )

2-In QGIS, import the file, and select the JGD2000 / UTM zone 54N Projection for the layer. Now, the distance measurement should be ok.

3-As @Andre Joost mentioned above, I have to use the GoogleOzi tool to download Google Satellite image, and import the raster image into QGIS as a background layer. This step hasn't finished yet, but it's ok for me.

Thank you all for your comments.

New proposition using leaflet-geodesy which seems a perfect fit for your need. It is exempt from Turf's bug (see Edit 2 below).

(center position in [latitude, longitude] degrees, radius in meters)

Quick comparison with nathansnider's solution: http://fiddle.jshell.net/58ud0ttk/2/

(shows that both codes produce the same resulting area, the only difference being in the number of segments used for approximating the area)

EDIT: a nice page that compares Leaflet-geodesy with the standard L.Circle: https://www.mapbox.com/mapbox.js/example/v1.0.0/leaflet-geodesy/

Unfortunately Turf uses JSTS Topology Suite to build the buffer. It looks like this operation in JSTS does not fit a non-plane geometry like the Earth surface.

The bug is reported here and as of today the main Turf library does not have a full workaround.

So **the below answer (edit 1) produces WRONG results**.

See nathansnider's answer for a workaround for building a buffer around a point.

You can easily build the described polygon by using Turf. It offers the turf.buffer method which creates a polygon with a specified distance around a given feature (could be a simple point).

So you can simply do for example:

Unfortunately it seems that there is currently no Leaflet plugin to do so.

It is also unclear what the Tissot indicatrix should represent:

- A true ellipse that represents the deformation of an infinitely small circle (i.e. distortion at a single point), or
- A circular-like shape that represents the deformation of a finite-size circle when on the Earth surface, like the OpenLayers demo you link to?

In that demo, the shape in EPSG:4326 is not an ellipse, the length in the vertical axis decreases at higher latitude compared to the other half of the shape.

If you are looking for that 2nd option, then you would have to manually build a polygon that represents the intersection of a sphere and of the Earth surface. If my understanding is correct, this is what the OL demo does. If that is an option for you, maybe you can generate your polygons there and import them as GeoJSON features into Leaflet? :-)

## Contents

Many properties can be measured on the Earth's surface independent of its geography:

Map projections can be constructed to preserve some of these properties at the expense of others. Because the curved Earth's surface is not isometric to a plane, preservation of shapes inevitably leads to a variable scale and, consequently, non-proportional presentation of areas. Vice versa, an area-preserving projection can not be conformal, resulting in shapes and bearings distorted in most places of the map. Each projection preserves, compromises, or approximates basic metric properties in different ways. The purpose of the map determines which projection should form the base for the map. Because many purposes exist for maps, a diversity of projections have been created to suit those purposes.

Another consideration in the configuration of a projection is its compatibility with data sets to be used on the map. Data sets are geographic information their collection depends on the chosen datum (model) of the Earth. Different datums assign slightly different coordinates to the same location, so in large scale maps, such as those from national mapping systems, it is important to match the datum to the projection. The slight differences in coordinate assignation between different datums is not a concern for world maps or other vast territories, where such differences get shrunk to imperceptibility.

### Distortion Edit

Carl Friedrich Gauss's Theorema Egregium proved that a sphere's surface cannot be represented on a plane without distortion. The same applies to other reference surfaces used as models for the Earth, such as oblate spheroids, ellipsoids and geoids. Since any map projection is a representation of one of those surfaces on a plane, all map projections distort.

The classical way of showing the distortion inherent in a projection is to use Tissot's indicatrix. For a given point, using the scale factor *h* along the meridian, the scale factor *k* along the parallel, and the angle *θ′* between them, Nicolas Tissot described how to construct an ellipse that characterizes the amount and orientation of the components of distortion. [2] : 147–149 [5] By spacing the ellipses regularly along the meridians and parallels, the network of indicatrices shows how distortion varies across the map.

#### Other distortion metrics Edit

Many other ways have been described for characterizing distortion in projections. [6] [7] Like Tissot's indicatrix, the **Goldberg-Gott indicatrix** is based on infinitesimals, and depicts *flexion* and *skewness* (bending and lopsidedness) distortions. [8]

Rather than the original (enlarged) infinitesimal circle as in Tissot's indicatrix, some visual methods project finite shapes that span a part of the map. For example, a small circle of fixed radius (e.g., 15-degrees angular radius). [9] Sometimes spherical triangles are used. [* citation needed *] In the first half of the 20th century, projecting a human head onto different projections was common to show how distortion varies across one projection as compared to another. [10] In dynamic media, shapes of familiar coastlines and boundaries can be dragged across an interactive map to show how the projection distorts sizes and shapes according to position on the map. [11]

Another way to visualize local distortion is through grayscale or color gradations whose shade represents the magnitude of the angular deformation or areal inflation. Sometimes both are shown simultaneously by blending two colors to create a bivariate map. [12]

The problem of characterizing distortion globally across areas instead of at just a single point is that it necessarily involves choosing priorities to reach a compromise. Some schemes use distance distortion as a proxy for the combination of angular deformation and areal inflation such methods arbitrarily choose what paths to measure and how to weight them in order to yield a single result. Many have been described. [8] [13] [14] [15] [16]

The creation of a map projection involves two steps:

- Selection of a model for the shape of the Earth or planetary body (usually choosing between a sphere or ellipsoid). Because the Earth's actual shape is irregular, information is lost in this step.
- Transformation of geographic coordinates (longitude and latitude) to Cartesian (
*x*,*y*) or polar plane coordinates. In large-scale maps, Cartesian coordinates normally have a simple relation to eastings and northings defined as a grid superimposed on the projection. In small-scale maps, eastings and northings are not meaningful, and grids are not superimposed.

Some of the simplest map projections are literal projections, as obtained by placing a light source at some definite point relative to the globe and projecting its features onto a specified surface. Although most projections are not defined in this way, picturing the light source-globe model can be helpful in understanding the basic concept of a map projection.

### Choosing a projection surface Edit

A surface that can be unfolded or unrolled into a plane or sheet without stretching, tearing or shrinking is called a *developable surface*. The cylinder, cone and the plane are all developable surfaces. The sphere and ellipsoid do not have developable surfaces, so any projection of them onto a plane will have to distort the image. (To compare, one cannot flatten an orange peel without tearing and warping it.)

One way of describing a projection is first to project from the Earth's surface to a developable surface such as a cylinder or cone, and then to unroll the surface into a plane. While the first step inevitably distorts some properties of the globe, the developable surface can then be unfolded without further distortion.

### Aspect of the projection Edit

Once a choice is made between projecting onto a cylinder, cone, or plane, the **aspect** of the shape must be specified. The aspect describes how the developable surface is placed relative to the globe: it may be *normal* (such that the surface's axis of symmetry coincides with the Earth's axis), *transverse* (at right angles to the Earth's axis) or *oblique* (any angle in between).

### Notable lines Edit

The developable surface may also be either *tangent* or *secant* to the sphere or ellipsoid. Tangent means the surface touches but does not slice through the globe secant means the surface does slice through the globe. Moving the developable surface away from contact with the globe never preserves or optimizes metric properties, so that possibility is not discussed further here.

Tangent and secant lines (*standard lines*) are represented undistorted. If these lines are a parallel of latitude, as in conical projections, it is called a *standard parallel*. The *central meridian* is the meridian to which the globe is rotated before projecting. The central meridian (usually written *λ*_{0}) and a parallel of origin (usually written *φ*_{0}) are often used to define the origin of the map projection. [17] [18]

### Scale Edit

A globe is the only way to represent the Earth with constant scale throughout the entire map in all directions. A map cannot achieve that property for any area, no matter how small. It can, however, achieve constant scale along specific lines.

Some possible properties are:

- The scale depends on location, but not on direction. This is equivalent to preservation of angles, the defining characteristic of a conformal map.
- Scale is constant along any parallel in the direction of the parallel. This applies for any cylindrical or pseudocylindrical projection in normal aspect.
- Combination of the above: the scale depends on latitude only, not on longitude or direction. This applies for the Mercator projection in normal aspect.
- Scale is constant along all straight lines radiating from a particular geographic location. This is the defining characteristic of an equidistant projection such as the Azimuthal equidistant projection. There are also projections (Maurer's Two-point equidistant projection, Close) where true distances from
*two*points are preserved. [2] : 234

### Choosing a model for the shape of the body Edit

Projection construction is also affected by how the shape of the Earth or planetary body is approximated. In the following section on projection categories, the earth is taken as a sphere in order to simplify the discussion. However, the Earth's actual shape is closer to an oblate ellipsoid. Whether spherical or ellipsoidal, the principles discussed hold without loss of generality.

Selecting a model for a shape of the Earth involves choosing between the advantages and disadvantages of a sphere versus an ellipsoid. Spherical models are useful for small-scale maps such as world atlases and globes, since the error at that scale is not usually noticeable or important enough to justify using the more complicated ellipsoid. The ellipsoidal model is commonly used to construct topographic maps and for other large- and medium-scale maps that need to accurately depict the land surface. Auxiliary latitudes are often employed in projecting the ellipsoid.

A third model is the geoid, a more complex and accurate representation of Earth's shape coincident with what mean sea level would be if there were no winds, tides, or land. Compared to the best fitting ellipsoid, a geoidal model would change the characterization of important properties such as distance, conformality and equivalence. Therefore, in geoidal projections that preserve such properties, the mapped graticule would deviate from a mapped ellipsoid's graticule. Normally the geoid is not used as an Earth model for projections, however, because Earth's shape is very regular, with the undulation of the geoid amounting to less than 100 m from the ellipsoidal model out of the 6.3 million m Earth radius. For irregular planetary bodies such as asteroids, however, sometimes models analogous to the geoid are used to project maps from. [19] [20] [21] [22] [23]

Other regular solids are sometimes used as generalizations for smaller bodies' geoidal equivalent. For example, Io is better modeled by triaxial ellipsoid or prolated spheroid with small eccentricities. Haumea's shape is a Jacobi ellipsoid, with its major axis twice as long as its minor and with its middle axis one and half times as long as its minor. See map projection of the triaxial ellipsoid for further information.

A fundamental projection classification is based on the type of projection surface onto which the globe is conceptually projected. The projections are described in terms of placing a gigantic surface in contact with the Earth, followed by an implied scaling operation. These surfaces are cylindrical (e.g. Mercator), conic (e.g. Albers), and plane (e.g. stereographic). Many mathematical projections, however, do not neatly fit into any of these three conceptual projection methods. Hence other peer categories have been described in the literature, such as pseudoconic, pseudocylindrical, pseudoazimuthal, retroazimuthal, and polyconic.

Another way to classify projections is according to properties of the model they preserve. Some of the more common categories are:

- Preserving direction (
*azimuthal or zenithal*), a trait possible only from one or two points to every other point [24] - Preserving shape locally (
*conformal*or*orthomorphic*) - Preserving area (
*equal-area*or*equiareal*or*equivalent*or*authalic*) - Preserving distance (
*equidistant*), a trait possible only between one or two points and every other point - Preserving shortest route, a trait preserved only by the gnomonic projection

Because the sphere is not a developable surface, it is impossible to construct a map projection that is both equal-area and conformal.

The three developable surfaces (plane, cylinder, cone) provide useful models for understanding, describing, and developing map projections. However, these models are limited in two fundamental ways. For one thing, most world projections in use do not fall into any of those categories. For another thing, even most projections that do fall into those categories are not naturally attainable through physical projection. As L.P. Lee notes,

No reference has been made in the above definitions to cylinders, cones or planes. The projections are termed cylindric or conic because they can be regarded as developed on a cylinder or a cone, as the case may be, but it is as well to dispense with picturing cylinders and cones, since they have given rise to much misunderstanding. Particularly is this so with regard to the conic projections with two standard parallels: they may be regarded as developed on cones, but they are cones which bear no simple relationship to the sphere. In reality, cylinders and cones provide us with convenient descriptive terms, but little else. [25]

Lee's objection refers to the way the terms *cylindrical*, *conic*, and *planar* (azimuthal) have been abstracted in the field of map projections. If maps were projected as in light shining through a globe onto a developable surface, then the spacing of parallels would follow a very limited set of possibilities. Such a cylindrical projection (for example) is one which:

- Is rectangular
- Has straight vertical meridians, spaced evenly
- Has straight parallels symmetrically placed about the equator
- Has parallels constrained to where they fall when light shines through the globe onto the cylinder, with the light source someplace along the line formed by the intersection of the prime meridian with the equator, and the center of the sphere.

(If you rotate the globe before projecting then the parallels and meridians will not necessarily still be straight lines. Rotations are normally ignored for the purpose of classification.)

Where the light source emanates along the line described in this last constraint is what yields the differences between the various "natural" cylindrical projections. But the term *cylindrical* as used in the field of map projections relaxes the last constraint entirely. Instead the parallels can be placed according to any algorithm the designer has decided suits the needs of the map. The famous Mercator projection is one in which the placement of parallels does not arise by projection instead parallels are placed how they need to be in order to satisfy the property that a course of constant bearing is always plotted as a straight line.

### Cylindrical Edit

A normal cylindrical projection is any projection in which meridians are mapped to equally spaced vertical lines and circles of latitude (parallels) are mapped to horizontal lines.

The mapping of meridians to vertical lines can be visualized by imagining a cylinder whose axis coincides with the Earth's axis of rotation. This cylinder is wrapped around the Earth, projected onto, and then unrolled.

By the geometry of their construction, cylindrical projections stretch distances east-west. The amount of stretch is the same at any chosen latitude on all cylindrical projections, and is given by the secant of the latitude as a multiple of the equator's scale. The various cylindrical projections are distinguished from each other solely by their north-south stretching (where latitude is given by φ):

- North-south stretching equals east-west stretching (sec
*φ*): The east-west scale matches the north-south scale: conformal cylindrical or Mercator this distorts areas excessively in high latitudes (see also transverse Mercator). - North-south stretching grows with latitude faster than east-west stretching (sec 2
*φ*): The cylindric perspective (or central cylindrical) projection unsuitable because distortion is even worse than in the Mercator projection. - North-south stretching grows with latitude, but less quickly than the east-west stretching: such as the Miller cylindrical projection (sec 4 / 5
*φ*). - North-south distances neither stretched nor compressed (1): equirectangular projection or "plate carrée".
- North-south compression equals the cosine of the latitude (the reciprocal of east-west stretching): equal-area cylindrical. This projection has many named specializations differing only in the scaling constant, such as the Gall–Peters or Gall orthographic (undistorted at the 45° parallels), Behrmann (undistorted at the 30° parallels), and Lambert cylindrical equal-area (undistorted at the equator). Since this projection scales north-south distances by the reciprocal of east-west stretching, it preserves area at the expense of shapes.

In the first case (Mercator), the east-west scale always equals the north-south scale. In the second case (central cylindrical), the north-south scale exceeds the east-west scale everywhere away from the equator. Each remaining case has a pair of secant lines—a pair of identical latitudes of opposite sign (or else the equator) at which the east-west scale matches the north-south-scale.

Normal cylindrical projections map the whole Earth as a finite rectangle, except in the first two cases, where the rectangle stretches infinitely tall while retaining constant width.

### Pseudocylindrical Edit

Pseudocylindrical projections represent the *central* meridian as a straight line segment. Other meridians are longer than the central meridian and bow outward, away from the central meridian. Pseudocylindrical projections map parallels as straight lines. Along parallels, each point from the surface is mapped at a distance from the central meridian that is proportional to its difference in longitude from the central meridian. Therefore, meridians are equally spaced along a given parallel. On a pseudocylindrical map, any point further from the equator than some other point has a higher latitude than the other point, preserving north-south relationships. This trait is useful when illustrating phenomena that depend on latitude, such as climate. Examples of pseudocylindrical projections include:

- , which was the first pseudocylindrical projection developed. On the map, as in reality, the length of each parallel is proportional to the cosine of the latitude. [26] The area of any region is true. , which in its most common forms represents each meridian as two straight line segments, one from each pole to the equator.

### Hybrid Edit

The HEALPix projection combines an equal-area cylindrical projection in equatorial regions with the Collignon projection in polar areas.

### Conic Edit

The term "conic projection" is used to refer to any projection in which meridians are mapped to equally spaced lines radiating out from the apex and circles of latitude (parallels) are mapped to circular arcs centered on the apex. [27]

When making a conic map, the map maker arbitrarily picks two standard parallels. Those standard parallels may be visualized as secant lines where the cone intersects the globe—or, if the map maker chooses the same parallel twice, as the tangent line where the cone is tangent to the globe. The resulting conic map has low distortion in scale, shape, and area near those standard parallels. Distances along the parallels to the north of both standard parallels or to the south of both standard parallels are stretched distances along parallels between the standard parallels are compressed. When a single standard parallel is used, distances along all other parallels are stretched.

Conic projections that are commonly used are:

- , which keeps parallels evenly spaced along the meridians to preserve a constant distance scale along each meridian, typically the same or similar scale as along the standard parallels. , which adjusts the north-south distance between non-standard parallels to compensate for the east-west stretching or compression, giving an equal-area map. , which adjusts the north-south distance between non-standard parallels to equal the east-west stretching, giving a conformal map.

### Pseudoconic Edit

- , an equal-area projection on which most meridians and parallels appear as curved lines. It has a configurable standard parallel along which there is no distortion. , upon which distances are correct from one pole, as well as along all parallels. and other projections in the polyconic projection class.

### Azimuthal (projections onto a plane) Edit

Azimuthal projections have the property that directions from a central point are preserved and therefore great circles through the central point are represented by straight lines on the map. These projections also have radial symmetry in the scales and hence in the distortions: map distances from the central point are computed by a function *r*(*d*) of the true distance *d*, independent of the angle correspondingly, circles with the central point as center are mapped into circles which have as center the central point on the map.

The mapping of radial lines can be visualized by imagining a plane tangent to the Earth, with the central point as tangent point.

Some azimuthal projections are true perspective projections that is, they can be constructed mechanically, projecting the surface of the Earth by extending lines from a point of perspective (along an infinite line through the tangent point and the tangent point's antipode) onto the plane:

## How to measure correct distances in a project with OpenLayers background? - Geographic Information Systems

**Projections and Coordinate Systems**

Projections and coordinate systems are a complicated topic in GIS, but they form the basis for how a GIS can store, analyze, and display spatial data. Understanding projections and coordinate systems important knowledge to have, especially if you deal with many different sets of data that come from different sources.

The best model of the earth would be a 3-dimensional solid in the same shape as the earth. Spherical globes are often used for this purpose. However, globes have several drawbacks.

- Globes are large and cumbersome.
- They are generally of a scale unsuitable to the purposes for which most maps are used. Usually we want to see more detail than is possible to be shown on a globe.
- Standard measurement equipment (rulers, protractors, planimeters, dot grids, etc.) cannot be used to measure distance, angle, area, or shape on a sphere, as these tools have been constructed for use in planar models.
- The latitude-longitude spherical coordinate system can only be used to measure angles, not distances or areas.

Here is an image of a globe, displaying lines of reference. These lines can only be used for measurement of angles on a sphere. They cannot be used for making linear or areal measurements.

Positions on a globe are measured by angles rather than X, Y (Cartesian planar) coordinates. In the image below, the specific point on the surface of the earth is specified by the coordinate (60 °. E longitude, 55 den. N latitude). The longitude is measured as the number of degrees from the prime meridian, and the latitude is measured as the number of degrees from the equator.

For this reason, projection systems have been developed. Map projections are sets of mathematical models which transform spherical coordinates (such as latitude and longitude) to planar coordinates (x and y). In the process, data which actually lie on a sphere are projected onto a flat plane or a surface. That surface can be converted to a planar section without stretching.

Here is a simple schematic designed to show how a projection works. Imagine a glass sphere marked with grid lines or geographic features. A light positioned in the center of the sphere shines ("projects") outward, casting shadows from the lines. A plane, cone, or cylinder (known as a *developable surface*) is placed outside the sphere. Shadows are cast upon the surface. The surface is opened flat, and the geographic features are displayed on a flat plane. As soon as a projection is applied, a Cartesian coordinate system (regular measurement in X and Y dimensions) is implied. The user gets to choose the details of the coordinate system (e.g., units, origin, and offsets).

The projection surfaces (i.e., cylinders, cones, and planes) form the basic types of projections:

Standard parallels are where the cone touches or slices through the globe.

The central meridian is opposite the edge where the cone is sliced open.

Different cylindrical projection orientations:

The most common cylindrical projection is the Mercator projection, which is the basis of the UTM (Universal Transverse Mercator) system.

Different orthographic projection parameters:

[Images placed with permission of Peter Dana]

Notice in these images how distortion in distance is minimized at the place on the surface that is closest to the sphere. Distortion increases as you travel along the surface farther from the light source. This distortion is an unavoidable property of map projection. Although many different map projections exist, they all introduce distortion in one or more of the following measurement properties:

Distortion will vary in at least one of each of the above properties depending on the projection used, as well as the scale of the map, or the spatial extent that is mapped. Whenever one type of distortion is minimized, there will be corresponding increases in the distortion of one or more of the other properties.

There are names for the different classes of projections that minimize distortion.

- Those that minimize distortion in shape are called
**conformal**. - Those that minimize distortion in distance are known as
**equidistant**. - Those that minimize distortion in area are known as
**equal-area**. - Those minimizing distortion in direction are called
**true-direction**projections.

It is appropriate to choose a projection based on which measurement properties are most important to your work. For example, if it is very important to obtain accurate area measurements (e.g., for determining the home range of an animal species), you will select an equal-area projection.

*Coordinate Systems*

Once map data are projected onto a planar surface, features must be referenced by a planar coordinate system. The geographic system (latitude-longitude), which is based on angles measured on a sphere, is not valid for measurements on a plane. Therefore, a Cartesian coordinate system is used, where the origin (0, 0) is toward the lower left of the planar section. The true origin point (0, 0) may or may not be in the proximity of the map data you are using.

Coordinates in the GIS are measured from the origin point. However, **false eastings** and **false northings** are frequently used, which effectively offset the origin to a different place on the coordinate plane. This is done in order to achieve several purposes:

- Minimize the possibility of using negative coordinate values (to make calculations of distance and area easier).
- Lower the absolute value of the coordinates (to make the values easier to read, transcribe, calculate, etc.).

In this image, Washington state is projected to State Plane North (NAD83). All of the locations on the map are now referenced in Cartesian coordinates, where the origin lies several hundred miles off the Pacific coast.

Some measurement framework systems define both projections and coordinate systems. For example, the Universal Transverse Mercator (UTM) system, commonly used by scientists and Federal organizations, is based on a series of 60 transverse Mercator projections, in which different areas of the earth fall into different 6-degree zones. Within each zone, a local coordinate system is defined, in which the X-origin is located 500,000 m west of the central meridian, and the Y-origin is the south pole or the equator, depending on the hemisphere. The State Plane system also defines both projection and coordinate system.

The two most common coordinate/projection systems you will encounter in the USA are:

The state plane system includes different projections for each state, and frequently different projections for different areas *within* each state. The State Plane system was developed in the 1930s to simplify and codify the different coordinate and projection systems for different states within the USA.

Three conformal projections were chosen: the Lambert Conformal Conic for states that are longer in the east-west direction, such as Washington, Tennessee, and Kentucky, the Transverse Mercator projection for states that are longer in the north-south direction, such as Illinois and Vermont, and the Oblique Mercator projection for the panhandle of Alaska, because it is neither predominantly north nor south, but at an oblique angle.

To maintain an accuracy of 1 part in 10,000, it was necessary to divide many states into multiple zones. Each zone has its own central meridian and standard parallels to maintain the desired level of accuracy. The origin is located south of the zone boundary, and false eastings are applied so that all coordinates within the zone will have positive X and Y values. The boundaries of these zones follow county boundaries. Smaller states such as Connecticut require only one zone, whereas Alaska is composed of ten zones and uses all three projections.

## Image overlay with black background using python numpy/ opencv

I have a task in which I have to do something very similar to Zoom immersive view. The idea is to segment out person from the image frame and put him/her to some other background like a concert hall or something.

Now, I am able to segment out person from the image using some Deep learning algorithm, through which I get image of the form shown below:

Here's the code which does this:

Now, The actual image which corresponds to this detected mask has random background. What I want is, to overlay these two images in such a way that, In the resulting image, I get black as background, but in the detected region (white part in the above image) I want to put the original Image back. So, In the end, it should look like, person is standing in black background. How do I achieve this?

What I have is, an API ( MODEL.run(frame) line) through which, when I feed my Image, I get seg_mask image as shown above. I do not know the implementation of the Deep learning network, not that I am interested to know in the first place. Consider mask's shape and original Image's shape to be equal.

I've thought of normalizing the mask and then multiplying with the original image, so the background pixels would become all 0s, and the rest will remain as it is. But I'm not sure whether this is a correct approach, or better [efficient] approaches are possible or not.

## Classification of Projections

A fundamental projection classification is based on the type of projection surface onto which the globe is conceptually projected. The projections are described in terms of placing a gigantic surface in contact with the earth, followed by an implied scaling operation. These surfaces are cylindrical (e.g. Mercator), conic (e.g., Albers), or azimuthal or plane (e.g. stereographic). Many mathematical projections, however, do not neatly fit into any of these three conceptual projection methods. Hence other peer categories have been described in the literature, such as pseudoconic (meridians are arcs of circles), pseudocylindrical (meridians are straight lines), pseudoazimuthal, retroazimuthal, and polyconic.

Another way to classify projections is according to properties of the model they preserve. Some of the more common categories are:

- Preserving direction (
*azimuthal*), a trait possible only from one or two points to every other point. - Preserving shape locally (
*conformal*or*orthomorphic*). - Preserving area (
*equal-area*or*equiareal*or*equivalent*or*authalic*). - Preserving distance (
*equidistant*), a trait possible only between one or two points and every other point. - Preserving shortest route, a trait preserved only by the gnomonic projection.

NOTE: Because the sphere is not a developable surface, it is impossible to construct a map projection that is both equal-area and conformal.

There are also times when working with large scales, such as districts or provinces within countries, that distortion doesn't play a significant role, in which any projection that is centered on the area of interest is acceptable.

## LiDAR Data Attributes: X, Y, Z, Intensity and Classification

LiDAR data attributes can vary, depending upon how the data were collected and processed. You can determine what attributes are available for each lidar point by looking at the metadata. All lidar data points will have an associated X,Y location and Z (elevation) values. Most lidar data points will have an intensity value, representing the amount of light energy recorded by the sensor.

Some LiDAR data will also be "classified" -- not top secret, but with specifications about what the data are. Classification of LiDAR point clouds is an additional processing step. Classification simply represents the type of object that the laser return reflected off of. So if the light energy reflected off of a tree, it might be classified as "vegetation". And if it reflected off of the ground, it might be classified as "ground".

Some LiDAR products will be classified as "ground/non-ground". Some datasets will be further processed to determine which points reflected off of buildings and other infrastructure. Some LiDAR data will be classified according to the vegetation type.

## Usage

This tool only updates the existing coordinate system information—it does not modify any geometry. If you want to transform the geometry to another coordinate system, use the Project tool.

The most common use for this tool is to assign a known coordinate system to a dataset with an unknown coordinate system (that is, the coordinate system is "Unknown" in the dataset properties). Another use is to assign the correct coordinate system for a dataset that has an incorrect coordinate system defined (for example, the coordinates are in UTM meters but the coordinate system is defined as geographic).

When a dataset with a known coordinate system is input to this tool, the tool will issue a warning but will execute successfully.

All feature classes in a geodatabase feature dataset will be in the same coordinate system. The coordinate system for a geodatabase dataset should be determined when it is created. Once it contains feature classes, its coordinate system cannot be changed.

I have an action that does this:

When I run this action I'm left with New document window . The width and height in the window are the clipboard image dimensions = your objects/layers dimensions.

You then can press Esc to close the window.

( On windows just think of the Cmd as Ctrl )

You can make a selection of the layer for example by ctrl or cmd clicking the layer thumbnail and then looking at the info panel F8 , it will show you the dimensions of the selection.

From the upper right corner where you can see the arrow pointing down, you can find the options and within there you can set the ruler unit to pixels or what ever you want it to show.

Use Free transform Ctrl + T and when free transform is active, go check the Info panel F8 as shown above. This works even if the object is outside the document area.

Here's another answer that is slightly related: How to measure the distances in .psd

Especially the bottom part of the answer that lists methods to exporting layer styles as css, which includes width and height, of course.

## A Master Class in Construction Plans: Blueprints, Construction Safety Plans, and Quality Plans

A construction plan shows what you intend to build and what it will look like when you complete it. There are a variety of names for construction plans: blueprints, drawings, working drawings, and house plans. To the uninitiated, construction plans, with their many unusual symbols, can be daunting. As with any complex document, construction plans require skill to decipher.

This guide covers all the different types of construction plans, including examples, samples, helpful templates, checklists, and worksheets. We will explain how to get started with construction plans and discuss construction safety and quality plans. You’ll be a pro before you know it.

### What Is a Construction Plan? Definition, Uses, and History

Construction plans differ from maps, which cover much larger areas and have much larger scale ratios. Rather, a typical construction plan depicts only one structure and its parts or sections. By changing perspectives and details, it can do so in a number of ways.

Construction drawings also fill an important role in the overall construction planning process. Building departments and local governments must review plans before they will issue construction or renovation permits. Planners estimate building material and labor costs based on plans. In the pre-construction planning and scheduling phase, contractors use plans to create work breakdowns and schedule construction tasks. Once construction gets underway, drawings guide the work.

As physicist John Swain writes for the Boston Globe, blueprints originated after an 1861 discovery by French chemist Alphonse Louis Poitevin. He found that the chemical ferro-gallate, derived from gum, could permanently turn a vivid shade of blue when exposed to strong light. To create a blueprint, one would first place the translucent paper of an architectural drawing over paper coated with unexposed ferro-gallate. Then, they would expose the paper layering to strong natural light. As light passed through the translucent top sheet, turning the ferro-gallate sheet beneath it blue (except for where the drawn lines on the top sheet prevented light from passing through to the bottom sheet), the chemical combination would reproduce a complex, finely detailed drawing in minutes.

This process was called contact printing, and the result was a *blueprint*: a white-lined, blue sheet of paper that formed a drawing. Blueprints cost a fraction of the money and time that other contemporary reproduction techniques did, so they quickly gained popularity among not only architects, but also scientists and artists who wanted to quickly reproduce complex diagrams.

True blueprints fell out of use in the 1950s. The name stuck, however, and today we continue to call complex design drawings blueprints. Of course, since the mid 20th century, architectural drawings have undergone several evolutions. With CAD (computer-aided design) software, we can now easily visualize them in 3D with varying levels of detail and from a variety of perspectives.

CAD software simplifies the architect’s work considerably. Blueprints’ background color made them very difficult to write on, and it’s much easier to make design changes digitally rather than on paper.

Though modern construction plans vary greatly in scale and complexity, representing everything from small residential to large commercial projects, all construction plans comprise the same essential elements. All buildings, no matter how complex, consist of structural components, mechanical systems, and finishes.

A construction plan will provide the same kind of information regardless of the size or complexity of a project. For example, a floor plan will provide a bird’s eye view of room dimensions and installations regardless of whether it’s drawn for an apartment or a convenience store, and a mechanical plan might detail mechanical systems for either a kitchen or a laboratory. If you can read one, you can read the other only the level of complexity will vary.

Construction plans are different from a construction company’s business plans, which tell little about specific construction projects and more about how a company wants to develop its business. Construction plans also differ from specifications: A construction plan tells you *what* you will build, while specifications tell you *how* you build it.

Specifications will include information on materials you use, installation techniques, and quality standards. While most designers and architects will follow these methods for presenting information, others will annotate specs on construction plans, so the difference isn’t always clear cut. If the information in the specifications conflicts with that of the plans, the usual practice is to follow the specs over the plan.

General contractors, subcontractors, and tradesmen must have a deep knowledge of plan reading, and owners of large commercial projects will want to understand at least the broad strokes of a plan. Small project owners have an advantage if they are familiar with construction plans because they can understand exactly what the builders are going to be build. If you’re a homeowner and you don’t understand the architect or designer depicts the project, ask them so you’re on the same page *before* construction gets underway.

In fact, the professionals at HomeBuildingSmart recommend that you familiarize yourself with house plans before beginning a construction project, so you know what your tastes are and can provide useful input as the architect creates your construction plan. Remember, you can modify plans, but you can’t undo construction. So, iron out the details while they’re still only on paper.

Blueprints can seem arcane when you’re starting out, but with practice, reading them will get easier. So, if you’re a project owner, don’t shy away from construction plans: Make sure you understand what’s going on with your project.