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71 lines
2.4 KiB
Markdown
71 lines
2.4 KiB
Markdown
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# Functions for working with geographical coordinates
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## greatCircleDistance
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Calculate the distance between two points on the Earth's surface using [the great-circle formula](https://en.wikipedia.org/wiki/Great-circle_distance).
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```
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greatCircleDistance(lon1Deg, lat1Deg, lon2Deg, lat2Deg)
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```
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**Input parameters**
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- `lon1Deg` — Latitude of the first point in degrees. Range: `[-90°, 90°]`.
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- `lat1Deg` — Longitude of the first point in degrees. Range: `[-180°, 180°]`.
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- `lon2Deg` — Latitude of the second point in degrees. Range: `[-90°, 90°]`.
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- `lat2Deg` — Longitude of the second point in degrees. Range: `[-180°, 180°]`.
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Positive values correspond to North latitude and East longitude, and negative values correspond to South latitude and West longitude.
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**Returned value**
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The distance between two points on the Earth's surface, in meters.
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Generates an exception when the input parameter values fall outside of the range.
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**Example**
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```sql
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SELECT greatCircleDistance(55.755831, 37.617673, -55.755831, -37.617673)
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```
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```text
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┌─greatCircleDistance(55.755831, 37.617673, -55.755831, -37.617673)─┐
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│ 14132374.194975413 │
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└───────────────────────────────────────────────────────────────────┘
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```
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## pointInEllipses
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Checks whether the point belongs to at least one of the ellipses.
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```
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pointInEllipses(x, y, x₀, y₀, a₀, b₀,...,xₙ, yₙ, aₙ, bₙ)
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```
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**Input parameters**
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- `x` — Latitude of the point.
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- `y` — Longitude of the point.
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- `xᵢ, yᵢ` — Coordinates of the center of the `i`-th ellipsis.
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- `aᵢ, bᵢ` — Axes of the `i`-th ellipsis in meters.
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The input parameters must be `2+4⋅n`, where `n` is the number of ellipses.
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**Returned values**
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`1` if the point is inside at least one of the ellipses; `0`if it is not.
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**Examples:**
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```sql
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SELECT pointInEllipses(55.755831, 37.617673, 55.755831, 37.617673, 1.0, 2.0)
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```
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```text
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┌─pointInEllipses(55.755831, 37.617673, 55.755831, 37.617673, 1., 2.)─┐
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│ 1 │
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└─────────────────────────────────────────────────────────────────────┘
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```
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