# Krovak

## Description

The Krovak projection, also known as S-JTSK, is an oblique case of the Lambert conformal conic projection. It is based on one standard parallel. An azimuth parameter tilts the apex of the cone from the North Pole. A standard parallel, called a pseudo standard parallel, defines the shape of the cone. A scale factor is applied to the parallel to create a secant case.

The projection is used in Czechia and Slovakia and was designed by Josef Krovak in 1922. It is available in ArcGIS Pro 1.0 and later and in ArcGIS Desktop 8.1.0 and later.

## Projection properties

The subsections below describe the Krovak projection properties.

### Graticule

Krovak is an oblique conic projection. In general, the meridians and parallels are projected as complex curves. Only the meridian of the central longitude is projected as straight line. The pole closest to the apex of the cone is split and projected along the two straight edges of the fan-shape. The other pole appears as a point along the central longitude line. The coordinates are usually positive to the south and west. The graticule is symmetric across the central longitude line.

### Distortion

Krovak is a conformal map projection. It does not maintain true directions, but angles and shapes are maintained at infinitesimal scale. Scale and distances are accurate along the pseudo standard parallel if the scale factor is 1.0. If the scale factor is less than 1.0, there are two complex curves parallel to the pseudo standard parallel with accurate scale. Area, distance, and scale distortions increases rapidly away from these curves.

## Usage

The use of the Krovak projection is limited to large-scale mapping of areas that are obliquely oriented rather than following a north-south or east-west orientation. The Krovak projection is used primarily for topographic and other mapping in Czechia and Slovakia.

## Limitations

The implementation of the Krovack projection in ArcGIS does not display the whole range of the world. The antipodal point of the cone's apex cannot be projected. The pseudo standard parallels can be at any latitude, except they can't be set at opposite pseudo poles.

## Parameters

Krovak parameters are as follows:

• False Easting
• False Northing
• Pseudo Standard Parallel 1
• Scale factor
• Azimuth
• Longitude Of Center
• Latitude Of Center
• X Scale
• Y Scale
• XY Plane Rotation

## Sources

Kostelecký, J., Kostelecký, J., and Pešek, I. (2010). Metodika převodu mezi ETRF2000 a S-JTSK varianta 2. Prague: Stavební fakulta ČVUT v Praze, Výzkumný ústav geodetický, topografický a kartografický.

Kostelecký, J., Cimbálník, M., Provázek, J. and Zajíček, L. (1998). "Reference Coordinate System S-JTSK/95: Its Establishment in the Czech Republic." Proceedings of Research Works 1998. - Roč.44. - Zdiby: VÚGTK, 1998. - S.55-63. - ISBN 80-85881-10-1.

Talhofer, V. (2007). Základy matematické kartografie. Brno: Univerzita Obrany, Fakulta vojenských technologií.