## Scientific Explorations: In-Depth Studies

## An In-Depth Tech Study By SGIS Desktop

# Enhancing GIS Precision: Millimeter-Exact Gaus-Krüger to WGS84 [WGS84 to Gaus-Krüger] Conversions in SGIS Desktop

## Introduction

Coordinates are numerical values that precisely pinpoint a specific location in space. In the context of geography and mapping, “space” is closely linked to the Earth and is used to represent areas of interest.

When we’re dealing with spatial relationships, especially over larger distances, we commonly express these relationships using coordinates on an ellipsoid. An ellipsoid is a mathematical shape that closely approximates the Earth’s geoid, which is a physical model representing the Earth’s surface as the average height of all seas and oceans influenced by gravity.

Ellipsoidal coordinates consist of two primary components: geographic latitude and geographic longitude.

**Geographic Latitude**: This represents the angle formed by the normal line to the ellipsoid at a specific point with the plane of the Equator. In simpler terms, it measures how far north or south a point is from the Equator.**Geographic Longitude**: This angle is formed by the normal line to the ellipsoid with the plane of the prime meridian, often referencing the Greenwich Meridian. It determines how far east or west a point is from the Prime Meridian.

Geographic longitude is commonly referred to as “Longitude,” and it can be measured both eastward and westward from the Greenwich Meridian, with positive values indicating eastward and negative values indicating westward. Conversely, geographic latitude is known as “Latitude,” measured positively northward from the Equator and negatively southward.

These coordinates are expressed either in degrees, minutes, seconds, and fractions of seconds, or as decimal degrees.

Cartographic projections are methods used to depict the Earth’s surface on flat paper or in two dimensions. They serve an essential role in mapping and representation. Let’s explore a classification of these projections:

**Conformal Projections**: These projections maintain the shape of small geometric elements, ensuring that angles between lines are preserved. In simpler terms, small features on the Earth’s surface look similar on the map.**Equal-Area Projections**: These projections ensure that the size of areas remains accurate. In other words, the relative proportions of regions are maintained. This is especially useful when comparing the sizes of different geographic areas.**Equidistant Projections**: These projections maintain the accuracy of distances in specific directions. This can be valuable for measuring distances between points on a map.

Another way to classify cartographic projections is based on the shape of the normal map grid:

**Conic Projections****Cylindrical Projections****Azimuthal Projections****Pseudo-Cylindrical Projections****Pseudo-Conic Projections****Pseudo-Azimuthal Projections****Polyconic Projections****Circular Projections**

Each of these projection types has its unique characteristics and advantages, making them suitable for specific mapping purposes. Choosing the right projection is crucial in ensuring accurate and meaningful representation of geographic data.

## Practical Example: Approach and Solution

Transformation tasks in geospatial work can be complex, involving various scenarios like moving data between different ellipsoids, converting from ellipsoids to map projections, transitioning between projections and ellipsoids, or even switching between different map projections. These operations often require specialized software for accurate execution.

However, SGIS Desktop simplifies this process by incorporating functions for the most commonly needed coordinate system transformations. This software primarily deals with GIS (Geographic Information System) data, which encompasses data with point, line, polyline, or polygon geometries. In practical terms, this means that when working with geographic data, there’s often a need to transform the geometry from one coordinate system to another.

In SGIS Desktop, the concept of a “coordinate system” is established through the “Coordinate System > Set Coordinate System” feature. This function consists of three distinct sections for defining your coordinate system:

** General:** This section encompasses parameters and names that are crucial in defining the coordinate system’s properties.

** Ellipsoid Data:** Here, you have the ability to specify the ellipsoid and its defining parameters. You simply select an ellipsoid and its associated parameters from a convenient dropdown list.

** Projection Data:** Within this section, you can choose one of three projection types from the dropdown list:

- Gauss Kruger – Transverse Mercator
- Universal Transverse Mercator – UTM
- Lambert Conformal Conic

Additionally, in this section, you can provide values for the central meridian, initial latitude, false easting and northing, and a scale factor. If you opt for the Lambert Conformal Conic projection, you also define standard parallel 1 as the southern parallel and standard parallel 2 as the northern parallel.

## Configuring Datum Transformation Parameters in SGIS Desktop

Within the “**Coordinate System > Datum Transformation Parameters**” form, you’ll find a list of predefined parameters available for selection. Additionally, you have the option to input new parameters or append them to the existing list. These parameters are generated using the Bursa-Wolf 7-parameter Helmert transformation, derived from points that are known in both coordinate systems. Importantly, when entering these parameters, they should be preceded by a negative sign.

Now, let’s dive into the transformation process. You can perform this transformation with or without a datum transformation. When we talk about datum transformation, we’re referring to the conversion of Cartesian XYZ coordinates from one ellipsoid to Cartesian coordinates on another ellipsoid. This transformation is accomplished using the selected transformation parameters.

It’s essential to note that this process assumes that the two ellipsoids are relatively similar in orientation, with minor translations and a negligible scale factor difference.

**Gauss-Krüger Projection**: This projection is a conformal, transverse, cylindrical method used to divide the Earth into meridian zones. It’s known for preserving angles accurately and is adopted as the national projection by many countries.**UTM Projection**: The Universal Transverse Mercator projection is essentially a modified Gauss-Krüger projection tailored for global applications.**Lambert Conformal Conic Projection**: This projection ensures that angles remain consistent and is widely embraced worldwide. It’s particularly useful for areas that stretch in an east-west direction.

## Example: Transforming coordinate data in SGIS Desktop

Consider this scenario: you’ve imported a file containing polygons or parcels. You’ve selected the first parcel from the list and exported the coordinates of its corner points in the Gauss-Krüger projection, represented in geodetic notation as follows:

Now, within SGIS Desktop, navigate to **Coordinate System > Coordinate Transformation**. Here, specify GK7 in the “Existing Coordinate System” (an alias for the ellipsoid and projection definitions) and WGS84 in the “New Coordinate System.” This represents a datum transformation between two ellipsoids, requiring the definition of transformation parameters

From the “Parameters Of Transformation” list, select **PRONeg** (an alias for 7 parameters encompassing 3 translations, 3 rotations, and a scale factor). The software will perform the transformation on the coordinates of the active layer. Upon clicking the “Transform” button, the function executes, resulting in the layer’s content shifting to the new coordinates on the screen.

I have reselected the first parcel, and here are its coordinates:

Performing the reverse transformation, which involves converting from ellipsoidal coordinates in WGS84 to projected coordinates in the Gauss-Kruger projection, and then selecting the first parcel once more, yields the following coordinate values:

As you can observe, the transformation between these coordinate systems, both forward and backward for verification, preserves the initial coordinates down to the millimeter. This demonstrates the accuracy of the transformation process.