In land management and urban planning, accurately calculating land area for various types such as land use categories and parcels is crucial. Therefore, SuperMap provides multiple functions for calculating both planar area and ellipsoidal area of vector polygon data to meet diverse application scenarios. Planar area calculation is suitable for simple geometric shapes on a two-dimensional plane and is straightforward and fast. Ellipsoidal area calculation takes into account the curvature of the Earth's surface and is suitable for large-scale or high-precision area calculations. The following sections elaborate on the principles of these two methods and the tools and functions that implement these calculations.

Planar Area Calculation

Planar area, also known as geometric area, is calculated directly using the x and y coordinates of a projected coordinate system based on Euclidean geometry principles. As it does not consider the Earth's curvature, significant errors may occur.

• Geographic Coordinate System: To reduce errors, data in a geographic coordinate system is first projected onto an Albers projected coordinate system, and then the planar area is calculated under this projection. This is because the Albers equal-area projection preserves area relationships of regions, avoiding area distortion caused by map projection. However, it should be noted that significant deviations may still occur if the span between two consecutive nodes is large.
• Projected Coordinate System, Custom Coordinate System, and No Coordinate System: Planar area is calculated directly.

Implementation Tools and Functions:

• Automatic Area Calculation: When importing, copying, or adding new polygon data in iDesktopX, the planar area is automatically calculated and populated into the SmArea system field.
• Update Area in Workspace: For datasets lacking the SmArea field, the area can be updated in the iDesktopX workspace. When the dataset is in a projected coordinate system, the planar area will be calculated.
• Map Area Measurement: Used in iDesktopX to directly measure the area between points to be measured on the map. It supports calculating the planar area of vector data. For data in a geographic coordinate system, it is first converted to an Albers projected coordinate system before calculation.

Ellipsoidal Area Calculation (Geodesic Area)

Ellipsoidal area is called geodesic area in SuperMap products. It refers to the area calculated on an Earth ellipsoid model. Since the Earth is not a perfect sphere but an ellipsoid with slight flattening differences, using an ellipsoid model can more accurately reflect the characteristics of the Earth's surface and provide more accurate area calculation results. As a calculation method for ellipsoidal area, geodesic area focuses on using geodesics (the shortest connecting line between two points on the Earth's ellipsoid surface) as boundaries to calculate the area.

Resampling Methods:

• Node Densification Method: When calculating geodesic area, if each edge is replaced with a geodesic, the computational complexity is very high. To simplify the calculation, the node densification method is used to simulate geodesic area. Referring to the specifications for calculating ellipsoidal area in the second and third national land surveys, temporary nodes are uniformly added for side lengths exceeding 70 meters. After node densification is completed, the ellipsoidal area is calculated. By densifying nodes, long edges can be split into multiple shorter line segments. The shorter the line segment, the more similar the geodesic distance and the geometric distance become. This approach allows for a simpler and more efficient method to approximate the geodesic length of each segment, effectively reducing computational complexity while keeping errors within an acceptable range.
• Gauss Projected Coordinate System Processing: For data in the Gauss_Kruger (Xian 1980) and Gauss_Kruger (CGCS2000) projected coordinate systems, node densification is performed first. Then, following the formulas for theoretical map sheet area and parcel ellipsoidal area calculation provided in the "Technical Regulations for the Third National Land Survey," the Gaussian plane coordinates of any closed parcel are transformed into corresponding geodetic coordinates on the ellipsoid using the inverse Gaussian projection transformation model. Subsequently, the ellipsoidal area is calculated using the area calculation model for any trapezoidal block on the ellipsoid surface.

Implementation Tools and Functions:

• View Polygon Object Properties on Map: When browsing a map in iDesktopX, selecting a single polygon object allows you to view its ellipsoidal area value in the properties under the geo section.
• Toolbox - Data Processing - Vector - Compute Geometric Properties: Calculates geometric properties for a vector dataset. Selecting "geodesic area" will update the calculation results directly to the source dataset. You can choose an existing field or create a new field to store these attributes.
• Toolbox - Big Data Vector Management Tool - Basic Processing - Calculate Area: Suitable for large-scale data, capable of using a distributed cluster environment for computation. The calculation results are consistent with the geodesic area from the "Compute Geometric Properties" tool.
• Toolbox - Data Processing - Vector - Calculate Total Area: Used to calculate the total area of an entire vector dataset. The result is output as a numerical value to the execution log.

Comparison of Different Area Calculation Functions

Use the table below to clearly understand the resampling methods used by various area calculation functions under geographic coordinate systems, projected coordinate systems, and custom coordinate systems.

It is important to note that since any area calculation tool can hardly completely avoid errors, in practical applications, data factors and coordinate system conditions should be comprehensively considered to select an appropriate calculation method, ensuring the accuracy and reliability of the results.