planesmetoder

Planesmetoder is a term used in several Nordic languages to describe methods for working with planar surfaces in two- or three-dimensional space. They cover mathematical, computational, and applied techniques for modeling, detecting, fitting, and manipulating planes, as well as for projecting points onto planes and computing intersections between planes.

In practice, planesmetoder are used to interpret and process 3D data, such as from point clouds generated by LIDAR or depth cameras, by identifying flat regions and fitting planes to sets of points. They also appear in cartography, surveying, computer vision, and computer-aided design, where planar representations are common and elevation may be treated separately.

Common methods include:

- Least-squares plane fitting, which minimizes the orthogonal distances from data points to a plane.

- Total least squares, which accounts for errors in all coordinates.

- Robust fitting, such as RANSAC, to handle outliers.

- PCA-based estimation of the plane normal, providing a simple normal vector from data covariance.

- Hough transform for detecting planes in noisy data.

- Projection, clipping, and computing intersections between planes.

A typical plane is represented by the equation ax + by + cz + d = 0, with the normal vector n = (a, b, c). Planesmetoder thus revolve around estimating this model from data, evaluating fit quality, and applying geometric operations on planes and their intersections.

The term is used across disciplines with field-specific nuances, and in some contexts may be related to or contrasted with planimetric methods that focus on 2D representations without elevation. See also plane geometry, plane fitting, point-cloud processing, and the Hough transform.

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