Line Simplification Pseudocodes

Line simplification is a process used to reduce the complexity and number of vertices in a polyline or polygon while preserving its overall shape and general characteristics. This can be useful for a variety of applications, including cartography, GIS, and computer graphics.

There are several algorithms that can be used for line simplification, including the Douglas-Peucker algorithm, the Visvalingam-Whyatt algorithm, and the Reumann-Witkam algorithm.

Pseudocode is a way to describe an algorithm using a combination of natural language and programming constructs. It is often used to describe algorithms in a way that is easy to understand for both programmers and non-programmers. Here is an example of pseudocode for the three main line simplification algorithms:

Douglas-Peucker algorithm:

procedure DouglasPeucker(PointList[1...n], tolerance: real)
    dmax := 0
    index := 0
    for i := 2 to n - 1 do
        d := PerpendicularDistance(PointList[i], Line(PointList[1], PointList[n]))
        if d > dmax then
            index := i
            dmax := d
    end for
    if dmax > tolerance then
        recResults1 := DouglasPeucker(PointList[1...index], tolerance)
        recResults2 := DouglasPeucker(PointList[index...n], tolerance)
        return concatenate(recResults1, recResults2)
    else
        return Line(PointList[1], PointList[n])
    end if
end procedure

Visvalingam-Whyatt algorithm:

procedure VisvalingamWhyatt(PointList[1...n], tolerance: real)
    for i := 1 to n - 2 do
        area := Area(PointList[i], PointList[i+1], PointList[i+2])
        if area < tolerance then
            remove PointList[i+1]
    end for
    return PointList
end procedure

Reumann-Witkam algorithm:

procedure ReumannWitkam(PointList[1...n], tolerance: real)
    for i := 1 to n-1 do
        d:= distance(PointList[i], Line(PointList[1], PointList[n]))
        if d > tolerance then
            remove PointList[i]
    end for
    return PointList
end procedure

In the pseudocode above, the Douglas-Peucker algorithm recursively divides the input line into smaller segments, using the point with the greatest perpendicular distance from the line as the dividing point. The Visvalingam-Whyatt algorithm iteratively removes the point with the smallest “area of effect” in the line, and the Reumann-Witkam algorithm iteratively removes the points that minimize the total square distance between the original line and the simplified line.

It’s important to note that, this pseudocode is just a representation of the algorithm and it may not be executable on any specific programming language. But it gives an idea about the main steps of the algorithm, which can be translated into any specific programming language.