Line generalization in the SDC include four algorithms: Ramer–Douglas–Peucker, Nth vertex, radial distance and perpendicular distance. All these algorithms retain the first vertex. The Ramer–Douglas–Peucker algorithm starts from retaining also the last vertex. Then, the vertex most distant from the line between the previous and next retained vertex is found and if the distance is larger than the tolerance, is added to the list of retained vertices. The simplification is repeated until all vertices are within tolerance of the simplification. Also the perpendicular distance algorithm compares pointtosegment distances to the given tolerance. Unlike the Ramer–Douglas–Peucker algorithm, it checks point distances to the line between previous and next vertex. All vertices whose distance is smaller than the given tolerance are removed. The Nth vertex algorithm keeps only each Nth point. The radial distance algorithm keeps the first vertex and removes vertices which are closer than the radial tolerance to the previous kept vertex. Overview of line generalization methods can be found e.g in www.codeproject.com, and in Wikipedia. 
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ID  P  Question or exercise  

3935  3  The line in the attached file represents antique road from France to Col de Tende (Colle di Tenda) pass in Alps. The elevation difference per 1820 m planar distance is 720 m, which means 22.7 degrees angle on a straight line. See photos of this pass. This line should be generalized for cartographic presentation.

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3950  2  The attached file contains automatically recorded track points from shrubby cinquefoil Potentilla fruticosa observation routes in summer 2014. The GPS receiver was switched off while a car was used to move from one observation site to another. Let us take 200 m between sequential track points as the critical distance to separate tracks crossed onfoot. If the distance between sequential track points is over 200 m, then this span was driven.

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