1. The automation of generalized curves method presentation on the map at any scales Prof. Tadeusz Chrobak AGH University of Science and Technology Poland

2. The subject of the presentation Definition of curves simplifying parameters, which determine generalization thresholds at any edited map scales, which are: simplifying, smoothing, symbolization, elimination.

3. The generalization thresholds distinguishing In the curves simplifying process conducted by the objective method converted curve maintains statistic distribution properties.

4. Probability density function of normal – f(x) and normalized – f(u) distribution

5. The generalization thresholds distinguishing...continuation Generalization thresholds are defined by dependance: where: n 0 – the number of the original curve points, n i – the number of points after generalization, c – the number of process invariable points, k – the factor, where k = 1, 2, 3,

6. The generalization thresholds distinguishing...continuation The generalization thresholds can be distinguished depending on standard deviation: 1  - broken curve simplification, 2  - curves simplification with smoothing, 3  - closed curve symbolization or open curve elimination.

7. The generalization thresholds according to scale changing

8. Example No.Scalen0/c Added points Rejected points nimink=1k=2k=3 123456789 1 1:1000133/1600133 1: 2000 11133 1: 3000 11133 1: 4000 22133-20No 1: 5000 1652977Yes 1: 6000 12727325 1:7000 58355 1:8000 19242 1:9000 0943917 1:10000 1105290 Yes 1:25000 16 Yes 1:50000 16 1:100000 16

9. The definition of the generalization method Objective factors of the method: drawing recognizability – the elementary triangle, points hierarchy, resulting from relative extrema, added points used to obtain optimal conformity and shape of generalized curves. Data accuracy after curves transformation is conserved, apart from scales range.

10. The definition of the generalization method...continuation Conservation of topology and objects classes. Usefulness for both open and cloesd curves.

11. The objective method functioning

12. Examples 1. Open curves generalization. 2. Closed curves generalization. 3. Statistics of an open curve nodes simplification when map scale is changing from 1:500 to 1:500 000

13. Open curves generalization, while map scale is changing from 1:500 to 1:2000

14. Open curves generalization, while map scale is changing from 1:500 to 1:50000

15. 2.

16. Statistics of simplification of nodes on an open polygon when map scale is changed from 1:500 to 1:500 000 A set of data for the scale Number of nodes Data acquisition M 2 Number of nodes changed removed M 5 Number of nodes Changed removed M 10 Number of nodes changed removed M 25 Number of nodes changed removed M 50 Number of nodes changed removed M 100 Number of nodes changed removed M 200 Number of nodes changed removed M 300 Number of nodes changed removed M 400 Number of nodes changed removed M 500 Number of nodes changed removed M 0 =1:500 161 nodes source data 159 0 2 117 0 44 74 0 87 29 0 132 17 0 144 9 0 152 4 0 157 3 0 158 3 0 158 2 0 159 M 2 =1:2000 159 nodes processed data - 117 0 42 74 0 85 29 0 130 17 0 142 9 0 150 4 0 155 3 0 156 3 0 156 2 0 157 M 5 = 1 : 5000 117 nodes processed data - - 73 1 44 29 0 88 17 0 100 9 1 108 4 0 113 3 0 114 3 0 114 2 0 115 M 10 = 1 :10000 74 nodes processed data - - - 28 0 46 17 2 x 57 9 1 65 4 1 70 3 0 71 3 1 71 2 0 72 M 25 = 1 :25000 29 nodes processed data - - - - 16 1 13 9 1 20 4 1 25 3 0 26 2 0 27 2 0 27 M 50 = 1 : 50000 17 nodes processed data - - - - - 819819 4 1 13 3 0 14 2 0 15 2 0 15 M 100 = 1 : 100000 9 nodes processed data - - - - - - 415415 306306 207207 207207 M 200 = 1 : 200000 4 nodes processed data - - - - - - - 301301 202202 202202 M 300 = 1 : 300000 3 nodes processed data - - - - - - - - 201201 201201 M 400 = 1 : 400000 3 nodes processed data - - - - - - - - - 201201

17. Conclusions The open and closed curves (simplified by the objective method) generalization thresholds can be defined by the based on the mathematical statistics method. The threshold defining correctness is proved by the conformity of generalization thresholds scales and the maximum of added points scale within 1σ range.

18. Thank you for your attention