#Mapinfo 10 intersection between circle how to#

If it isnвЂ™t clear that the area of the green region is indeed (x1 y2 вЂ“ x2 y1)/2, then read this. Now the first term is the following area, which is positive in our case: To see why this formula works, letвЂ™s rearrange it so it is in the formДЄ=(x1 y2 вЂ“ x2 y1)/2 + (x2 ењ“ вЂ“ x3 y2)/2 + (x3 y1 вЂ“ x1ењ“ )/2. Then you can compute the area by the formulaДЄ=(x1 y2 + x2 ењ“ + x3 y1 вЂ“ x2y1- x3 y2 вЂ“ x1ењ“)/2. LetвЂ™s assume we have a triangle with vertices (x1,y1), (x2,y2), and (x3,ењ“) as you go around the triangle counter-clockwise, as shown in the following figure: LetвЂ™s look at the case of a triangle, because all the essential logic appears there. Once we have done this, the algorithm to find the intersection between a polygon and a circle should be easy to understand.

#Mapinfo 10 intersection between circle how to#

10вЂ“13.First I will remind us how to find the area of a polygon. and Kozhechkin, V., On the new method of winter route accounting, Okhota Okhot. Priklonsky, S.G., The recalculation factor for the processing of winter tracking data for game animals by the tracks, Byull. Popper, K., Logika i rost nauchnogo znaniya (The Logic of Scientific Discovery), Moscow: Progress, 1983. Naumov, P.P., Problems of methodical support of resource accounting of game animals, in Klimat, ekologiia, selвЂ™skoe khoziaistvo Evrazii: materialy IV mezhdunadnoi nauchno-prakticheskoi konferentsii (Climate, Ecology, and Agriculture of Eurasia: Proceedings of IV International Scientific-Practical Conference), Irkutsk: Irkutsk. Naumov, P.P., How to deal with the problem of the introduction and implementation of techniques of winter trip for hunting animals (winter route counts 2001вЂ“2013), in Klimat, ekologiya, selвЂ™skoe khozyaistvo Evrazii: materialy III mezhdunarodnoi nauchno-prakticheskoi konferentsii (Climate, Ecology, and Agriculture of Eurasia: Proceedings of III International Scientific-Practical Conference), Irkutsk: Irkutsk. Kuzyakin, V.A., Winter route accounting: problems remained. Kuzyakin, V.A., Uchet chislennosti okhotnichвЂ™ikh zhivotnykh (Accounting the Number of Game Animals), Moscow: KMK, 2017. Kuzyakin, V.A., Results of modelling winter transect counts, in Zimnii marshrutnyi uchet okhotnichвЂ™ikh zhivotnykh (Winter Transect Counts of Game Animals), Moscow: TsNIL Glavokhoty RSFSR, 1983, pp. Kondratenkov, I.A., Some aspects of the theory of winter route counting of game animals, Biol. Kondratenkov, I.A., Improving the accuracy of game animal population censuses in small areas, Biol. 158вЂ“189.Д¬helintsev, N.G., Matematicheskie osnovy ucheta zhivotnykh (Mathematical Basis of Animal Censuses), Moscow: GU TsentrokhotkontrolвЂ™, 2000. All possible discrepancies in the estimates of the numbers of game animals determined by the WRC method with their actual values should be attributed to shortcomings in the direct organization of this count rather than to its mathematical justification.Д¬helintsev, N.G., Mathematical foundations of winter route accounting, in Zimnii marshrutnyi uchet okhotnichвЂ™ikh zhivotnykh (Winter Transect Counts of Game Animals), Moscow: TsNIL Glavokhoty RSFSR, 1983, pp. At present, there are no grounds for abandoning the practical use of winter route censuses for game animals. The mathematical justification of WRC has once again passed a simulation test, now with the means of geographical information systems and data from satellite navigators.

The results of our experiment made it possible to formulate a corollary arising from the fundamental properties of Euclidean geometry on the directly proportional dependence between the number of intersections between the lines of daily animal tracks and route lines and the product of the total lengths of these lines. Ninety-five different actual values of the proportionality coefficient were obtained for various locations of the tracks on the model territory no violations of the above-mentioned deduction have been found. In total, 19 electronic daily tracks of various animal species have been used. We selected a frequency of the route grid (the distance between parallel routes) for different tracks such that the total number of all intersections of a single track of all directions was not less than a thousand. Then, a grid of parallel routes oriented along 12В directions equally displaced relative to each other was applied to the model territory. The essence of our digital experiment was the following: in several places of the model territory (aВ circle 5 km in diameter), daily tracks of animals were placed. A simulation was carried out using the MapInfo software. In a model experiment, an attempt was made to falsify (refute) a deduction from the mathematical justification of winter route counting (WRC) of game animals, which is the mathematical expectation of the proportionality coefficient of this count being equal to ПЂ/2.