u32-SIMPLE ALGORITHMS I - INTERSECTION OF LINES

u32-SIMPLE ALGORITHMS I - INTERSECTION OF LINES - UNIT 32...

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Sheet1 Page 1 UNIT 32 - SIMPLE ALGORITHMS I - INTERSECTION OF LINES <toc.html#UNIT32> UNIT 32 - SIMPLE ALGORITHMS I - INTERSECTION OF LINES Compiled with assistance from David H. Douglas, University of Ottawa and David M. Mark, State University of New York at Buffalo # A. INTRODUCTION <#SEC32.1> # B. DEFINITIONS <#SEC32.2> * Algorithms <#SEC32.2.1> * Heuristics <#SEC32.2.2> # C. SIMPLEST CASE <#SEC32.3> * Question <#SEC32.3.1> * Procedure <#SEC32.3.2> * Solution <#SEC32.3.3> * General form <#SEC32.3.4> * Simple program <#SEC32.3.5> # D. SPECIAL CASES <#SEC32.4> * Vertical lines <#SEC32.4.1> * Parallel lines <#SEC32.4.2> * Solution <#SEC32.4.3> # E. COMPLEX LINES <#SEC32.5> * Minimum enclosing rectangle <#SEC32.5.1> * Monotonic sections <#SEC32.5.2> * Sorting lines <#SEC32.5.3> # REFERENCES <#SEC32.6> # DISCUSSION AND EXAM QUESTIONS <#SEC32.7> # NOTES <#SEC32.8> UNIT 32 - SIMPLE ALGORITHMS I - INTERSECTION OF LINES Compiled with assistance from David H. Douglas, University of Ottawa and David M. Mark, State University of New York at Buffalo A. INTRODUCTION <#OUT32.1> * the intersection of two lines is a critical operation in GIS o is used in polygon overlay operations, merging and dissolving polygons and lines o is the basis for point in polygon operations and critical

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Sheet1 Page 2 for sliver removal * therefore, an efficient algorithm to determine the intersection of two lines is very important in any GIS. * GIS algorithms for complex processes are often built up from simple ones o this section will review a few simple algorithms, later sections will show how they can be built up into complex operations * the first operation here determines if two lines cross o begin by examining the algorithm for two straight lines, then go on to two complex lines or polygons. o eventually will see that this algorithm forms the core of numerous GIS operations, including the point in polygon and polygon overlay processes. * the algorithm illustrates one of the principles of this type of programming, that there are numerous special cases which have to be dealt with. B. DEFINITIONS <#OUT32.2> Algorithms <#OUT32.2.1> * an algorithm is a procedure consisting of a set of unambiguous rules which specify a finite sequence of operations that provides the solution to a problem, or to a specific class of problems * each step of an algorithm must be unambiguous and precisely defined o the actions to be carried out must be rigorously specified for each case * an algorithm must always arrive at a problem solution after a finite number of steps o this must also be a reasonable number of steps * every meaningful algorithm provides one or more outputs * it is preferable that the algorithm be applicable to any member of a class of problems rather than only to a single problem * in general, the cost of obtaining a solution increases with the
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This note was uploaded on 10/05/2010 for the course GEO 591 taught by Professor Davidm.mark during the Fall '10 term at SUNY Buffalo.

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u32-SIMPLE ALGORITHMS I - INTERSECTION OF LINES - UNIT 32...

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