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i need a code
the first code must complete a circle and form a minimum distance route for a TSP. the second code should improve the result of the first code by simulated annealing with 2 opt. Again thank you for the help.
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What is the shortest most direct route between any two points on te surface of the earth?
Assuming the earth to be a perfect sphere, the shortest distance is an arc of the great circle. The two places and the centre of the earth define a plane. The great circle is the circle formed by the intersection of that plane and the surface of the earth. The shortest route between the two places is the smaller of the two arcs along that circle.
Why are great-circle paths commonly used in navigation?
Because on a globe, a great-circle route is the shortest route between two places.
The distance from one point to another?
It depends on the route that you take. There is nothing in the question to suggest that the distance of interest is the shortest distance. In real life, the quickest route is not necessarily the shortest since travelling on highways may be faster even if longer. In such cases the relevant distance may not be the shortest. Also, you might wish to take the "scenic" route. In any built-up area the shortest meaningful distance between two points will not be "as the crow flies": the taxicab metric (for example 3 blocks East and 4 blocks North), which was developed by Minkowsky, is more appropriate. On the surface of a sphere, such as the Earth, the shortest distance is an arc of the great circle. In most cases this is not the straight line on a map.
How many inches in a 12 inch diameter circle?
-- 12 inches across the circle, along any route that passes through the center -- 6 inches along any radius -- 12 pi = 37.7 inches (rounded) around the circle's curvy line
What is the converse of a straight-line distance between two points?
There is not a converse, as such, but there are other metrics that may be applicable in different circumstances. One such is the Manhattan distance (deeloped by Minkovsky) which uses the grid pattern of roads as a way to measue distances. On the non-planar surface, such as that of the earth, the shortest distance between two points will be along the "Great Circle" passing through the two points. In some situations people may be interested in the fastest route between two points even if it is not the shortest straight line distance.
