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MathGroup Archive 2003

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Concentric contours about the centroid, having the same length, and interior to an initial contour.

  • To: mathgroup at smc.vnet.net
  • Subject: [mg43954] Concentric contours about the centroid, having the same length, and interior to an initial contour.
  • From: gilmar.rodriguez at nwfwmd.state.fl.us (Gilmar Rodr?guez Pierluissi)
  • Date: Wed, 15 Oct 2003 04:59:31 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

I have a basic contour defined by:

In[1]:

contour = {{10545, 28012}, {10232, 28166}, {10027, 28218},
{9714, 28115}, {9354, 28166}, {9042, 28115}, {8785, 28064},
{8575, 27858}, {8160, 27858}, {7954, 27546}, {8108, 27238},
{8421, 27238}, {8836, 27079}, {9042, 26874}, {9247, 26510},
{9406, 26197}, {9611, 25992}, {9662, 25627}, {9560, 25268},
{9196, 25007}, {8939, 24750}, {8678, 24750}, {8421, 24386},
{8216, 24125}, {8160, 23919}, {8006, 23607}, {8006, 23401},
{7852, 23037}, {7749, 22832}, {7539, 22678}, {7179, 22678},
{6918, 22570}, {6713, 22468}, {6451, 22365}, {6036, 22365},
{5728, 22468}, {5677, 22104}, {5625, 21693}, {5625, 21483},
{5364, 21483}, {5159, 21950}, {5000, 22211}, {4846, 22519},
{4538, 22570}, {4641, 22160}, {4949, 21950}, {4949, 21642},
{5159, 21278}, {5313, 21068}, {5569, 20862}, {5569, 20708},
{5518, 20447}, {5415, 20190}, {5415, 19929}, {5313, 19565},
{5000, 19308}, {4743, 19308}, {4589, 19411}, {4431, 19565},
{4225, 19672}, {4020, 19621}, {3758, 19621}, {3758, 19359},
{4020, 19154}, {4328, 18944}, {4482, 18585}, {4897, 18739},
{5210, 18841}, {5364, 18426}, {5467, 18118}, {5625, 17754},
{5831, 17339}, {5625, 17026}, {5364, 16821}, {5056, 16667},
{4897, 16200}, {5000, 15887}, {5159, 15579}, {5107, 15318},
{4897, 15005}, {4538, 15005}, {4174, 15215}, {4020, 15420},
{4071, 15112}, {4277, 14851}, {4589, 14697}, {4897, 14594},
{4897, 14179}, {4897, 13866}, {4743, 13507}, {4795, 13143},
{4795, 12830}, {4692, 12363}, {4589, 12107}, {4589, 11794},
{4328, 11486}, {3964, 11327}, {3861, 10968}, {4020, 10604},
{3861, 10086}, {3810, 9670}, {3707, 9255}, {3446, 8737},
{3292, 8219}, {3343, 7804}, {3502, 7337}, {3189, 6977},
{2928, 6926}, {2620, 6870}, {2466, 6613}, {2256, 6147},
{2050, 6352}, {1948, 6613}, {1686, 6767}, {1481, 6716},
{1117, 6716}, {804, 6926}, {650, 6819}, {547, 6562},
{445, 6352}, {393, 5993}, {235, 5941}, {81, 5629},
{286, 5475}, {701, 5423}, {911, 5372}, {963, 5111},
{860, 4905}, {650, 4695}, {650, 4280}, {1014, 4126},
{1271, 3869}, {1686, 3659}, {2050, 3505}, {2466, 3402},
{2774, 3351}, {3086, 3454}, {3446, 3659}, {3861, 3710},
{4174, 3659}, {4589, 3710}, {5056, 3608}, {5313, 3244},
{5467, 2726}, {5677, 2469}, {5933, 2418}, {6195, 2208},
{6451, 1900}, {6503, 1484}, {6713, 1171}, {6815, 812},
{7179, 653}, {7488, 551}, {7800, 345}, {8057, 551},
{8267, 397}, {8575, 187}, {8836, 33}, {8836, 238},
{8626, 499}, {8524, 705}, {8472, 966}, {8626, 1171},
{8267, 1274}, {8216, 1069}, {8057, 966}, {7800, 1069},
{7539, 1171}, {7385, 1330}, {7282, 1690}, {7590, 1741},
{7642, 1900}, {7642, 2208}, {7800, 2469}, {7590, 2674},
{7282, 2572}, {7021, 2418}, {6815, 2418}, {6815, 2833},
{6918, 3038}, {7123, 3090}, {6918, 3244}, {6713, 3454},
{6605, 3556}, {6451, 3869}, {6713, 3972}, {7021, 4126},
{7385, 4228}, {6918, 4331}, {6713, 4438}, {6451, 4592},
{6195, 4228}, {5882, 4387}, {5728, 4695}, {5728, 5008},
{5625, 5475}, {5728, 5890}, {6143, 5890}, {6661, 5890},
{7072, 5941}, {6815, 6198}, {6400, 6198}, {6087, 6147},
{6246, 6511}, {6451, 6819}, {6713, 7080}, {6969, 7495},
{7231, 7495}, {7800, 7598}, {7436, 7752}, {7179, 7855},
{7072, 8168}, {6764, 8480}, {6713, 9050}, {6918, 9465},
{7123, 9824}, {7282, 10240}, {7590, 10968}, {8057, 11379},
{8318, 11794}, {8785, 12312}, {8990, 12727}, {9406, 13091},
{9457, 13661}, {9714, 14333}, {10027, 14748}, {10339, 15420},
{10909, 15579}, {11632, 15733}, {11945, 15630}, {12355, 15318},
{12981, 15215}, {13443, 14800}, {13653, 14333}, {13756, 13918},
{13910, 13451}, {14222, 13091}, {14586, 12830}, {14689, 12415},
{14638, 11948}, {14535, 11430}, {14274, 11071}, {13961, 10707},
{13807, 10655}, {13602, 10394}, {13961, 10394}, {14274, 10553},
{14428, 10342}, {14376, 9983}, {14535, 9773}, {14843, 9824},
{14946, 9568}, {15104, 9358}, {15258, 9101}, {15361, 8788},
{15566, 8840}, {15982, 8947}, {16243, 8891}, {16603, 8788},
{16864, 8532}, {17279, 8373}, {17587, 8270}, {17849, 7911},
{18208, 7649}, {18315, 7080}, {18469, 6767}, {18782, 6665},
{18936, 6408}, {19193, 6044}, {19557, 5834}, {19972, 6044},
{20178, 6352}, {20644, 6511}, {20747, 6870}, {20798, 7234},
{20542, 7547}, {20388, 8014}, {20229, 8322}, {20075, 8634},
{19921, 9152}, {20229, 9465}, {20490, 9722}, {20747, 9876},
{20490, 9876}, {20178, 9824}, {19972, 9619}, {19660, 9619},
{19608, 9876}, {19300, 10086}, {18885, 10137}, {18675, 10342},
{18623, 10604}, {18782, 10809}, {18936, 11019}, {18572, 11173},
{18469, 10912}, {18315, 10655}, {18208, 10291}, {17900, 10394},
{17587, 10394}, {17177, 10342}, {16761, 10394}, {16551, 10450},
{16295, 10604}, {15879, 10707}, {15566, 11019}, {15622, 11379},
{15828, 11794}, {16033, 12107}, {15725, 12522}, {15622, 12779},
{15515, 13143}, {15776, 13451}, {15776, 13764}, {15464, 14025},
{15258, 14333}, {15048, 14543}, {14894, 14748}, {14843, 14902},
{14689, 15164}, {14689, 15420}, {14586, 15836}, {14376, 16200},
{14222, 16615}, {14120, 16872}, {13910, 16923}, {13756, 17026},
{13499, 17236}, {13186, 17236}, {12981, 17390}, {12668, 17493},
{12304, 17651}, {12047, 17703}, {11786, 17600}, {11427, 17544},
{11011, 17600}, {10493, 17600}, {9924, 17651}, {9611, 17908},
{9457, 18169}, {9714, 18585}, {10181, 18944}, {10391, 19462},
{10339, 19878}, {10232, 20293}, {10181, 20657}, {10699, 20862},
{11063, 21278}, {11375, 21847}, {11735, 22160}, {12201, 22468},
{12514, 22314}, {12719, 21898}, {13032, 21586}, {13084, 22052},
{13238, 22314}, {13238, 22519}, {12873, 22570}, {12719, 22883},
{12719, 23350}, {13032, 23765}, {12925, 24125}, {12719, 24437},
{12463, 24801}, {12355, 25058}, {12047, 25525}, {11837, 25940},
{11632, 26253}, {11319, 26253}, {11011, 26253}, {10750, 26458},
{10596, 26822}, {10596, 27182}, {10596, 27494}, {10545, 28012}};


The length of the contour is given by:

In[2]:

Length[contour]

Out[2]:

375

A plot of this contour is given by:

In[3]:

plt1 = ListPlot[contour, PlotStyle -> {Hue[0], PointSize[.01]}]

Out[3]: graphics

The centroid of the contour is given by:

In[4]:

centroid = N[Plus @@ contour/Length[contour]] 

Out[4]: {9426.41, 12877.6}

My question is:

How can I generate (say) five contours, so that:

(1.) Each contour (set) have the same length as the original contour

 (in this case, each contour should contain  375 {x,y} points).

(2.) Each contour is equidistant, and concentric (with respect to

 the centroid) to the previous contour.

(3.) The five contours are inside the original contour defined above?

Thank you for your help!


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