Assignment P6 Student: Jan Hendrik Dithmar, 2031259, jadi5003@stud.uni-saarland.de Parameters are not given if they are explicitely stated in the problem. Problem 2 ========= We have learned in the lecture that topologically connected objects stay connected under MCM where topologically unconnected objects stay unconnected. Since the objects in check1.pgm are not topologically connected they stay unconnected. In check2.pgm, the objects are connected and stay it under MCM. This is not in contradiction to the theory. Problem 3 ========= corner01.pgm: ##### file name : corner01-0.01-10000.pgm time step size: 0.01 iterations : 10000 estimated corner: (128.999435, 64.651859) estimated evolution vector: (0.000025, 0.971015) estimated velocity: 0.971015 estimated corner angle: 93.368626 ##### ##### file name : corner01-0.01-5000.pgm time step size: 0.01 iterations : 5000 estimated corner: (128.998871, 64.786547) estimated evolution vector: (0.000085, 0.959457) estimated velocity: 0.959457 estimated corner angle: 94.737236 ##### ##### file name : corner01-0.01-1000.pgm time step size: 0.01 iterations : 1000 estimated corner: (129.000031, 65.174432) estimated evolution vector: (-0.000008, 0.875936) estimated velocity: 0.875936 estimated corner angle: 105.004586 ##### ##### file name : corner01-0.01-500.pgm time step size: 0.01 iterations : 500 estimated corner: (128.999985, 65.291093) estimated evolution vector: (0.000010, 0.819774) estimated velocity: 0.819774 estimated corner angle: 112.195465 ##### ##### file name : corner01-0.01-125.pgm time step size: 0.01 iterations : 125 estimated corner: (128.999908, 65.999992) estimated evolution vector: (0.000101, 0.000010) estimated velocity: 0.000101 estimated corner angle: 179.999999 ##### corner02.pgm: ##### file name : corner02-0.01-10000.pgm time step size: 0.01 iterations : 10000 estimated corner: (128.999435, 64.626403) estimated evolution vector: (0.000025, 1.385877) estimated velocity: 1.385877 estimated corner angle: 55.008023 ##### ##### file name : corner02-0.01-5000.pgm time step size: 0.01 iterations : 5000 estimated corner: (128.998871, 64.718791) estimated evolution vector: (0.000085, 1.378570) estimated velocity: 1.378570 estimated corner angle: 55.505778 ##### ##### file name : corner02-0.01-1000.pgm time step size: 0.01 iterations : 1000 estimated corner: (129.000031, 64.916810) estimated evolution vector: (-0.000008, 1.335164) estimated velocity: 1.335164 estimated corner angle: 58.581232 ##### ##### file name : corner02-0.01-500.pgm time step size: 0.01 iterations : 500 estimated corner: (128.999985, 65.147459) estimated evolution vector: (0.000010, 1.219631) estimated velocity: 1.219631 estimated corner angle: 67.823408 ##### ##### file name : corner02-0.01-125.pgm time step size: 0.01 iterations : 125 estimated corner: (128.999908, 65.590364) estimated evolution vector: (0.000101, 0.788634) estimated velocity: 0.788634 estimated corner angle: 116.241460 ##### corner01_50.pgm: ##### file name : corner01_50-0.01-10000.pgm time step size: 0.01 iterations : 10000 estimated corner: (129.026611, 64.704768) estimated evolution vector: (-0.000942, 0.976245) estimated velocity: 0.976246 estimated corner angle: 92.753833 ##### ##### file name : corner01_50-0.01-5000.pgm time step size: 0.01 iterations : 5000 estimated corner: (129.049652, 64.790413) estimated evolution vector: (-0.002899, 0.968602) estimated velocity: 0.968606 estimated corner angle: 93.652663 ##### ##### file name : corner01_50-0.01-1000.pgm time step size: 0.01 iterations : 1000 estimated corner: (129.146378, 64.845883) estimated evolution vector: (-0.022899, 0.964781) estimated velocity: 0.965052 estimated corner angle: 94.072914 ##### ##### file name : corner01_50-0.01-500.pgm time step size: 0.01 iterations : 500 estimated corner: (129.083511, 64.853581) estimated evolution vector: (0.011155, 0.947571) estimated velocity: 0.947637 estimated corner angle: 96.151340 ##### ##### file name : corner01_50-0.01-125.pgm time step size: 0.01 iterations : 125 estimated corner: (128.999908, 65.999992) estimated evolution vector: (0.000101, 0.000010) estimated velocity: 0.000101 estimated corner angle: 179.999999 ##### corner02_50.pgm: ##### file name : corner02_50-0.01-10000.pgm time step size: 0.01 iterations : 10000 estimated corner: (128.999435, 64.935150) estimated evolution vector: (0.000025, 1.377379) estimated velocity: 1.377379 estimated corner angle: 55.587433 ##### ##### file name : corner02_50-0.01-5000.pgm time step size: 0.01 iterations : 5000 estimated corner: (128.998871, 65.061145) estimated evolution vector: (0.000085, 1.367909) estimated velocity: 1.367909 estimated corner angle: 56.242180 ##### ##### file name : corner02_50-0.01-1000.pgm time step size: 0.01 iterations : 1000 estimated corner: (129.000031, 64.177756) estimated evolution vector: (-0.000008, 1.587767) estimated velocity: 1.587767 estimated corner angle: 43.273246 ##### ##### file name : corner02_50-0.01-500.pgm time step size: 0.01 iterations : 500 estimated corner: (128.999985, 63.977417) estimated evolution vector: (0.000010, 1.676926) estimated velocity: 1.676926 estimated corner angle: 39.151658 ##### ##### file name : corner02_50-0.01-125.pgm time step size: 0.01 iterations : 125 estimated corner: (128.999908, 65.999992) estimated evolution vector: (0.000101, 0.000010) estimated velocity: 0.000101 estimated corner angle: 179.999999 #####