257d5d22-3673-45af-b7c6-9cb573e8d918 32 3 5 auto
&[DATE] &[TIME] - &[FILENAME]
&[PAGENUM] / &[COUNT]

Digitizing an implicit contour

Step_1 => save the contour to file, as image

f2 1 1 sys 35 s *
Explain . . .
Some implicit functions have NO Maple expansion.
Alternately, here, we plot X_Y and collect as image.
The XY digitized is MicMac in the center region,
cleaned manually in the collapsed area [subject to
human typos ... re-check].
]]> 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 iVBORw0KGgoAAAANSUhEUgAAAJAAAACCCAIAAAAmOtZ/AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAANbSURBVHhe7dZRctswDIRhX9L3P0qyCTyeROZIIgUCC2r/p7bTNsR+SZvHlyqVwIolsGIJrFgCK5bAiiWwYgmsWAIrlsCKJbBiCaxYj+fz+fqhog9YP19hMiuRMb3+ScRPxEbbX51//4fJjLANyvabDplR9cnR+C5RZiQ1IRpgCL9VbInt7N8Gs2SW0v7se2BIZsEdDn4AhmQW1pmpj8EQ/iKxze7kwqfALJlN6vfL4ey2HWBIZu71TtoHhmTm2MCY3WBIZi6NzTgChvDBxDbclfUGwSyZDXRxtEtgSGZdXZ/rKhiS2clchnIAQzI7zGsiHzCEB4mtme8ybmCWzDa5D+IMhmT2bsYU/mBIZmjSCFPA0M3N5p0/Cwzd1mzq4RPBEJ5+N7bZ984Fs25i9vvJOf3SCDC0vFnYgUFgaGGzyNPiwNCSZsFHhYKhxcziz4kGQ8uYpRySAIYWMMs6IQcMlTZLfHwaGCpqlvvsTDBUziz9wclgqJAZw1PzwVAJM5JHUoAhcjOe57GAIVozqocRgSFCM7YncYEhqoEIP4EEtpfATkUyE6EWYgRD6WNxaiGBtRNYd4mT0WohgTUS2GApwzFrIYFtE9h4AvtMYNsENp7APhPYNoGNJ7DPBLZNYIMlDsdsJrBGAusufTJaM4G1E1hHJGNxmtGBUc1EaCawvQR2EOFAbE8iAiPUsqgexgJGq2XxPI8CjFzLInlkPlgJLYvhqclghbSs9AdngpXTsnKfnQZWVMtKfHwOWGktK+uEBLAFtKyUQ6LBltGy4s8JBVtMywo+Kg5sSS0r8rQgsIW1rLADI8CW17JwZsClc8FibqBq9r0Twe5G9W7q4bPAbqtlzTt/CtjNtaxJI/iDSevdjCmcwaS1CYP4buIG5v6ylXJcxgdMVId5TeQAJq2TuQx1FUxaXV2f6xKYtAa6ONogGD6qtIa7st4ImKhcGpuxG0xajg2M2QcmLfd6J+0Ak9akMOz5bU+Bdf2NaqyTCx+DiSqsM1MfgEkruMPB98CkldL+7G0w/BlpJbazfwNMVCQ1IbZg0qLqk+MfmLQI26C8wPCr0qLtr84PmKhKZEwPaRUKWI3vEhVzAiuWwIolsGIJrFgCK5bAiiWwYgmsWAIrlsCKJbBSfX19A/vmuyG4sscIAAAAAElFTkSuQmCC Gray

Raw extraction to be cleaned

 XY 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 N

Step_2 => clean/collect the branches

<p> raw XY ... strpped XY </p> 1 117 1 12 2 116 2 13 3 115 3 14 4 115 4 14 5 114 5 15 6 113 6 16 7 112 7 17 8 111 8 18 9 111 9 18 10 110 10 19 11 109 11 20 12 108 12 21 13 107 13 22 14 107 14 22 15 106 15 23 16 105 16 24 17 104 17 25 18 103 18 26 19 102 19 27 20 102 20 27 21 101 21 28 22 100 22 29 23 99 23 30 24 98 24 31 25 97 25 32 26 97 26 32 27 96 27 33 28 95 28 34 29 94 29 35 30 93 30 36 31 92 31 37 32 91 32 38 33 91 33 38 34 90 34 39 35 89 35 40 36 88 36 41 37 87 37 42 38 86 38 43 39 85 39 44 40 84 40 45 41 83 41 46 42 82 42 47 43 81 43 48 44 80 44 49 45 79 45 50 46 78 46 51 47 77 47 52 48 76 48 53 49 75 49 74 49 55 49 54 50 73 50 56 51 72 51 71 51 58 51 57 52 70 52 69 52 60 52 59 53 68 53 67 53 66 53 65 53 64 53 63 53 62 53 61 92 68 92 67 92 66 92 65 92 64 92 63 92 62 92 61 93 70 93 69 93 60 93 59 94 72 94 71 94 58 94 57 95 73 95 56 96 75 96 74 96 55 96 54 97 76 97 53 98 77 98 52 99 78 99 51 100 79 100 50 101 80 101 49 102 81 102 48 103 82 103 47 104 83 104 46 105 84 105 45 106 85 106 44 107 86 107 43 108 87 108 42 109 88 109 41 110 89 110 40 111 90 111 39 112 90 112 39 113 91 113 38 114 92 114 37 115 93 115 36 116 94 116 35 117 95 117 34 118 96 118 33 119 97 119 33 120 97 120 32 121 98 121 31 122 99 122 30 123 100 123 29 124 101 124 28 125 102 125 27 126 102 126 27 127 103 127 26 128 104 128 25 129 105 129 24 130 106 130 23 131 106 131 23 132 107 132 22 133 108 133 21 134 109 134 20 135 110 135 19 136 111 136 18 137 111 137 18 138 112 138 17 139 113 139 16 140 114 140 15 141 115 141 14 142 115 142 14 143 116 143 13 144 117 144 12 236 2 mat 1 1 mat

Strip paired 0's

data Strip2 u data 1 col : v data 2 col : k 0 : i 1 data rows range u i el v i el * 0 ≠ R k k 1 + : el u i el v i el 1 2 mat : 1 1 line Undefined if 1 1 line for R 3 1 line 3 1 line :

The cleaned branches

 C1 C2 2 1 sys

Step_3 => Export the collected branches

 106

Electron Parabolic Path

 blueC redC 72.5 64.5 + 100 green 1 5 mat 3 1 sys
Once bueC, redC in hand .... =>
you can scale each direction as you wish.
]]>