Algorithm for automatically fitting digitized curves thus diq for convenience
XI.8 AN ALGORITHM FOR AUTOMATICALLY FITTING DIGITIZED CURVES Thus,
| ∂S | = | n ∑ |
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] | ||
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i=1 | |||||
| 3 B1 |
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| Q | n ∑i=1 |
di |
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(6) | |||||||||||||||
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| Expanding Q(ui), | |||||||||||||||||||
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Q | ||||||||||||||||||
| = | n ∑i=1 |
Ai,1 | |||||||||||||||||
| = | n ∑i=1 |
Ai,1 | ⋅V0B0 3 ui ( )+α1 | n ∑i=1 |
Ai,1 | + | n ∑i=1 |
Ai,1 | |||||||||||
| +α 2 | n ∑i=1 |
Ai,1 | ⋅Ai,2+ | n ∑i=1 |
Ai,1 |
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| ∑i=1 | Ai,1 | α 1+ |
| Ai,1 | ⋅Ai,2 |
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) | ) |
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619 | |||
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| = | ( | ||||||||||||
| GRAPHICS GEMS I Edited by ANDREW S. GLASSNER | |||||||||||||
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Ai,1⋅Ai,2 |
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∑i=1 | Ai,2 | ) | ) | |||||
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| = | ( |
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If we represent the previous two equations by
| we need only solve | ||||||||
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| for α1 and α2. If we let | ( | c1,1c2,2 | )α 2 | )=X2 | ||||
| )=C1C2 | ||||||||
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| (α1 | )=� |
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| α 1=det �C2 det C1C2 ( ( | 620 | |
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| α 1=det C1�det C1C2 ( ( |
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| GRAPHICS GEMS I Edited by ANDREW S. GLASSNER | ||
