80 |
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81 |
If two completely unrelated coordinate systems are to be interpolated, |
If two completely unrelated coordinate systems are to be interpolated, |
82 |
linear (or other) interpolation of the **transformed points** shall be |
linear (or other) interpolation of the **transformed points** shall be |
83 |
used as a fallback. This means that :: |
used as a fallback. This means that a point ``x`` will be transformed as:: |
84 |
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85 |
interp.cs(x) = (1-fract)*vs1.cs(x) + fract*vs2.cs(x) |
interp.cs(x) = (1-fract)*vs1.cs(x) + fract*vs2.cs(x) |
86 |
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87 |
instead of the parameterwise interpolation :: |
where ``interp.cs`` is the interpolated coordinate system at fraction ``fract`` |
88 |
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and ``cs(x)`` is ``x`` transformed according to ``cs``. |
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interp.cs(x) = ((1-fract)*vs1.cs + fract * vs2.cs)(x) |
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(the equation is not good; what is meant is that a set of *parameters* |
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between ``vs1.cs`` and ``vs2.cs`` is found). |
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89 |
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90 |
We shall not define the exact circumstances when this shall happen; |
We shall not define the exact circumstances when this shall happen; |
91 |
we shall define one circumstance where this shall not happen: if |
we shall define one circumstance where this shall not happen: if |