Hi,
Graeme, in the online document of argyllcms, you have mentioned:
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"To simplify things, we work in a 'Simplex parameter' space, in which there
are only <dimension> parameters, and each directly corresponds with a cartesian
coordinate, but the parameter order corresponds with the baricentric order."
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Can you explain more detailly what "simplex parameter space" is?
Also, I couldn't understand the deduction as below:
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"For example, given cartesian coordinates D0, D1, D2 these should be sorted
from smallest to largest, thereby choosing a particular simplex within a cube,
and allowing a correspondence to the parameter coordinates, ie:
D1 D0 D2 Smallest -> Largest cartesian sort
P2 P1 P0 Corresponding Parameter coordinates (note reverse order!)
B0 = P0 Conversion to Baricentric coordinates
B1 = P1 - P0
B2 = P2 - P1
B3 = 1 - P2
The vertex values directly correspond to Baricentric coordinates,
giving the usual interpolation equation of:
VV0 * B0
+ VV1 * B1
+ VV2 * B2
+ VV3 * B3
where VVn is the vertex value for each of the 4 vertices of the simplex.
Reversing the Parameter -> Baricentric equations gives the
following interpolation equation using Parameter coordinates:
VV0 - VV1 * P0
+ VV1 - VV2 * P1
+ VV2 - VV3 * P2
+ VV3 "
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My question is that if I substitute P0,P1,P2,P3 for B0,B1,B2,B3 respectively,
shouldn't I get:
VV0* P0 + VV1 * (P1 - P0) + VV2 * (P2 - P1) + VV3 * (1 - P2)
or
VV0 * P0 - VV1 * P0
+ VV1 * P1 - VV2 * P1
+ VV2 * P2 - VV3 * P2
+ VV3
?
