# Geometric error calculation in geomipmapping

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Hi I'm implementing a geomipmapped terrain and i have some doubts on how the calculation of the geometric error is done. I have made some figures to illustrate the calculations:
  - - - - -
|\|\|\|\|
- - - - -
|\|\|\|\|
a)- - - - -
|\|\|\|\|
- - - - -
|\|\|\|\|
- - - - -

- x - x -
|\|\|\|\|
x x x x x
|\|\|\|\|
b)- x - x -
|\|\|\|\|
x x x x x
|\|\|\|\|
- x - x -

-   -   -
|\  |\  |
|  \|  \|
c)-   -   -
|\  |\  |
|  \|  \|
-   -   -

-   x   -
|\  |\  |
|  \|  \|
d)x   x   x
|\  |\  |
|  \|  \|
-   x   -

-       -
|\      |
| \     |
e)|   \   |
|    \  |
|      \|
-       -

- Figure a) is a 5x5 block of the terrain where each vertice is marked with a "-" - In Figure b) the vertices that will disappear on the next level (3x3) are marked with a "x" - In Figure c) we have the resulting 3x3 block - In Figure d) the vertices that will disappear on the next level (2x2) are marked with a "x" - In Figure c) we have the resulting 2x2 block I know that to calculate the geometric error of a vertice that will dissapear in the transition between a higher level and a lower level i need to calculate the difference between the true vertex height and the calculated vertex height for example between
1   2   3     1       3
|\  |\  |     |\      |
|  \|  \|     | \     |
4   5   6 and |   \   |
|\  |\  |     |    \  |
|  \|  \|     |      \|
7   8   9     7       9

to calculate the geometric error of 5 (this vertex disapears between the two levels of detail) i need to sum the height of 1 and the height of 9 and divide by 2 to obtain the estimated position of this vertex in the new level of detail. Then i have only to calculate the difference between the true hieght and the calculated height. The geometric error of the block is the max of the geometric errors. So far so good. Know my problem... I've noticed that i have in some cases levels with the same geometric error. As i'm doing morphing this is a problem since I'm observing popping in this situations. In each level i'm calculating the maximum geometric error of all the vertices that dissapear, this includes not only the vertices that dissapear from the current highest level to next lowest level but also the vertices from previous levels that dissapear also. So for example in the transition from a) to c) i'm calculating the max geometric error of all the x's in b) and in the transition from c) to e) i'm calculating the max geometric error of all the x's in b) and all the x's in d). This the way i should do it ? I suspect this is where my problem lies. Maybe i can use the previous geometric error and add to that the geometric error of only the vertices that dissapear from the current level to the next. That's the way i should do it ? Tnks for any help. (sorry for the long post)

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Rutin
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