. Upsampling/downsampling and . Van-hooft, , 2018.

, Ou encore : si une cellule qui n'est pas une feuille est inactive, alors sa mère l'est aussi 13. Ce sont feuilles de l'arbre induit par la hiérarchie parentale sur la partie active de l'octree

, Et pour cause : les calculs ne sont pas faits sur ? tout entier mais seulement sur ? c 15. Et ce, pour des raisons de calculs dans Basilisk, 2003.

, par symétrie centrale en X 4. dont le filtre ? cos de Peskin (1977) 5. la seule éventuelle exception, de probabilité nulle, ie. superposables et symétriques l'une par rapport à l'autre

, Nous avons alors ?(x, q, k) ? Q × 0..1 2 × (2Z) 2 , g 1 (x + q + k) = g 1 (x + q)

. ?(x,-k)-?-q-×-z-2,

, 11) montrent ce que nous voulions : l'étude de ? peut être réduite à Q = [0, 1] 2 . Les nouvelles conditions de compatibilité s'en trouvent donc simplifiées : ?(x, q) ? Q × 0

, 13) forment clairement un système de rang plein de 6 équations linéaires. Voyons à présent combien d'inconnues est-ce que ce système implique réellement : ?(x, j) ? Q × Z 2 \K , ?(x ? j)

, De plus, la continuité souhaitée (1) de ? force ? |?K ? 0, de sorte que ?x ? Q, ?j ? K ? Z 2 , || x ? j || 2 = N ? ?(x ? j)

, 15) et en posant T = ?N, N ? 1 2 , nous obtenons finalement ?(x, j) ? Q × Z 2 \T , ?(x ? j) = 0, p.17

. Ainsi,

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