Interactive out-of-core visualisation of 4-D+t plasma data

HAL Id: inria-00070563

https://hal.inria.fr/inria-00070563

Submitted on 19 May 2006

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Interactive out-of-core visualisation of 4-D+t plasma data

Christophe Mion, Florence Zara, Jean-Michel Dischler

To cite this version:

Christophe Mion, Florence Zara, Jean-Michel Dischler. Interactive out-of-core visualisation of 4-D+t

plasma data. [Research Report] RR-5444, INRIA. 2004, pp.28. �inria-00070563�

ISRN INRIA/RR--5444--FR+ENG

a p p o r t

d e r e c h e r c h e

Thème NUM D

Interactive out-of-core visualisation of 4-D+t plasma data

Christophe Mion — Florence Zara — Jean-Michel Dischler

N° 5444

Décembre 2004

Unité de recherche INRIA Lorraine

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X pimn¢PnqikXWv{´nqikds{ŠlE‰Wnsik‰WviuhXˆ{oX‡{|hloXWrIpoXˆimnVYdPxsXrrXRlov{ŽpodGvgp´ikX\lodsv(l X;ly‡Ÿns‰ XG¬(…©iXlyp&nsjur(lojnsjklohwfXwloX{oXr(fg{|Xw‰WdsVY‡gpoXw}Gv(XikXpoXVY‡(lžfgXw‰nqim‰ vifgXw‰WX pyp|X{|X‰Wdsr(lypo{|v(‰p|judGr

fhW‡MXWr(f»fgjk{oX;‰p|XWVYXWrIpfgXYikn.{|hlodsikvgpojkdsr lydGvT(nsj³p|hWXS«‡ikv(limn!{|hlodsikvgp|judGr?fgXYimn!{|X‰Wdsr(lypo{|v(‰ pojkdsrKX;l€p

£Énsju(iuXGts‰ Xlypy¦P¦©fgjk{oX‡ikv(lŽikXRrjk¢sXnsv4f(nqr(limnž‡zxI{ŠnqVYjmfgXXlypEhWikXW¢GhˆX pEVYdsjkr(lŽikXlp|XWVY‡(lfXR‰Wnqim‰ v(i(lydGrIp

jkVY‡ŸdG{ypŠnqrIp|l¬

_ nsvgpo{|X\‡Ÿnq{optz‰ dsVYVYX\iXWr(loXWVwiuX&fgXl¢PnqikXWv({|ljkl|lyv(XlfgX\imnp|{|nsr(l€£¤dG{oVYhX

H(D u,v )

‰Wds{|{oX;ly‡Mdsr¦

fXWrIp fgX;lfgjMh{oXr(‰ X;lWtG‰ XWikikXly¦¯‰Wj(lydGrIpE‡{odg‰ŠTX;lEfgXRºhW{|d(¬sƒn‰ dGV4‡({oX;lolojudGr4‰Wdsr(lojml€p|XRnqikds{Šl &°¥gXW{v(r

loXWv(juirdspoh

0

tX pfgXwVYXWpypo{|X —ºhW{|d—iXr(lyXVikXwfXl&¢PnqikXWv{Šl^fX

H(D u,v )

jkrg£¤hW{|juXv{|Xl

0

¬«Z\dsv(l

ns‡‡MXWikdsr(l

H ⁰ (D u,v )

iuX{|hloviup|nqpˆfX‰ X popoXVYjmlyX 4ºWh{odŸ¬

0,2 0 0,1

−0,2 0,1

−0,1

−0,1

−0,1

0,2 0 0,1

−0,2 0,1

−0,1

−0,1

−0,1

0,2 0 0,1

−0,2 0,1

−0,1

−0,1

−0,1 0 0,1

0,1

−0,05

0 0,1 0,1

−0,05

0,2 0 0,1

−0,2 0,1

−0,1

−0,1

−0,1 0 0,1

0,1

−0,05 0,2

−0,2 0

−0,2 0

0 0 0 0 0 0 0 0 0,1625 1,01875

−0,125

0 0

0 0

0

1 1 1

1 0

0 0 1

0

1 0

1,01875 −0,2 0,2 0,1625 −0,125 −0,2

différence moyenne

différence moyenne

différence moyenne

différence moyenne

1,1 0,9 1,3 1,2

1 1 1,1 1,2

1 0,9 1 0,8

0,9 0,8 1 1,1

1 1,25 1,15 1

1,05

0,9 0,95 0,85

1 0,875

1,2 1

1,1 0,9375

−0,2

−0,125

−0,2 1,01875

0,1625−0,125

Filtre avec

H ⁰ (D u,v ) H (D u,v ) D u,v

D u,v

T u,v

N u,v = 6

B u,v

0 = 0,1

Nju”Gv{|X&ES5\Ž¥gXWVY‡ikXfgX‰ dGVY‡{oX;lolojkdsr!f(nqr(likX‰WnGlˆfv(r lodsvŸl€¦¯Xlo‡(ns‰WX^fgXžpŠnqjkiuikX

N = 4

^¬

ƒnpo{Šnqr(ly£¤ds{|VYhWX

H ⁰ (D u,v )

Xlyp#XWr(lovjupoXŽ{|X‰WdzfhWXElodsv(limn£¤ds{|VYXEfv(r‰ dsv(‡iuX

(B u,v [N][N], T u,v [N u,v ])

^¬

B u,v

Xlyp&v(rXwVnqpo{|jk‰WXwfgX4jup|lž}Ivjjur(fjk}IvX4iuX;l&¢§nsiuXv{Šl\rzvikiuX;l\dGvKrdGrKfgX

H ⁰ (D u,v )

tMp|nsr(fgjml&}IvX

T u,v

XlypRvr p|nsiuX;nqveikjur(hnqjk{|X‰ dsrIp|XWr(nsrGpRv(rjk}IvXVYXWrIp\ikXl

N u,v

¢PnqikXWv{ŠlˆrdGrerzviuikXl\fgX

H ⁰ (D u,v )

^¬

^v(XWim}Gv(XlodsjupikXlydGv(l€¦¯Xlo‡(nG‰ X

D u,v

‰ dGr(lojkfgh{ohGtikX‡iknsrwfgXjup|ldg‰W‰Wv‡MXnsjur(lojzvr4Xlo‡(ns‰WXVYhWVYdsjk{|XfgX

pŠnqjkiuikX

N ² /8

dz‰ poXWp|ltgp|nsr(fgjmlˆiuXrdsVw{oXfdg‰p|X p|lRrh‰WXl|lonsju{|Xlnqve‰Wdzf(nq”sXfgv.pŠnqikXnsv

T u,v

fghW‡MXWr(f

ikvj(fju{|X‰ poXWVYXrGpfX

N u,v

fgh‡ŸXr(fnsrGp´iuvju¦¯Vg?VYXRfgvlyXvjui

0

¬q~Žnq{nsjuikikXWv{ŠlWtPinsl|lydg‰ jmnPp|judGrXrGp|{oX

T u,v

XWp

B u,v

lyXž£Énsj³pRXre‡(nq{Š‰ dGv{|nsrIp´imnYVYnqpo{|jk‰WX

B u,v

fgX”Gnsv(‰ŠTX Yfg{odGj³p|XX p\fgXTŸnqvgpRXr.Ÿnsl¬(‚Rjkr(lojiuX

‡({oXV4jkXW{jup\fgX

B u,v

rdsr.rzvi‰ dG{o{|Xlo‡ŸdGr(f 4imn‡{|XWVYjkUW{|X^XrIpo{|hWXfnqrŸl

T u,v

tgX p\nsjur(loj«fgXlyv(j³p|Xs¬ƒ#n

°Ÿ”sv{|Xž4{|hlovVYX‰ XWpypoX‡({odg‰ h;fgv{|X&f(nqr(likX‰WnGlˆfv(r lodsvŸl€¦¯Xlo‡(ns‰WX^fgXžpŠnqjkiuikX

4 × 4

^¬

:'ml *,+ :;09s1s1p+- 6= + <O=)0 < -:p q.03< p <O6.-:+.sd/5p 0

‚\‡{|Ulimn¡‡(T(nsloXKfgX ‰ dsVY‡{|Xl|lojudGr%‡Ÿnq{—dGr(fgXiuXWpypoX;l—fgX \nGnq{;tEpodGv(likXl.lodsv(l—Xlo‡(ns‰WXl

D u,v

lydGrIp

{|XW‡({oh;lyXrGp|hl\‡(nq{fgX;l&lypo{|v(‰ pov{|Xl^ŸdzdGiuhXWrrX;l

B u,v

nGlolodg‰ jkhWXl !fXl^p|nsiuX;nqvg¥

T u,v

‰ dGrIpoXWrŸnqrIp^ikXl

¢PnsiuXv{|lrdGr rIv(iuikXlˆfgX

H ⁰ (D u,v )

^¬

´XR‡({oXV4jkXW{rju¢GXnsvYfX\‰ dGV4‡({oX;lolojudGrYrXˆpojkXWrIp‡ŸnslE‰WdsVY‡gpoX^fgXl´‰ ds{|{|hWimnPpojkdsrŸl}IvjkiŸ‡MXWvgp´x4n§¢Gdsjk{

XrIpo{|X—ikXlYfgjMh{oXrGpŠlwlodsvŸl€¦¯Xlo‡(ns‰WXlwfv(r V ?WVYX fgjkns”srdIl€p|jk}IvX

D

^¬ X;l€pY‡Mdsv{Š}Ivdsj8tv(rX.loX‰Wdsr(fX

‡(T(nsloXfgX‰ dsVY‡{|Xl|lojudGr—XlypR{|hnqikjmlyhX^Xr fXWvg¥—hWp|ns‡ŸX;l S

U

¬ š ›g™WBÁ D  D ÂiBɜs™CBÁ DiD ›Bɚ ½ œ Á D­Xr £¤vŸlyjkdsrrŸnqrIpwp|dsvgp|Xl4ikXlwp|nsiuX;lYfgX!¢PnsiuXv{|l

rdsr?rzviuikXl

T u,v

1

‡{|UltnP°(rKfX£¤dG{oVYXW{^vrX4vrjm}IvXpŠnqikX

T D

‰WdsVYVvr(X iXWr(loXWVwiuX

fgXl\lydGv(l€¦¯Xlo‡(nG‰ Xlfgvefgjmnq”GrdGlypojm}IvXs¬

‘g¬wÁ

Xš

½

˜˜WB

Á D

 ÂiBɜs™CB

ÁEDiD

›B¤š

½ œ Á D

T D

‡(nq{´vr—nsiu”Gds{|j³p|TVYXRfgXR‡(ns{yp|j³p|judGrrXWVYXrGp

fXW{|{oXv{

2

¬

~dsv({^X MX;‰pov(XW{&ikn ˜WBÁ D  ½ ˜!™›g– ½ ˜

T u,v

t‰ Xl\p|nsikXl\lodsrIp^podsvp&fnqMds{Šf po{|jkhWXl\‡(nq{^ds{Šfg{|X

fh‰ {|dsjml|lonsrGp;t‡vjmlXWikiuX;llodsrIp‡{|ds”s{|Xl|loju¢GXWVYXWrIp\£¤vŸlyjkdsrr(hWXl‡(nq{jkrIpoXW{o¦©‰ imnsl|lyXV4XrIpžXr»{oXWpojk{|nsrGpikXl

fdsvikdsrŸl

1

‡{|Ul¬;´X´‡{odg‰WXl|lyv(l‡MXW{|VYX pfdGgpoXrjk{#imnp|nsiuX

T D

fgXp|nsjuikiuX

N T _D

tfdsrIp#ikXlhiuhVYXWrIp|l

lodsrIppo{|jkhlŽ‡(ns{Eds{Šfg{|Xˆfgh‰W{odGjkl|lonsrIptPlydGj³p

∀k

^t

T D [k] > T D [k + 1]

¬q~Žnq{EnqjkikiuXv{|ltqimn&£¤v(lojudGrYfXlŽ¢PnqikXWv({|l {|hWXiuikXlhWp|nqrIpR{|hnsiujmlyhX

1

‡{|UltgrdsvŸlˆn§¢sdsrŸl

∀k

^t

T D [k] ≥ T D [k + 1] + 1

¬

\Er¡po{|jknsrGpwiuX;lpŠnqikXl

T u,v

t#r(dsv(lwn§¢sdsrŸl‡ŸX{|fv·ikne{|XWimnPp|judGr¡}Ivjkix·n§¢PnqjupXWrIp|{oXikXlŸdzdGiuhXWr(l

fXeikn·Vnqpo{|jk‰WX

B u,v

XWp—ikXlhiuhVYXWrIp|lfX

T u,v

¬…©i^Xlyp—fgdsrŸ‰erh‰WXl|lonsju{|X fjkrIpo{|dgfgvjk{oXevr(Xep|nsiuX

jkrIpoX{oVYhfjknsju{|X\fjurŸfgX ¥

I u,v

‡MXW{|VYX pypŠnqrIpˆfgX\{|Xlyp|nsv{oX{´‰WX pyp|X^{|XWimnPp|judGr¬z´X;‰ jM{oX¢zjuXrGprdqpŠnqVYVYXWrIp

X MX;‰p|vXW{Rv(r nGfg{|Xl|lons”sX&jur(fju{|X‰ p¬

I u,v

Xlyp\fgdsrŸ‰fgh °(r(juXfgXžp|XWikiuXlods{opoX}IvX

T D [I u,v [k]]

lodsjupRhW”GnsiuX

T u,v [k]

1

‡{|Ul¬g‚Rjkr(loj«‡(nq{ˆ‰ dGr(lypo{|v(‰p|judGrtziknp|nsjuikiuXžfgX;ljur(fX ¥

I u,v

¢Pns{ojkX^Xr—£¤dGr(‰p|judGr!fgX

N u,v

¬

\rK‡{ŠnPp|jk}IvXGtMfgX;l\XrIpojkXW{Šl\‰ dgfgh;l^lov{

24

jup|lžlodsrIp&lov5@l|nqrIp|lt(‡v(jkl|}Ivjkiml\‡MXW{|VYX pyp|XWrIpžidsgp|XWrIpojkdsr fX

2 ²⁴ = 16 777 216

XrIpo{|hWXl&‡MdGl|lyjkikXlfnsr(l

T D

¬«~dGv{{|hlovVYXW{;t ‰WXYlyp|nGfgXYfgv»‡{odg‰WXl|lyv(lžfgX

‰WdsVY‡{|Xl|lyjkdsr#tIv(r.lodsv(ly¦¯Xlo‡(ns‰WX

D u,v

Xlyp 4‡{|hloXWrIpRfgh °(r(jlydGv(liknw£¤dG{oVYXfvre‰ dsv(‡iuX

(B u,v , I u,v )

nGlolodg‰ jkh&nsv.fjk‰ pojkdsrr(nsju{|X

T D

‰ dGVYVvr wpodGv(liuX;lRlodsv(ly¦8X;ly‡Ÿns‰ X;l´fv.V ?V4Xfgjmnq”GrdGlypojm}IvX

D

^¬

Z\dsv(lYX MX;‰pov(dsr(lYXr(lyv(j³p|X.imn œ Á Xš ½ ˜;˜CBÁED Â-ÂBAœq™WBÁ DD ›B¤š ½ œ Á D

T D

¬Ž~dsv({Y‰WXWimnt

r(dsv(lvgp|juikjklodsrŸlvr.‡(ns{yp|j³p|judGrrXWVYXrGp(nGlyh&lyv{iT(jklypodG”s{ŠnqVYVYX^fgXžfgjml€p|{ojkvgp|judGr!fgX;l¢§nsiuXv{Šl´fgX

T D

U

Xr.‰Wdsr(lojmfghW{ŠnqrIp´r(dqp|nsVYV4XrIpikX&£ÉnqjupR}Gv(X&ikXlhiuhVYXWrIp|lˆfgX

T D

lodsrIppo{|juh;l‡(nq{dG{|fg{|Xžfgh‰W{odGjkl|lonsrIp´X p

}IvXžimn4¢§nsiuXv{

T D [0]

{oX‡{|hloXWrIpoXnqjkr(loj«iuXžVnP¥gjkVvV fgXl¢PnsiuXv{|lˆfgX

T D

¬

ƒnp|nsikX

T D

Xlyp\£¤{Šns‰p|judGrrhXXWr

K

‡(nq{opojupojkdsr(l^fgdsrIp&iuX;lRMds{|rXl

v l

n§¢sX;‰

l ∈ [0, K − 1]

^tMlodsrIp

fh °(rjkXlw‡(ns{

v l = T D [0] − l × 2 × 2 ⁸

¬_^X.‡iuvŸlWtlyj

T D [k]

loXp|{odGv¢sX.nqv loXWjkr fgX!iknK‡(nq{opojupojkdsr

l

^{tŽ‰ Xlypy¦}P¦©fgju{|X—loj

v l ≥ T D [k] ≥ v l+1

tnsiudG{|lwjkiXW¥gjklypoX fgXWv¥ XWrIpojkXW{Šlw‡ŸdIlyjupoju£Él

a m

XWp

a m+1

n§¢sX;‰

a m < a m+1

poXWimlR}IvX S

v l − a m × 2 ≥ T D [k] ≥ v l − a m+1 × 2 .

ƒ jmfghX ‰Wdsr(lojml€p|X nsiudG{|l »lypodg‰ŠµsX{

T D [0]

^XWpYiXWr(loXWVwiuX¶fXlYXWrIp|juX{|l

a m

tŽ‡iuvp qp—}IvXeikXlY¢PnsiuXv{|l

{|hWXiuikXl\X ¥g‡ikjk‰Wj³p|Xl

T D [k]

¬‚\ve°(r(nsiAtMimnp|nsikX

T D

‰ dGV4‡({oX;lolohWXfXW¢zjuXrIp^vrXwiujmlypoXwfX‡(ns{yp|j³p|judGr(lRddk

‰ŠTŸns}IvX.‡(nq{opojupojkdsr%XlypvrX¶lypo{|v(‰p|v{|X.‰WdsrIpoXr(nqrIpvrXe¢PnqikXWv({VYnq¥gjuVnqikX.jurjupojmnqikXeX pv(r pŠnqikXnsv

fXrGp|juX{|l¬z…©iXlyp wrdqp|XW{ˆ}IvX&iuX&rdsVw{|X&fgXžlovMfju¢zjmlyjkdsr(lnsv!loXWjkr!fvrXž‡(ns{yp|j³p|judGr—Xlyp{oX;l€p|{oXjurIp

256

ikjuVYjup|nsrGpŽnqjkr(lojziuXrdsVw{|X´fgX´j³pŠlrh‰WXl|lonsju{|Xl#nqvwlypodg‰ŠµPnq”GXfgX;l

a m

¬Pƒ#nRp|nq(iuXnqjkr(lojz‰WdsVY‡{|Xl|lyhX

X;l€pr(dqpohX

T _D ⁰

¬ƒ#n.°(”Gv{oX!jkiuikv(lypo{|Xvr»X ¥gXWVY‡ikXXWr»‡{|XWr(nsrIp

2 = 0.01

‡Mdsv{v(rXYp|nsiuX

T D

fgX

pŠnqjkiuikX

N T _D = 15

n§xInqrIp‰WdsVYVYX¢PnqikXWv{ŠlhS

T D = {9.9 ; 9.8 ; 9.07 ; 9.03 ; 9 ; 8.7 ; 7.4 ; 7.1 ; 7.09 ; 7.08 ; 7.05 ; 7 ; 4.6 ; 4 ; 3.9}.

v ₂ = 4.78 v ₃ = 2.22 v ₁ = 7.34

v ₀ = 9.9

Njk”sv({oX5S\E¥zXVY‡iuXfX&‡Ÿnq{opojupojkdsrrXVYXWrIpR‡ŸdGv{ˆvrefgjm‰p|judGrr(nqjk{|X&fgXžpŠnqjkiuikX

N T _D = 15

^¬

Z\dsv(ln§¢Gdsr(l«nsjurŸlyjPp|{odGjkl‡Ÿnq{opojupojkdsr(l

{9.9 ; 9.8 ; 9.07 ; 9.03 ; 9 ; 8.7 ; 7.4}

^t

{7.1 ; 7.09 ; 7.08 ; 7.05 ; 7}

XWp

{4.6 ; 4 ; 3.9}

fghiujkVYj³p|hWXl—‡(nq{ikXl—fgjhW{|XWrIp|XlYMds{|rXl

v 0 = 9.9

^t

v 1 = 7.34

^t

v 2 = 4.78

^{X p}

v 3 = 2.22

¬gZ\dsv(lˆ‡Mdsv(¢sdsrŸlnsiudG{|lXW¥z‡({ojkVYXW{ˆimnw‡({oXV4jkUW{|Xž‡(nq{opojupojkdsr lodsv(limn4£¤ds{|V4X S

{v 0 = 9.9 ; v 0 − 10 × 2 ; v 0 − 83 × 2 ; v 0 − 87 × 2 ; v 0 − 90 × 2 ; v 0 − 93 × 2 ; v 0 − 107 × 2 }

dGv¡XWrŸ‰ ds{|X

{9.9 ; −10 ; −83 ; −87 ; −90 ; −93 ; −107}

^{¬ \Er} £ÉnqjmlonsrIp4‰ XWpyp|X—Vnqrjk‡vimnPp|judGr¡‡Mdsv{

iXWr(loXWVwiuXfgX;lˆ‡(ns{yp|j³p|judGr(lWtzrdGv(lˆdGgpoXrdsr(limn4p|nsiuX‰WdsVY‡{|Xl|lyhX

T _D ⁰

lyvjk¢PnqrIpoX S

T D ⁰ = {9.9 ; −10 ; −83 ; −87 ; −90 ; −93 ; −107 ; 7.1 ; −1 ; −2 ; −5 − 10 ; 4.6 ; −60 ; −70}.

Z\dqpodGr(lˆ}IvX‰ XWpyp|XžpoX‰ŠT(rjk}IvXfX‰ dsVY‡{|Xl|lojudGr—rX&£¤dsrŸ‰pojkdsr(rX}IvXlyj«ih‰Wns{ypˆXrGp|{oXžikXlˆ¢PnsiuXv{|l

fX

T D

lyXfjklypo{|ju(vXWrIp\fgXžVnqrjkUW{|Xžrdsr¦8vr(j³£¤dG{oVYXn§¢sX;‰&fXlˆnq”G{oh”Gnqp|ljuVY‡Mds{op|nsrGpŠlˆfgX¢PnqikXWv{Šl´po{|Ul

‡({odg‰ŠTX;lW¬

ˆ , Š." žW 1!*" / .1.,.,? ˆ

ƒn°(”Gv{oX {|hlovVYXEiuX;lfjhW{|XWrIpoX;l#hWp|ns‡ŸX;l#fgX´inqik”sdG{ojupoTVYX}IvjznRhWpoh´V4jmlXWrdzXWv(¢I{|XEXWpikXEp|nsikXnqv

U

iXWr(loXWVwiuXfgX;lRloxIVwŸdGiuX;lXWVY‡ikdPxshl¬

Génération des triangles Affichage au sein de la loupe Reconstruction des Transformation en ondelettes

inverse des

à un niveau de résolution m Création des cartes de hauteur

Boucle itérative de la visualisation

Sélection d’un pas de temps t Déplacement de la loupe

sous−espaces de Chargement des moyennes des

Affichage des quad non sélectionnés

Décompression en mémoire

nouvellement sélectionnés Chargement des

Phase de pré−calculs :

génération des fichiers des données compressées (dictionnaire et sous−espaces pour chaque pas de temps) Lancement de l’outil de visualisation 4D+t

commun

par la loupe de

Chargement du dictionnaire

(pour tous les sous−espaces) nouvellement sélectionnés)

(pour les sous−espaces H ⁰ (D u,v )

H ⁰ (D u,v )

H _u,v ^m D ^t

(B _u,v ^t , I _u,v ^t ) T _D ^t

T ^0t _D

Njk”sv{|X S(Åg‰ŠT(hWVnYnqik”sds{|jupoTVYjm}Gv(X&fgXiXWr(loXWVwiuXfgXimn4‡{|dz‰Whfgv({oX&VYjkloXXWr ‡imns‰WX

U ¾ ?– Á ½ ˜ 9Bj D BœG›g™CBÁED ˜

r _^juVYXr(lyjkdsr fgXiX;ly‡Ÿns‰ X

T

fnqr(lr(dqpo{|X‰WnGlrž‘

V

Z †ˆh;lydGiuvpojkdsr fgXžiknfgjml|‰ {|h pojml|nPpojkdsr

t

^SXWVY‡(l

~x

„ŽX‰ poXv{RfgX‡MdGloj³p|judGr

~v

„ŽX‰ poXv{RfgX¢zj³p|Xl|lyX

f (~v, ~x, t)

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(u, v)

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