Mass-Spring Systems Surface Reconstruction

Transcription

1 Mass-Spng Syses Physally-Based Modelng: Mass-Spng Syses M. Ale O. Vasles Mass-Spng Syses Mass-Spng Syses Snake pleenaon: Snake pleenaon: Iage Poessng / Sae Reonson: Iage poessng/ Sae Reonson: Mass-Spng Syses Sae Reonson Snake pleenaon: Sae Reonson: Bodes o eepy ales:

2 Daa Ses Node 1..N Mass: Poson: [ y z ] Veloy: d /d Aelaaon a d /d Ne nodal oe: ne ypede s node{ loa ass; eo poson; eo eloy; eo oe; } node; Lagange eqaons o oon: Syse Dynas: g Spng Connes node o node Naal lengh l Sness k ypede s spng{ node *n1; node *n; doble es_lengh; doble spng_onsan; } spng; s dapng oeen s he eenal oe a node g oal nenal oe on he node de o neghbong nodes Lagange eqaons o oon: F Syse Dynas: g oal F oal s dapng oeen s he eenal oe a node g oal nenal oe on he node de o neghbong nodes g Lagange eqaons o oon: g s dapng oe s he eenal oe a node g oal oe on he node de o spngs onneng node o neghbong nodes Epl Ele e negaon: ne g ne a a Eqaons o Moon od ope_oesn n_nodes node *nds n n_spngs spng *sps { zeoze_oesn_nodes nds; spng_oesn_spngs sps; dapng_oesn_nodes nds; eenal_oesn_nodes nds; } od e_seploa d n n_nodes node *nds n n_spngs spng *sps {eo ael dela_el dela_pos:n ; ope_oesn_nodes nds n_spngs sps; o ; <n_nodes; { sale1 / nds[].ass nds[].oe ael; saled ael dela_el; plsdela_el nds[].eloy nds[].eloy; saled nds[].eloy dela_pos; ndela_pos nds[].poson;}} Foe Copaon Con. Dapng Foes: Eenal oe ey sple : spngs aahed o he daa o eah esh node k daa daa poe he poson o node no he daa and ea he ale a ha loaon daa allae he oe sng a daa spng onsan k daa od dapng_oes n n_nodes node *nds { eo oe; n ; o ; <n_nodes; { saledamping nds[].eloy oe; deoe nds[].oe;}} od eenal_oesn n_nodes node *nds { n ; node *nd; eo p; loa al; o ; <n_nodes; { nd nds[]; p nd->poson; alage_nepp. p.y IMAGE_DATA; nd->oe.z IMAGE_CONST*al - p.z; }} Mass-Spng Foes Spng Foes: g oal oe on he node de o spngs onneng o neghbong nodes N g s N he oe spng ees on node s k e node sepaaon aal spng lengh 1 4 e l spng deoaon l naal spng lengh k s he spng onsan o he spng onneng node and node 3

3 Spng Foes: g oal oe on he node de o spngs onneng o neghbong nodes N g s N he oe spng ees on node s e hee s sepaaon o nodes Foe Copaon od spng_oes n n_spngs spng *sps { n ; o ; <n_spngs; spng_oesps[];} od spng_oe spng *s { node *node1 *node; doble lengh eenson sale_ao; eo deon oe; node1 s->n1; node s->n; nsnode->posonnode1->poson deon; Adape Iage Reonson s aal lengh o spng e l s deoaon o spng lengh lenghdeon ; deoaon lengh - s->es_lengh; sale_ao deoaon * s->spng_onsan/lengh; salesale_ao deon oe; noe node1->oe; deoe node->oe;} Adape Iage Reonson Adape Meshes Use Lagangan eqaons o oon o slae esh dynas. g The nenal spng oes hae spng onsans ha ay aodng o a daa dependen non sh as he agnde o he gaden. g s s k e N Dgal Iage: d k l Adapaon non: Obseaon: ad G d O a d y G gassan Spng Consan : - aes aodng o he adapaon non k 1 ρ k n ρ k ρ 5 O O a. Adape Sae Reonson Adape Sae Reonson

4 Mass-Spng Syses Snake pleenaon: Iage poessng: Mass-Spng Syses Applaons Heang and Melng Deoable Models Sae Reonson: Deoable obes apable o: Hea ondon Theoelasy Melng and ld-lke behao n he olen sae Cloh slaon spng heal onde eleen Theoelasy Spng sness k s a non o spng k k k ν heal onde eleen a s ν k a s s a < a < s Hea/Dson Eqaon Dson o hea n aeals: µσ C q Hea s onded o hgh epeae o lo epeae. The ae o hea ondon pe n aea s popoonal o he gaden o he epeae. The aon o hea eqed o ase he epeae o a aeal hea degees s popoonal o he ass o he saple pe n ole and he popoonaly ao sga he spe hea o he aeal.

5 ae o hea geneaon/loss pe n ole spe hea ole/kg. Keln aeal popey epeae Keln heal ondy a aeal popey q µσ C Hea/Dson Eqaon Dson o hea n aeals: ass densy kg/ 3 µ σ C gaden opeao q Hea/Dson Eqaon Hoogeneos soop aeal: q µσ q µσ Dseze he hea eqaon: Updae q µσ Theoelasy Lqds Pale Models Model long ange aaon and sho ange eplson oes beeen pas o pales aodng o Lennad-Jones poenals. Foes nolng nese poes o pale sepaaon n eqed sepaaon beeen pales Dsee Fld Model b a β ς α g g g The oal oe on a pale de o all ohe pales and deene he sengh o he aaon and eplson oes α β ζ aaon e eplson e a and b4

6 Pale-Based Lqd Pa s Ge s Gae Vsoelas Eleen es lengh l sness dapng Eqaons o oon ke e k ke e og eleen ass poson eloy aeleaon a e l Vsoelas Eleen eee sness: ke e M G K Ipl Neal Solon M G K dseze e: M / M L L G K K M Ipl Neal Solon M G M A K G K K M b K A eee syse a b eee load a

7 Se-Ipl Ele Skylne Soage Shees o Syse Ma A A s a n n a ha ypally eqes On 3 soage. Solng o Nodal Veloes Faoze: A T LDL T hee D dagonal a L loe angla Q D L 1 T Q DL T T b DL L b Q L Faoze: A T LDL T Sole loe angla syse o Q oad-sbson Sole ppe angla syse bak-sbson