KaVo Everest (a) (b) (c) 3. CAD

Size: px

Start display at page:

Download "KaVo Everest (a) (b) (c) 3. CAD"

衬紫苗
9 years ago
Views:

1 CAD 3. CAD [59] CAD Itelliget Detal Care System Fuctioally Geerated Path, FGP [60] Cerec3D [] Cerec3D 3. 3.a 3.b 3.c

2 KaVo Everest (a) (b) (c) 3. CAD

3 CAD a 3.2b 3.2a STL (a) (b) 3.2 Orieted Boudig Box, OBB

4 [6][62] Hough [63] [64] 3 [64] P0( x0, y0, z0) ϕ0( l0, m0, 0) Ni - 4 -

5 CAD N i m = A j = j NF j (3.) m NF j A j 3. ϕ l, m, ) 3.3a i ( i i i 3.3b ϕ i (a) (b) (3.2) CV λ3 ξ3 ϕ l, m, ) i ( i i i 2 li limi lii i= i= i= = 2 CV 3 3 limi mi mii (3.2) i= i= i= 2 lii mii i i= i= i=

6 KN max () (2) (3) (4) σ f( X) < σ X f ( x) ()~(4) KNmax (5) [65] [66][67] (Space Decompositio) (Hierarchical Boudig Volume)

7 CAD k-d [68] [69] BSP [70][7] S.Sur [72-74] AABB OBB K-DOPs AABB OBB K-DOPs (a) (b)aabb (c)obb (d)6-dop (K=6) a x y z

8 x y z [75][76] Axis-Aliged Boudig Box, AABB 3.4b AABB x y z AABB 3 AABB 6 [77][78] Orieted Boudig Box, OBB 3.4c OBB OBB OBB OBB OBB OBB [79] K Discrete Orietatio Polytopes, K-DOPs K 3.4d FDH Fixed Directio Hull FDH D FDH AABB D k/2 [80] FDH K-DOPs K-DOPs AABB OBB AABB OBB OBB

9 CAD OBB OBB OBB OBB [7][23] OBB OBB Gottschalk [79] i S i p q i r i S

10 u C u = 3 i= ( p i + q i i + r ) (3.3) p i = p i u, C ( p p q q r r ) j, k 3 (3.4) i i q q u i i i i i i jk = j k + j k + j k 3 i = =, i i r r u =, S C 3 3 OBB S OBB u i C i Ai p q i r i ( i i ) ( i i i Ai = q p r p ) 2 A= A i u C Ai i i i u = ( p + q + r ) (3.5) 3A i= A C ( p p q p r r ) j, k 3 (3.6) i i i i i i i jk = j k + j k + j k i= 3A p i = p i u q i = q i u r i = r i u 2 OBB OBB S [8][82]

11 CAD S [83][84] OBB OBB L L 0 L 0 Normal m Normalim 0 Normalim 0 Normalim OBB

12 [83] TraverseTree( VE, VF) VE VF [84-86] TraverseTree( V E, V F ) if bs ( E) bs ( F) the if VE the if VF the if SE SF the S E S F retur edif else for VF 2 vf TraverseTree( V E, v f ) ed for edif else if V the F for VE 2 ve TraverseTree( v e, V F ) ed for else for VE 2 ve for VF 2 vf TraverseTree( v e, v f ) ed for ed for

13 CAD edif edif edif E F S E S F VE V F bs ( E ) bs ( F ) 2 OBB OBB i) ii) OBB 3.7 SA 3 3 ( PB PA) i SA > DA[] i i OA[] i i SA + DB[] i i OB[] i i SA (3.7) i= i= OA[3] OB[3] A B DA[3] DB[3] PA PB A B SA

14 A OA[0]iDA[0] OB[0]iDB[0] B ABC PQR 3.8 Q B SA F A R G P C 3.8 ABC PQR i PQR ABC Ψ ABC PQR PQR ABC Ψ Ψ = AB AC = ( b a) ( c a) sp = AP sq = AQ sr = AR - 5 -

15 CAD a) sp sq sr P Q R Ψ ABC PQR b) sp sq sr 2 PQR Ψ sp sq sr 2 PQR Ψ sp sq sr PQR ABC PQR ABC c) sp sq sr 2 sp sq sr PQR ABC Ψ ii PQR Ψ ABC PQR PQ sp sq PQ Ψ 3.9 PQ Ψ ABC PQ ABC sp sq PQ Ψ PQ ABC A P Q C B 3.9 PQ ABC PQ d R ( t) = P+ td, 0 t + (3.8) ABC { VA, VB, VC} Ψ R R = wv + uv + vv (3.9) uvw,, A B C u+ v+ w= ( uvw R,, ) P+ td = ( u v) V A + uv B + vv C t [ d VB VA VC VA] u = [ P VA] w (3.0) (3.)

16 3. P VA VB VA VC V t A u d P VA VC V = A d VB VA VC V A v d VB VA P V A ( P VA) ( VB VA) ( VC VA) = ( d ( VC VA) ) ( P VA) ( d ( VC VA)) ( VB VA) (( P VA) ( VB VA)) d (3.2) tu, v PQ Ψ ABC 0 u,0 v, u+ v ABC Ψ ABC [87] iii PQR ABC ABC PQR 3 ABC Ψ PQR ABC ϕ0( l0, m0, 0) P0( x0, y0, z0) Ax ( a, ya, za) A ' ' ' ' ' α A( xa, ya, za ) A A A ϕ0 α A A [88][89]

17 CAD A ϕ α R ϕ0 m0 / lxy l0 / lxy l0 / lxy m0 / l 0 0 xy 0 z0 l 0 xy R= RZRXR RX RZ = lxy z cosα siα m0 / lxy l0 / lxy 0 0 siα cosα z0 lxy 0 l0 / lxy m0 / l 0 0 xy lxy z (3.3) l xy ϕ0 xoy RZ ϕ 0 z yoz RX ϕ0 x xoy 2 T A T = (3.4) x0 y0 z0 3 A W A α W = T R T = R (3.5) x0 y0 z0 x0 y0 z0 ' ' ' ' 4 A A( x, y, z ) a a a OBB ' ' ' xa ya za = xa ya za W (3.6) OBB OBB OBB

18 AtosII KNmax 200 σ 0.05mm mm

19 CAD OBB 0.0rad (a) (b)

20 OBB OBB

( CIP).:,3.7 ISBN TB CIP (3) ( ) ISBN O78 : 3.

( CIP).:,3.7 ISBN TB CIP (3) ( ) ISBN O78 : 3. ( CIP).:,3.7 ISBN 7 568 383 3.......... TB CIP (3) 334 3 37 ( ) 64536 www.hdlgpress.com.c 7879 6 9.75 479 3 7 3 7 45 ISBN 7 568 383 3O78 : 3. 995,.,.,.,. :,,,,.. :,,,,,,.,,,,.,,. ,,.,,,.,,,.,,,,.,.,,,