CAD 3. CAD [59] CAD Itelliget Detal Care System Fuctioally Geerated Path, FGP [60] Cerec3D [] Cerec3D 3. 3.a 3.b 3.c - 38 -
KaVo Everest (a) (b) (c) 3. CAD 3.2-39 -
CAD 3.2 3.2a 3.2b 3.2a STL (a) (b) 3.2 Orieted Boudig Box, OBB - 40 -
3.3 3.3. 9 [6][62] Hough [63] [64] 3 [64] P0( x0, y0, z0) ϕ0( l0, m0, 0) 3 3.3.2 3.3.2. Ni - 4 -
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 - 42 - (a) (b) 3.3.2.2 3.3 (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= 3.3.2.3
KN max () (2) (3) (4) σ f( X) < σ X f ( x) ()~(4) KNmax (5) 3.4 3.4. [65] [66][67] (Space Decompositio) (Hierarchical Boudig Volume) - 43 -
CAD k-d [68] [69] BSP [70][7] S.Sur [72-74] AABB OBB K-DOPs AABB OBB K-DOPs 3.4-44 - (a) (b)aabb (c)obb (d)6-dop (K=6) 3.4 3.4a x y z
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 - 45 -
CAD 3.4.2 OBB 3.4.2. OBB 2 3.5 7 2-46 - 3.5 OBB OBB [7][23] OBB OBB Gottschalk [79] i S i p q i r i S
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 3.3 3.3 3.4 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] - 47 -
CAD S 3.6-48 - 3.6 [83][84] OBB OBB L L 0 L 0 Normal m Normalim 0 Normalim 0 Normalim 0 3.4.2.2 OBB
[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 - 49 -
CAD edif edif edif E F S E S F VE V F bs ( E ) bs ( F ) 2 OBB OBB i) 5 6 9 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 5-50 -
A OA[0]iDA[0] OB[0]iDB[0] B 3.7 3 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 -
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 - 52 - 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,, ) 3.8 3.9 P+ td = ( u v) V A + uv B + vv C t [ d VB VA VC VA] u = [ P VA] w (3.0) (3.)
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 3.5 3.5. 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] - 53 -
CAD A ϕ α R ϕ0 m0 / lxy l0 / lxy 0 0 0 0 0 l0 / lxy m0 / l 0 0 xy 0 z0 l 0 xy R= RZRXR RX RZ = 0 0 0 0 lxy z0 0 0 0 0 0 0 0 cosα siα 0 0 0 0 0 m0 / lxy l0 / lxy 0 0 siα cosα 0 0 0 z0 lxy 0 l0 / lxy m0 / l 0 0 xy 0 0 0 0 lxy z0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 (3.3) l xy ϕ0 xoy RZ ϕ 0 z yoz RX ϕ0 x xoy 2 T A 0 0 0 0 0 0 T = (3.4) 0 0 0 x0 y0 z0 3 A W A α 0 0 0 0 0 0 0 0 0 0 0 0 W = T R T = R (3.5) 0 0 0 0 0 0 x0 y0 z0 x0 y0 z0 ' ' ' ' 4 A A( x, y, z ) a a a 3.5.2 OBB ' ' ' xa ya za = xa ya za W (3.6) OBB OBB OBB - 54 -
3.5 3.6 3.6 3.6 3.6 AtosII 3.0 398900 27600 3.0 978 3745 KNmax 200 σ 0.05mm 3. 3.2mm 3. - 55 -
CAD OBB 0.0rad 3.2 3.2 3.3 (a) (b) 3.3 3.7-56 -
OBB OBB - 57 -