COMPU STRU GRAPHICS
COMPU STRU GRAPHICS CAP 4730
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This 8 page Class Notes was uploaded by Sierra Gorczany on Friday September 18, 2015. The Class Notes belongs to CAP 4730 at University of Florida taught by Staff in Fall. Since its upload, it has received 21 views. For similar materials see /class/206734/cap-4730-university-of-florida in System Engineering at University of Florida.
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Date Created: 09/18/15
Spatial Rational BSpline Motions Yu Zhang I r 1 r in 4l 4 Reference ComputerAided Design with Spatial Rational B spline Motions by B Jiittler and M G Wagner Outline of no will 7 7 t x t 1 lg l J 9 Introduction o Theory 9 Implementation Introduction Given Data of a moving system esign BSpline Motion of a Cube Theory 1 Spatial Kinematics Fixed space E3 Moving space E3 Euclidean 3spaces Lineartransformation M E gtEfHpMf 2 2 2 2 0 O 0 0 Where v0v0d0d1d2d3 lt 0 Iii i lt I 2d1d2 dods dlz 2d2d3 dodi doz di2 d32 2d1d2 d0d3 2d1d3 dodz v U U 2d1d3 dodz 2d2d3 dodl 0 02 d12 d d 3 Spatial displacement displacement v v0 v1 v2 v3T rotation axis F and angle q cosi sinif 2 c2 dfdjd32 2 d dfd d32 d Mt EA gtE 131H pzMz13 2 BSpline Functions Bspline basis functions N I wZTtNZ1t 1 6031 IDN 1 I l l l em 4 39 1f 1quot lt 1 0 1 1f It s t lt rm h COLT t iq ti NiT t 0 otherwise Matrixvalued Bspline function Ma iNZ 0141 where Ai are m1 constant coefficient matrices from control points 0 otherwise A 3 Interpolation 1 Determine unknown control points 2 End conditions 3 Finding a knot sequence 4 Produce Bspline basis 5 Spatial displacements Mt E gt E m gt pt Mtf Implementation BSpline Motion of a Gn39pper