| Curve fitting is an important research direction in computer-aided design and computer graphics.In this paper,the curve fitting method based on shape-changing chain and the curve fitting method based on discrete cosine transform(DCT)are mainly studied.The main work and conclusions are as follows.A shape-changing chain containing only M-segment(mean segment,with constant shape and size),C-segment(constant-curvature segment,with constant curvature and variable length)or H-segment(helical segment,with constant curvature and torsion and variable length)is called a rigid-body shape-changing chain.It is difficult to use a unified standard to measure the length change of C-segments(or H-segments)and the angle change between segments when connecting the rigid-body chains with revolute joints(or spherical joints).In addition,segments containing a large number of datapoints may lead to a huge amount of calculation.In this paper,In order to solve these problems,virtual chain method to connect rigid-body chains with revolute or spherical joints is proposed.The application of shape-changing chain curve fitting method in key frame animation,including 2D and 3D contour animation,2D skeletal animation,is proposed.Shape-changing chain-based keyframe animation describes the motion of an animated image from the perspective of mechanism motion,and provides a new idea for complementing keyframe occlusion.Two-dimensional and three-dimensional contour animations based on shape-changing chain only need to interpolate fewer parameters and combine the segment information to determine the initial configuration of each segment in the intermediate frame,and use the fmincon function of MATLAB to determine the final configuration of each segment in the intermediate frame.The two-dimensional skeletal animation based on shape-changing chain is suitable for images such as people or animation characters.The intermediate frame of the skeleton is generated through the two-dimensional contour animation of the shape-changing chain,and the intermediate frame of skin is generated through the binding method and interpolation strategy of the skeletal and the skin.On the basis of the shape-changing chain curve fitting method,the related methods of plane surface shape fitting are developed.The plane surface shape fitting method based on the shape-changing chain fits a group of simple plane shapes through E-unit(elongation),and E-unit is tensile/compressive deformation unit.In order to fit the more complex plane shape,shear deformable S-unit(shear)and bendable B-unit(bending)are proposed.Truss structure is proposed to simulate the deformation modes of the above three units,which can be widely used in machining and industrial production.As for DCT method,this thesis mainly introduces its morphometric applications.In order to ensure the mathematical homology of fitting parameters and improve the fitting accuracy,an optimization algorithm for amplitude selection is proposed.The amplitude selection algorithm in this paper ensures that the amplitudes with larger absolute values are retained,and other amplitudes are set to zero.DCT can be used to fit surface,and surface can be defined as a path passing through all points on the surface.The curve representing the surface can be determined by the experience of researchers,or by the relevant algorithm of the traveling salesman problem.Subsequent research only needs to fit the curve through DCT.The curve fitting method of DCT is applied to fit different curve and surface samples respectively and perform morphological analysis.The nasal aperture,right orbit and right zygomatic curve are extracted from the infant skull data set of coronal craniosynostosis.The fitting parameters were visualized and classified by linear discriminant analysis,and leave-one-out was used for cross validation.Surface fitting studies a set of simulated mathematical surfaces and two sets of surfaces extracted from the infant skull data set of coronal craniosynostosis,and the fitting parameters visualize differences between different samples by principal component analysis.Experiments show that the application of the curve fitting method based on DCT in morphometrics is stable and effective. |
