A B-Spline Least-Squares Surface-Fitting Method for Articular Surfaces of Diarthrodial Joints

1993 ◽  
Vol 115 (4A) ◽  
pp. 366-373 ◽  
Author(s):  
G. A. Ateshian
Keyword(s):  
Least Squares ◽  
Articular Surface ◽  
Three Dimensional ◽  
Surface Fitting ◽  
B Spline ◽  
Spline Surface ◽  
Articular Surfaces ◽  
Diarthrodial Joint ◽  
Surface Data ◽  
Fitting Method

The B-spline least-squares surface-fitting method is employed to create geometric models of diarthrodial joint articular surfaces. This method provides a smooth higher-order surface approximation from experimental three-dimensional surface data that have been obtained with any suitable measurement technique. Akima’s method for surface interpolation is used to provide complete support to the B-spline surface. The surface-fitting method is successfully tested on a known analytical surface, and is applied to the human distal femur. Applications to other articular surfaces are also shown. Results show that this method is precise, highly flexible, and can be successfully applied to a large variety of articular surface shapes.

Three-dimensional filtering of engineering surfaces using a least squares non-parametric B-spline surface

1997 ◽  
Vol 211 (7) ◽  
pp. 557-564 ◽  
Author(s):  
J Tholath ◽  
V Radhakrishnan
Keyword(s):  
Surface Roughness ◽  
Least Squares ◽  
Three Dimensional ◽  
B Spline ◽  
Spline Surface ◽  
Filtering Procedure ◽  
Dimensional Surface ◽  
Non Parametric

With the advent of cheap and powerful computers, three-dimensional evaluation of surfaces is possible. The three-dimensional surface requires a filtering procedure for waviness separation. This paper deals with the waviness plane construction through a least squares non-parametric B-spline surface. Roughness values obtained by two-, two-and-a-half- and three-dimensional evaluations of typical surfaces are also given.

scholarly journals Complex Uncertainty of Surface Data Modeling via the Type-2 Fuzzy B-Spline Model

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1054
Author(s):  
Rozaimi Zakaria ◽  
Abd. Fatah Wahab ◽  
Isfarita Ismail ◽  
Mohammad Izat Emir Zulkifly
Keyword(s):  
Complex Surface ◽  
Complex Data ◽  
Fuzzy Data ◽  
Control Points ◽  
B Spline ◽  
Spline Surface ◽  
Data Control ◽  
Surface Data ◽  
Model Complex

This paper discusses the construction of a type-2 fuzzy B-spline model to model complex uncertainty of surface data. To construct this model, the type-2 fuzzy set theory, which includes type-2 fuzzy number concepts and type-2 fuzzy relation, is used to define the complex uncertainty of surface data in type-2 fuzzy data/control points. These type-2 fuzzy data/control points are blended with the B-spline surface function to produce the proposed model, which can be visualized and analyzed further. Various processes, namely fuzzification, type-reduction and defuzzification are defined to achieve a crisp, type-2 fuzzy B-spline surface, representing uncertainty complex surface data. This paper ends with a numerical example of terrain modeling, which shows the effectiveness of handling the uncertainty complex data.

Computation of Voxel Maps Containing Tool Access Directions for Machining Free-Form Shapes

1996 ◽  
Author(s):  
Johan W. H. Tangelder ◽  
Joris S. M. Vergeest ◽  
Mark H. Overmars
Keyword(s):  
Free Form ◽  
Geometric Accuracy ◽  
Surface Sampling ◽  
B Spline ◽  
Spline Surface ◽  
Surface Data

Abstract An algorithm that derives tool access directions for machining free-form shapes is presented. A free-form shape to be machined is given by a preliminary B-spline model. We allow that the B-spline surface data are as inaccurate as the user-selected geometric accuracy of the prototype to be machined. Using surface sampling a visibility voxel map is obtained. From this map a voxel map is derived that contains per voxel a set of tool access directions. From the obtained voxel map regions can be selected that can be machined with a fixed tool access direction per region.

B-spline surface fitting to random points with bounded boundary conditions

2007 ◽  
Vol 30 (4) ◽  
pp. 281
Author(s):  
Kuo Jen Chen ◽  
Yao Chen Tsai ◽  
Jiing Yih Lai ◽  
Wen Der Ueng
Keyword(s):  
Boundary Conditions ◽  
Surface Fitting ◽  
B Spline ◽  
Spline Surface

Topographic matching of distal radius and proximal fibula articular surface for distal radius osteoarticular reconstruction

2015 ◽  
Vol 41 (6) ◽  
pp. 657-663 ◽  
Author(s):  
H. Zhang ◽  
S. Chen ◽  
Z. Wang ◽  
Y. Guo ◽  
B. Liu ◽  
...  
Keyword(s):  
Distal Radius ◽  
Articular Surface ◽  
Three Dimensional ◽  
Three Dimensional Model ◽  
Optimal Position ◽  
Fibula Graft ◽  
Proximal Fibula ◽  
Articular Surfaces ◽  
Computed Tomography Scanning

During osteoarticular reconstruction of the distal radius with the proximal fibula, congruity between the two articular surfaces is an important factor in determining the quality of the outcome. In this study, a three-dimensional model and a coordinate transformation algorithm were developed on computed tomography scanning. Articular surface matching was performed and parameters for the optimal position were determined quantitatively. The mean radii of best-fit spheres of the articular surfaces of the distal radius and proximal fibula were compared quantitatively. The radial inclination and volar tilt following reconstruction by an ipsilateral fibula graft, rather than the contralateral, best resembles the values of the native distal radius. Additionally, the ipsilateral fibula graft reconstructed a larger proportion of the distal radius articular surface than did the contralateral. The ipsilateral proximal fibula graft provides a better match for the reconstruction of the distal radius articular surface than the contralateral, and the optimal position for graft placement is quantitatively determined.

Reverse Engineering Physical Models Employing Wrap-Around B-Spline Surfaces and Quadrics

1996 ◽  
Vol 210 (2) ◽  
pp. 147-157 ◽  
Author(s):  
D J Weir ◽  
M J Milroy ◽  
C Bradley ◽  
G W Vickers
Keyword(s):  
Reverse Engineering ◽  
Computer Aided Design ◽  
Laser Scanning ◽  
Three Dimensional ◽  
Surface Fitting ◽  
Physical Models ◽  
Scanning System ◽  
Cad Model ◽  
Three Dimensional Model ◽  
B Spline

Reverse engineering involves digitizing a three-dimensional model or part, by means of a tactile or non-contact optical sensor, converting the data to a CAD (computer aided design) database description and manufacturing by CNC (computer numerical controlled) machines. This paper demonstrates an effective approach to the reverse engineering of physical models by employing a three-dimensional laser scanning system in conjunction with surface-fitting software developed by the authors. Accurate surface data are collected by the laser scanner and then input to the surface-fitting software. Surface entities such as B-spline and quadric functions are employed to build the CAD model. The CAD model is compatible with popular design and manufacturing software packages. A telephone receiver is used to illustrate the efficiency of the process.

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