This module explains B-splines, which form a basis for splines.
Topics in surface modeling: b-splines, non-uniform rational b-splines, physically based deformable surfaces, sweeps and generalized cylinders, offsets, blending and filleting surfaces. Non-linear solvers and intersection problems. Solid modeling: constructive solid geometry, boundary representation, non-manifold and mixed-dimension boundary representation models, octrees. Robustness of geometric computations. Interval methods. Finite and boundary element discretization methods for continuum mechanics problems. Scientific visualization. Variational geometry. Tolerances. Inspection methods. Feature representation and recognition. Shape interrogation for design, analysis, and manufacturing. Involves analytical and programming assignments.
Topics in surface modeling: b-splines, non-uniform rational b-splines, physically based deformable surfaces, sweeps and generalized cylinders, offsets, blending and filleting surfaces. Non-linear solvers and intersection problems. Solid modeling: constructive solid geometry, boundary representation, non-manifold and mixed-dimension boundary representation models, octrees. Robustness of geometric computations. Interval methods. Finite and boundary element discretization methods for continuum mechanics problems. Scientific visualization. Variational geometry. Tolerances. Inspection methods. Feature representation and recognition. Shape interrogation for design, analysis, and manufacturing. Involves analytical and programming assignments.
Fractional B-splines are extension of B-splines.
To perform geometric transforms on discrete images such as a rotation or zooming we need to first fit the discrete data to a continuous function. This can be done using splines. B-splines can be used to interpolate and form the continuous image from the discrete samples.
Basic introduction to splines. Link to other modules.
B-splines form a simple set of scaling functions satisfying the dilation equation with binomial filter coefficients. However B-Splines other than the zeroth order B-spline (the Haar function) are not orthogonal to its own shifts. Hence to form a perfect reconstruction(PR) filter bank system, biorthogonal scaling functions are used. Also semiorthogonal filter banks can be used to form a PR filter bank system.
