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The Mitchell–Netravali filters or BC-splines are a group of reconstruction filters used primarily in computer graphics, which can be used, for example, for anti-aliasing or for scaling raster graphics. They are also known as bicubic filters in image editing programs because they are bi-dimensional cubic splines. [1] [2] [3]
The library provides bindings for the C and C++ languages. Its stand-alone command-line tools can generate graphs and perform numerical calculation of spline curves and systems of ordinary differential equations. Plotutils is a GNU package and is distributed under a free software licence, the GPL.
Example showing non-monotone cubic interpolation (in red) and monotone cubic interpolation (in blue) of a monotone data set. Monotone interpolation can be accomplished using cubic Hermite spline with the tangents m i {\displaystyle m_{i}} modified to ensure the monotonicity of the resulting Hermite spline.
Cubic polynomial splines are extensively used in computer graphics and geometric modeling to obtain curves or motion trajectories that pass through specified points of the plane or three-dimensional space. In these applications, each coordinate of the plane or space is separately interpolated by a cubic spline function of a separate parameter t.
Bicubic interpolation can be accomplished using either Lagrange polynomials, cubic splines, or cubic convolution algorithm. In image processing , bicubic interpolation is often chosen over bilinear or nearest-neighbor interpolation in image resampling , when speed is not an issue.
Dynamic cubic splines with JSXGraph; Lectures on the theory and practice of spline interpolation; Paper which explains step by step how cubic spline interpolation is done, but only for equidistant knots. Numerical Recipes in C, Go to Chapter 3 Section 3-3; A note on cubic splines; Information about spline interpolation (including code in ...
It was devised by Edwin Catmull and Jim Clark in 1978 as a generalization of bi-cubic uniform B-spline surfaces to arbitrary topology. [1] In 2005/06, Edwin Catmull, together with Tony DeRose and Jos Stam, received an Academy Award for Technical Achievement for their invention and application of subdivision surfaces. DeRose wrote about ...
The second class of generalizations to multi-dimensional smoothing deals directly with this scale invariance issue using tensor product spline constructions. [ 10 ] [ 11 ] [ 12 ] Such splines have smoothing penalties with multiple smoothing parameters, which is the price that must be paid for not assuming that the same degree of smoothness is ...