From any points in the plane, the program creates a Bezier curve (with eligible points) and can interpolate the generated points for any x set: the lower the number, the smoother the final curve. The user chooses whether an interpolated curve and a graph with points curves are created.
The interpolation curve can be applied to scatter or noisy xy data, in order to resample and smooth the original data.
function [bezcurve, intcurveyy] = bezier_(points, numofpbc, intcurvexx, fig)
Creates Bezier curve (output 'bezcurve') from 'points' (1st input argument) and the number of points (2nd input argument) and can create from it another interpolated curve (whose xcoordinates are in the input 'intcurvexx' and whose ycoordinates are in the output 'intcurveyy').
INPUTS:
points: matrix ((n+1) x 2) with the original points in xy plane
numofpbc: number of points in the Bezier curve (by default 100)
intcurvexx: vector with xcoordinates of the interpolation curve. If this argument does not exist or is empty, the program generates Bezier curve, but no interpolation curve
fig: any value if you want a figure of points and curve (otherwise, do not enter 4th argument). You can enter here the representing symbol for the points (for instance, 'ks' for black squares).
OUTPUTS:
bezcurve: the Bezier curve, not interpolated, in the format [x y], i.e. a (numofpbc x 2) matrix.
intcurveyy: vector with ycoordinates (by nonparametric interpolation from intcurvexx) of the interpolation curve; it has sense only if intcurvexx elements are monotonically increasing.
Example: x = (1:100)';
y = 0.2*randn(size(x))  sin(pi*x/100) + 0.5*x/100;
points = [x y];
bezier_(points, 500, [], 1); % Creates only the Bezier curve and represents it together with the original points
Or: bc = bezier_(points); % You want the Bezier curve (with 100 points), but no graph nor interpolated curve
Or: [bc, intcyy] = bezier_(points, 500, (1:0.1:20)', 1); % You want all the Bezier curve, the interpolation of part of it and the graph of all.
