Parameterised Spline fit, calling with function handles, storage and calling in cell arrays

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Geoffrey Rivers
Geoffrey Rivers about 19 hours 前
编辑： Geoffrey Rivers about 18 hours 前
I am trying to take a set of X and Y coordinate arrays of unknown (but matching) size, fit a spline to them in a manner that allows me to call the spline as a parametric function of 0 <= t <= 1 at high resolution. When I say high resolution, I mean that I want to use the parametric equation with an arbitrary double between 0 and 1, when I'm fitting my spline with anywhere from 8 to 2000 points.
Here's the annoying bit: I need to be able to do this in a "generate, store, then unpack and use later" format. These coordinate arrays are coming from another function in the form of a cell array, where each cell contains a set coordinates in another format where multiple splines worth of data is combined*. The purpose of the function I'm working on is to unpack them from the cell array one cell at a time, unstitch them into by-spline sets, then for each by-spline set fit a spline as a parametrically-evaluatable equation and then package all those back into organised cells so I can later call on and evaluate specific ones.
I found another answer on here that suggested a method for parametric splines using function handles, but it doesn't seem to work. I've stripped the problem down to just the fit-evaluate-store step, and I've put specific questions about clarifications in comments.
*to clarify: I'm converting isocontour matrices into sets of parameterised splines, where I have several isocontour matrices each for a different thing, each containing multiple (unknown number) isocontours.
function runtests
x=double([1 1 2.5 3.5 2 2.5 2 3 3.5 4 5 6 7 5 5 4 3 2 2.5 2.5 1]); %this is mock data, my actual sets are larger
y=double([2 3 5 4 2 4 3 4 5 6 5.5 4 3 2 1 1.5 2 3 4 4 2]);
%data sets are closed loops where the first and last point are the same, and tangents should be smooth.
n = size(x,2);
t = linspace(0,1,n); %--> I need a t for calling Spline (it seems)?
%There's a whole other problem here where t should be equally spaced along the arclength of the spline
% which with this method it is not, so there may actually be a whole preceeding step necessary
% where we fit the data with a simple spline(x,y) to assess arclength positions of the ource points
% and somehow evaluate it for t and then parameterise it? I'm hoping there's a more clever way of
% doing that
z = linspace(0,1,(4*n)); % --> once I generate pp as a spline fit for t,
% can I call it with a function handle that uses a different value in the
% @(), such as @(z) so long as they have the same total range (0 to 1)?
% If so, does z need to be initialised, or left uninitialised prior to the
% function handle call? Does z and t need to be the same size?
tailslope = ((y(2)-y(1))/(x(2)-x(1))+(y(n)-y(n-1))/(x(n)-x(n-1)))/2;
% this will be the assigned start and end slopes.
%This parametric spline code is from
% https://www.mathworks.com/matlabcentral/answers/1584539-blind-parametric-interpolation-fitting-for-a-set-of-points
pp = spline(t,[x(:),y(:)].'); %how do I add assigned start and end slopes to this (the Help example is much
%simpler and not parametric).
xy = @(t) ppval(pp,t) %parametric curve xy(t)
%can I then store "xy" to a cell for exporting to other functions? or would I need to store "pp"? how do I call
%these if I have multiple pp structures from multiple cells in a later function?
%can you do xy = @(t) ppval(cell{k},t) ?
hold on;
plot(x,y,"o"); % points used for spline
%once parameterised and a function handle of xy(t), how do I plot it from the function handle over 0<z<1 at a
%different resolution on an x-y plot?
end

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