Maybe something like this:
x = [5 10 36 20 17 5 51 60 40 13];
L = numel(x);
fs = 4;
t=0:1/fs:(L-1)/fs;
idx = find(abs(diff(x))>25);
% i'm just going to build a whole new t vector
tf = [];
for d = 1:numel(idx)
a = idx(d);
if d==1 && a>1
tf = t(1):0.25:t(a); % pad head
end
% refine this segment
tseg = t(a):0.05:t(a+1);
tf = [tf(1:end-1) tseg];
if d==numel(idx) && a<numel(t)
tf = [tf(1:end-1) t(a):0.25:t(end)]; % pad tail
elseif d<numel(idx) && idx(d+1)>(a+1)
tf = [tf(1:end-1) t(a+1):0.25:t(idx(d+1))]; % pad between
end
end
% interpolate the whole thing
xf = interp1(t,x,tf,'spline')
plot(t,x); hold on
plot(tf,xf)
