Please help me vectorize my loop to construct query vector from sample points

I want to construct a vector xq (the query vector) from xs (sample point vector) for use in interp1. Ideally, xq would:

1. contain all element from xs
2. evenly spaced when between any xs(i) and xs(i+1)
3. xq(i+1)-xq(i)<t always true for a given threshold t.
4. for xs(i+1)-xs(i)<t already, no xq between the 2 points (but just on xs(i+1) and xs(i))

I cannot think of any code to achieve all of 4 without some kind of loop. Does anyone have a good idea? Thanks in advance

Here is a loop version I wrote. I am sorry if I didn't prase my original question clearly.

t=2;
xs=cumsum(10*rand(1,10))
xsdelta=diff(xs)

xq=[];
for i=1:length(xsdelta)
    xq=[xq,xs(i),nan([1,floor(xsdelta(i)/t)])];
end
xq=[xq,xs(end)]
xq=fillmissing(xq,"linear",2)

Answer 1

[Bruno Luong]

xs=cumsum(ceil(10*rand(1,10)))

t=pi;
p=cumsum([0 ceil(diff(xs)/t)]);
xq=interp1(p,xs,0:p(end))

[Yi-xiao Liu]

Awsome, thank you!