odextend.m and deval.m

Dear all,
I am using ode15s.m to integrate a set of ODEs, with an event. Then, I am using odextend.m to integrate a slighlty different set of ODEs. The final solution is dicontinuous, as shown below. Note that I am just using y-values and the x-values represent the indices for the x data points.
I've been using deval.m over the entire domain to get the solution with a specified number of x data points. However, I learned that deval.m does not reproduct the results correctly, as shown below:
I am wondering how we should handle the discontinuity so that we get the correct solution, represented by the user-specified number of data points (i.e., 25 in this case)?
Thank you and Happy New Year!
Sincerely,
Tae

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I guess one solution is to assess a set number of points from the original solution vector...

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