I would like to ask if there are any articles or researches on the use these methods in interpolation or interpolation applications ..And What is the difference between them?
NURBS surfaces are based on regular rectangular grid of control points and two knot vectors for both directions. The interpolation methods are e.g. in NURBS book (Piegl, Tiller) and are based on solving the system of equations to find positions of control points to interpolate given data.
More exactly:
Given a grid of ( m+1) × ( n+1) data points D_ij (0 ≤ i ≤ m and 0 ≤ j ≤ n) and a degree (p, q), find a B-spline surface of degree (p,q) defined by ( m+1) × ( n+1) control points that passes all data points in the given order.
T-spline surfaces does not need regular control grid, the positions are in T-mesh and the knot vectors are only local for every control point (their size depends on the degree of surface, in details in T-spline, Sederberg).
T-spline are used as approximating methods - it only uses the input points as control points and try to find local knot vectors:
http://www.merl.com/publications/docs/TR2017-141.pdf
https://pdfs.semanticscholar.org/3eef/b82928636a3b0a35b2d1929109f3e351f678.pdf
T-spline interpolation will find new T-mesh with new control points and their knot vectors that after computation goes throw the input points but I have not see this algorithms yet.
Best regards,
Jana
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