Re: interpolation with cubicmx.mexmaci from griddata

On Jul 15, 4:23 pm, "Steven Lord" <sl...@xxxxxxxxxxxxx> wrote:
"JennieB" <jagbart...@xxxxxxxxx> wrote in message

news:0759c503-d7e9-4320-b761-f3b0d4e4ab9d@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

Hello,

I am trying to verify the exact technique used by griddata to perform
cubic interpolation.  Cubicmx (the file called by griddata that
performs the zi interpolation) is not accessible, and a phone call to
tech support did not convince them to transfer me to someone who could
answer this question or allow me to sneak a peak at the source code
(likely against policy, but I figured trying wouldn't hurt).

You shouldn't try using the cubicmx MEX-file directly; it's intended as a
helper function for GRIDDATA, not to be invoked directly by the user.

I was curious if anyone here had some insider info on how the function
works and could explain it to me?  I need to verify that the
interpolation is fairly rigorous (preferably basis functions), and
what I am really after is the derivatives used in the interpolation so
that I can more specifically characterize the 3D surface elements that
are the end goal of my work.

Take a look at the Algorithm and References sections of the reference page
for GRIDDATA for some information about the algorithms GRIDDATA uses.

http://www.mathworks.com/access/helpdesk/help/techdoc/ref/griddata.html

--
Steve Lord
sl...@xxxxxxxxxxxxx

Hi Steve,

Thanks so much for your reply. While I had skimmed the QHull web site
that the GRIDDATA page references, I hadn't noticed the paper that
they cited and reading that definitely helped my understanding of the
Delaunay tesselation algorithm. However, I am still unsure about
exactly what nonlinear interpolation methods GRIDDATA uses. Those
seem to be buried in CUBICMX, the mex file I don't have access to.

I understand that GRIDDATA uses Delaunay tesselation to form planar
triangles corresponding to the original nonuniform data that I'm
inputting to create a surface. The interpolation points are then
matched to the planar triangles using TSEARCH, and fed into CUBICMX to
actually determine the z values corresponding to the x-y interpolation
points. How, at this step, does Matlab interpolate? I understand
that linear interpolation is simple using the single triangular
element, but when you move to cubic interpolation, you need more than
the 3 vertices of the triangle for a nonlinear fit. Does the
interpolation use surrounding triangles? If so, does it use only the
nearest triangles in contact with the element in question or a region
of triangles? I am used to doing surface element fitting that sorts my
scattered data into uniform elements rather than this flipped method
that seems to sort the interpolation points into a nonuniform
triangular grid of my scattered data. Understanding exactly how
rigorous this process is would be really useful.

Thanks for your help,
Jennie
.

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