1. spline toolbox - interpolation of topologically rectangular 3D data set

hi

i need to create a bivariate cubic Bspline interpolation to a

_topologically_ rectangular grid of data, being control polygon points of

a CAD patch which is highly 3D, and not _geometrically_ rectangular.

(.mat file has data as 3 matrices - xcoords mtx, ycoords mty, zcoords mtz)

however the demo TSPDEM.m only details this for _geometrically_

rectangular data, which in addition has (x,y) mapped to the unit square.

i can't work out the solution - some of the problems i have are as

follows:

a) the bivariate interpolation

SPAPI({KNOTS1,...,KNOTSm},{X1,...,Xm},Y)

seems to assume that X1,Xm are geometrically perpendicular. how do

i account for the fact that my surface parametric directions are not

aligned with (x,y)?

b) to obtain the 2 knot vectors, i have to use chord-wise normalised

parameterisation on each line of u=const, v=const points. i then take as

the u or v knot sequence the average of the knot sequences for u=const &

v=const.

for i=1:nu,

coefv(:,:,:,i) = [mtx(i,:);mty(i,:);mtz(i,:)];

ddv = diff(coefv(:,:,:,i)')'

tv(i,:) = cumsum([0,sqrt([1 1 1]*(ddv.*ddv))])

tv(i,:) = tv(i,:)/tv(i,nv)

lt = length(tv(i,:));

kv = kv + [0,0,0,(optknt(tv(i,:),3)),1,1,1]

end

knotsv = kv/nu

spv(i) = spapi(knotsv,tv(i,:),mtz)

%similar for u-direction

if i try and use the subsequent knotsu,knotsv vectors in SPAPI

with {X1..Xm} = {coefu,coefv} and Y = mtz, i get [any number of] errors.

c) if i try and use SPCOL to gain the collocation matrix and then

construct the bivariate spline values 'by hand', i have problems with TAU

since my KNOTS are chord-wise normalised vectors but my data TAU isn't.

i would greatly appreciate some ideas.

regards

will kellar

+-------------------------------------------------------------------------+

Mr William P Kellar Tel: +44 1223 3 32869 (day)

Div. A +44 1223 367459 (eve)

Cambridge University Engineering Department

Trumpington Street, Cambridge CB2 1PZ, UK

+-------------------------------------------------------------------------+

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