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Action:
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Creates a bicubic surface that interpolates or fits a set of points, with specified boundary derivatives and twist vectors.
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Prototype:
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bs3_surface bs3_surface_interp_knots (
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int nu,
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// number points in u
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int nv,
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// number points in v
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SPAposition* points,
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// position array
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double knotsu[],
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// u knot array
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double knotsv[],
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// v knot array
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SPAvector* deru,
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// u derivative array of
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// end conditions
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SPAvector* derv,
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// v derivative array of
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// end conditions
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SPAvector deruv[]
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// uv derivative array of
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// corner twist vectors
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);
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Includes:
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#include "kernel/acis.hxx"
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#include "baseutil/vector/position.hxx"
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#include "baseutil/vector/vector.hxx"
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#include "kernel/spline/bs3_srf/bs3surf.hxx"
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#include "kernel/spline/d3_bs3/spd3rtn.hxx"
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Description:
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This function interpolates or fits an array of positions, using knot vectors in the u and v directions, boundary derivatives (i.e., tangent vectors) and twist vectors.
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nu is the number of positions in the u direction,
nv the number of positions in the v direction.
points is a two dimensional array of positions [nu*nv].
knotsu is the u knot vector,
knotsv the v knot vector. Initially there is a one-to-one correspondence between knots and positions; however, it is required that the -1, -2,
n and
n+1 element of the knot vectors be addressable, though they need not be set. Therefore the
knotsu and
knotsv should both be of size
[nu+4]. The point for
u knot
i and
v knot
j is points
[j*nu + i]. The increasing u values are stored contiguously.
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deru contains the start and end derivatives for the u direction, elements 0 to
nv-1 for the bottom u knot end, and elements
nv to 2*nv-1 for the top end. Specifying a zero length vector means that natural end conditions will be used for that place on the surface.
derv and
deru work the same way, replacing
nv by
nu.
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Finally,
deruv is an array of four vectors giving the twist vectors, i.e., the uv cross derivative at the corners of the domain. They are stored in the following order:
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(lo_u,lo_v), (hi_u,lo_v), (lo_u,hi_v), (hi_u,hi_v)
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As with first derivatives along the boundaries, a zero length vector is an indicator to use natural end conditions.
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The interpolation algorithm assumes that all the knot values are distinct, the surface is open in both directions, and that there is generally nothing unusual going on.
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As a side effect of the interpolation algorithm, this routine will set any vectors in
derv which you have passed in as zero vectors.
deru is left alone.
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Library:
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kernel
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Filename:
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kern/kernel/spline/d3_bs3/spd3rtn.hxx
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Effect:
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Changes model
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