Surface

class pyspline.pySurface.Surface(recompute=True, **kwargs)

Create an instance of a b-spline surface. There are two ways to initialize the class

• Creation: Create an instance of the Surface class directly by supplying the required information: kwargs MUST contain the following information: ku, kv, tu, tv, coef.

• LMS/Interpolation: Create an instance of the Surface class by using an interpolating spline to given data points or a LMS spline. The following keyword argument information is required:

  1. ku and kv Spline Orders

  2. X real array size (Nu, Nv, nDim) of data to fit. OR

     1. x (2D) and y (2D) for 2D surface interpolation

     2. x (3D) and y (3D) and z (3) for 3D surface

  3. u, v real array of size (Nu, Nv). Optional

  4. nCtlu, nCtlv Specify number of control points. Only for LMS fitting.

Parameters:

kuint

Spline order in u

kvint

Spline order in v

nCtluint

Number of control points in u

nCtlvint

Number of control points in v

coefarray, size (nCtlu, nCtl, nDim)

b-spline coefficient array.

tuarray, size(nCtlu + ku)

knot array in u

tvarray, size(nCtlv + kv)

knot array in v

Xarray, size (Nu, Nv, ndim)

Full data array to fit

xarray, size (Nu, Nv)

Just x data to fit/interpolate

yarray, size (Nu, Nv)

Just y data to fit/interpolate

uarray, size (Nu, Nv)

Explicit u parameters to use. Optional.

varray, size (Nu, Nv)

Explicit v parameters to use. Optional.

scaledParamsbool

default is to use u,v for parameterization. If true use u,v as well. If false, use U,V.

nIterint

Number of Hoscheks parameter corrections to run

Notes

The orientation of the nodes, edges and faces is the same as the bottom surface as described in Volume documentation.

calcKnots()

Determine the knots depending on if it is interpolated or an LMS fit

calcParameterization()

Compute a spatial parameterization

computeData(recompute=False)

Compute discrete data that is used for the Tecplot Visualization as well as the data for doing the brute-force checks

Parameters:

recomputebool

If True, recompute the data even if it has already been computed.

getBasisPt(u, v, vals, istart, colInd, lIndex)

This function should only be called from pyGeo The purpose is to compute the basis function for a u, v point and add it to pyGeo’s global dPt/dCoef matrix. vals, row_ptr, col_ind is the CSR data and lIndex in the local -> global mapping for this surface

getBounds()

Determine the extents of the surface

Returns:

xMinarray of length 3

Lower corner of the bounding box

xMaxarray of length 3

Upper corner of the bounding box

getDerivative(u, v)

Evaluate the first derivatives of the spline surface

Parameters:

ufloat

Parametric u value

vfloat

Parametric v value

Returns:

derivarray size (2,3)

Spline derivative evaluation at u,vall points u,v. Shape depend on the input.

getOrigValueCorner(corner)

Return the original data for he spline at the corner if it exists

Parameters:

cornerint

Corner index 0<=corner<=3

Returns:

valuefloat

Original value at corner

getOrigValuesEdge(edge)

Return the endpoints and the mid-point value for a given edge.

Parameters:

edgeint

Edge index 0<=edge<=3

Returns:

startValuearray size nDim

Original value at start of edge

midValuearray size nDim

Original value at mid point of edge

endValuearray size nDim

Original value at end of edge.

getSecondDerivative(u, v)

Evaluate the second derivatives of the spline surface

deriv = [ (d^2)/(du^2) (d^2)/(dudv) ]

[ (d^2)/(dudv) (d^2)/(dv^2) ]

Parameters:

ufloat

Parametric u value

vfloat

Parametric v value

Returns:

derivarray size (2,2,3)

Spline derivative evaluation at u,vall points u,v. Shape depend on the input.

getValue(u, v)

Evaluate the spline surface at parametric positions u,v. This is the main function for spline evaluation.

Parameters:

ufloat, array or matrix (rank 0, 1, or 2)

Parametric u values

vfloat, array or matrix (rank 0, 1, or 2)

Parametric v values

Returns:

valuesvaries

Spline evaluation at all points u,v. Shape depend on the input. If u,v are scalars, values is array of size nDim. If u,v are a 1D list, return is (N,nDim) etc.

getValueCorner(corner)

Evaluate the spline spline at one of the four corners

Parameters:

cornerint

Corner index 0<=corner<=3

Returns:

valuefloat

Spline evaluated at corner

getValueEdge(edge, s)

Evaluate the spline at parametric distance s along edge ‘edge’

Parameters:

edgeint

Edge index 0<=edge<=3

sfloat or array

Parameter values to evaluate

Returns:

valuesarray size (nDim) or array of size (N,nDim)

Requested spline evaluated values

insertKnot(direction, s, r)

Insert a knot into the surface along either u or v.

Parameters:

directionstr

Parameteric direction to insert. Either ‘u’ or ‘v’.

sfloat

Parametric position along ‘direction’ to insert

rint

Desired number of times to insert.

Returns:

rint

The actual number of times the knot was inserted.

projectCurve(inCurve, nIter=25, eps=1e-10, **kwargs)

Find the minimum distance between this surface (self) and a curve (inCurve).

Parameters:

inCurvepySpline.curve object

Curve to use

nIterint

Maximum number of Newton iterations to perform.

epsfloat

Desired parameter tolerance.

sfloat

Initial solution guess for curve

ufloat

Initial solution guess for parametric u position

vfloat

Initial solution guess for parametric v position

Returns:

ufloat

Surface parameter u yielding min distance to point x0

ufloat

Surface parameter v yielding min distance to point x0

sfloat

Parametric position on curve yielding min distance to point x0

Dfloat

Minimum distance between this surface and curve. is equivalent to ||surface(u,v) - curve(s)||_2.

projectPoint(x0, nIter=25, eps=1e-10, **kwargs)

Perform a point inversion algorithm. Attempt to find the closest parameter values (u,v) to the given points x0.

Parameters:

x0array

A point or list of points in nDim space for which the minimum distance to the curve is sought.

nIterint

Maximum number of Newton iterations to perform.

epsfloat

Desired parameter tolerance.

ufloat or array of length x0

Optional initial guess for u parameter

vfloat or array of length x0

Optional initial guess for v parameter

Returns:

ufloat or array

Solution to the point inversion. u are the u-parametric locations yielding the minimum distance to points x0

vfloat or array

Solution to the point inversion. v are the v-parametric locations yielding the minimum distance to points x0

Dfloat or array

Physical distances between the points and the curve. This is simply ||surface(u,v) - X0||_2.

recompute()

Recompute the surface if any data has been modified

setEdgeCurves()

Create curve spline objects for each of the edges

splitSurface(direction, s)

Split surface into two surfaces at parametric location s

Parameters:

directionstr

Parameteric direction along which to split. Either ‘u’ or ‘v’.

sfloat

Parametric position along ‘direction’ to split

Returns:

surf1pySpline.surface

Lower part of the surface

surf2pySpline.surface

Upper part of the surface

windowSurface(uvLow, uvHigh)

Create a surface that is windowed by the rectangular parametric range defined by uvLow and uvHigh.

Parameters:

uvLowlist or array of length 2

(u,v) coordinates at the bottom left corner of the parameteric box

uvHighlist or array of length 2

(u,v) coordinates at the top left corner of the parameteric box

Returns:

surfpySpline.surface

A new surface defined only on the interior of uvLow -> uvHigh

writeDirections(handle, isurf)

Write out and indication of the surface direction

writeIGES_directory(handle, Dcount, Pcount)

Write the IGES file header information (Directory Entry Section) for this surface

writeIGES_parameters(handle, Pcount, counter)

Write the IGES parameter information for this surface

writeTecplot(fileName, surf=True, coef=True, orig=True, directions=False)

Write the surface to a tecplot .dat file

Parameters:

fileNamestr

File name for tecplot file. Should have .dat extension

surfbool

Flag to write discrete approximation of the actual surface

coef: bool

Flag to write b-spline coefficients

origbool

Flag to write original data (used for fitting) if it exists

directionsbool

Flag to write surface direction visualization

writeTin(handle)

Write the pySpline surface to an open handle in .tin format