Volume

class pyspline.pyVolume.Volume(recompute=True, **kwargs)[source]

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

Creation: Create an instance of the Volume class directly by supplying the required information: kwargs MUST contain the following information: ku, kv, kw, tu, tv, tw, coef.
LMS/Interpolation: Create an instance of the Volume 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 and kw Spline Orders
2. X real array size (Nu, Nv, Nw, nDim) of data to fit. OR
  1. x (3D) and y (3D) z (3D) 3D volume interpolation/fitting
3. u, v, w real array of size (Nu, Nv, Nw). Optional
4. nCtlu, nCtlv, nCtlw. Specify number of control points. Only for LMS fitting.

Parameters

kuint: Spline order in u
kvint: Spline order in v
kwint: Spline order in w
nCtluint: Number of control points in u
nCtlvint: Number of control points in v
nCtlwint: Number of control points in w
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
twarray, size(nCtlw + kw): knot array in w
Xarray, size (Nu, Nv, Nw, ndim): Full data array to fit
xarray, size (Nu, Nv): Just x data to fit/interpolate
yarray, size (Nu, Nv, Nw): Just y data to fit/interpolate
zarray, size (Nu, Nv, Nw): Just z data to fit/interpolate
uarray, size (Nu, Nv, Nw): Explict u parameters to use. Optional.
varray, size (Nu, Nv, Nw): Explict v parameters to use. Optional.
warray, size (Nu, Nv, Nw): Explict w parameters to use. Optional.
nIterint: Number of Hoscheks parater corrections to run
recomputebool: Specifies whether the actual fitting is completed.

Notes

The orientation of the nodes, edges and faces for the volumes is given below:

          NODES      |           EDGES         |           FACES
      6           7|             5          |
      #-----------#|       #------------#  |          #-----------#
     /           / |      /|           /|  |         /|          /|
    /           /  |     / |          / |  |        / |         / |
   /           /   |   6/  |        7/  |  |       /  |   1    /  |
  /           /    |   /   |10      /   |11|      /   |    ---------- 5
 /           /     |  /    |    4  /    |  |     /    |      /    |(back)
#-----------#      | #------------#     |  |    #-----------#     |
4           5      | |     |      |     |  |    |     |     |     |
                   | |     |      |     |  |    |     |     |     | <-3
      2           3| |     |   1  |     |  |2-> |     |     |     |
      #-----------#| |     #------|-----#  |    |     #-----|-----#
     /           / | |8   /       |9   /   |4 ----------    |    /
    /           /  | |   /        |   /    |    |   /       |   /
   /           /   | |  /2        |  /3    |    |  /      0 |  /
  /           /    | | /          | /      |    | /         | /
 /           /     | |/           |/       |    |/          |/
#-----------#      | #------------#        |    #-----------#
0           1      |         0             |

calcKnots()[source]: Determine the knots depending on if it is inerpolated or an LMS fit

calcParameterization()[source]: Compute distance based parametrization. Use the fortran function for this

computeData(recompute=False)[source]

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, w, vals, istart, colInd, lIndex)[source]: This function should only be called from pyBlock The purpose is to compute the basis function for a u, v, w point and add it to pyBlocks’s global dPt/dCoef matrix. vals, rowPtr, colInd is the CSR data and lIndex in the local -> global mapping for this volume

getBounds()[source]

Determine the extents of the volume

Returns

xMinarray of length 3: Lower corner of the bounding box
xMaxarray of length 3: Upper corner of the bounding box

getMidPointEdge(edge)[source]

Get the midpoint of the edge using the original data.

Parameters

edgeint: Edge index. Must be 0<edge<11.

Returns

midpointarray of length nDim: Mid point of edge

getMidPointFace(face)[source]

Get the midpoint of the face using the original data.

Parameters

faceint: Face index. Must be 0, 1, 2, 3, 4 or 5

Returns

midpointarray of length nDim: Mid point of face

getOrigValueCorner(corner)[source]

Get the value of the original spline data on the corner if it exists

Parameters

cornerint: Index of corner, 0<=corner<=7

Returns

valuefloat: Original data on corner.

getOrigValuesFace(face)[source]

For a given face index, face, return the 4 corners and the values of the midpoints of the 4 edges on that face.

Parameters

faceint: Index of face, 0<=face<=5

Returns

coordsarray of size (8, ndim): The first 4 entries are the corner, and the last 4 are the midpoints.

getValue(u, v, w)[source]

Get the value at the volume points(s) u, v, w. This is the main evaluation routine for the volume object.

Parameters

uscalar, vector or matrix or tensor of values: u position
vscalar, vector or matrix or tensor of values: v position
wscalar, vector or matrix or tensor of values: w position

Returns

valuesscalar, vector, matrix or tensor of values: The spline evaluation at (u, v, w)

getValueCorner(corner)[source]

Get the value of the volume spline on the corner.

Parameters

cornerint: Index of corner, 0<=corner<=7

Returns

valuefloat: Volume spline evaluation at corner.

getValueEdge(edge, s)[source]

Get the value at the volume points(s) u, v, w

Parameters

edgeint: Index of edge. Must be between 0 and 11.
sfloat or array: Parameter position(s) along edge to evaluate.

Returns

valuesarray: Array of values evaluated along edge.

insertKnot(direction, s, r)[source]

Insert a knot into the volume along either u, v, w:

Parameters

directionstr: Parameteric direction to insert. Either ‘u’, ‘v’, or ‘w’
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.

projectPoint(x0, nIter=25, eps=1e-10, **kwargs)[source]

Project a point x0 or points x0 onto the volume and return parametric positions

Parameters

x0array of length 3 or array of size (N, 3): Points to embed in the volume. If the points do not actually lie in the volume, the closest point is returned
nIterint: Maximum number of Newton iterations to perform
epsfloat: Tolerance for the Newton iteration
ufloat or array of len(X0): Optional initial guess for u position.
vfloat or array of len(X0): Optional initial guess for v position.
wfloat or array of len(X0): Optional initial guess for w position.

Returns

ufloat or array of length N: u parametric position of closest point
vfloat or array of length N: v parametric position of closest point
wfloat or array of length N: w parametric position of closest point
Dfloat or array of length N: Distance between projected point and closest point If the points are ‘inside’ the volume, D should be less than eps.

recompute()[source]: Recompute the volume if any driving data has been modified

setEdgeCurves()[source]: Create edge spline objects for each edge

setFaceSurfaces()[source]: Create face spline objects for each of the faces

writeTecplot(fileName, vols=True, coef=True, orig=False)[source]

Write the volume to a tecplot data file.

Parameters

fileNamestr: Tecplot filename. Should end in .dat
volsbool: Flag specifiying whether the interpolated volume should be used. This is usually True if you want to get an approximation of the entire volume.
coefbool: Flag specifiying if the control points are to be plotted
origbool: Flag specifiying if original data (used for fitting) is to be included. If on original data exists, this argument is ignored.