Curve
- class pyspline.pyCurve.Curve(**kwargs)[source]
Create an instance of a b-spline curve. There are two ways to initialize the class
Creation: Create an instance of the spline class directly by supplying the required information. kwargs MUST contain the following information:
k, t, coef
.LMS/Interpolation: Create an instance of the spline class by using an interpolating spline to given data points or a LMS spline. The following keyword argument information is required:
k
Spline OrderX
real array size (N, nDim) of data to fit. ORx
(1D) ands
for 1Dx
(1D) andy
(1D) for 2D spatial curvex
(1D) andy`
(1D) andz
1D for 3D spatial curve
s
real array of size (N). Optional for nDim >= 2
- Parameters
- k{2, 3, 4}
Order for spline. A spline with order \(n\) has at most \(C^{n-2}\) continuity. The \(n-1\) derivative will be piecewise constant.
- nCtlint
Number of control points. If this is specified then LMS will be used instead of interpolation.
- tarray, list
Knot vector. Used only for creation. Must be size
nCtl + k
- coefarray, size (nCtl, nDim)
Coefficients to use. Only used for creation. The second dimension determine the spatial order of the spline
- Xarary, size (N, ndim)
Full array of data to interpolate/fit
- xarray, size (N)
Just x coordinates of data to fit
- yarray, size (N)
Just y coordinates of data to fit
- zarray, size (N)
Just z coordinates of data to fit
- sarray, size(N)
Optional parameter to use. Not required for nDim >=2
- nIterint
The number of Hoscheks parameter correction iterations to run. Only used for LMS fitting.
- weightarray, size(N)
A array of weighting factors for each fitting point. A value of -1 can be used to exactly constrain a point. By default, all weights are 1.0
- derivarray, size (len(derivPtr), nDim)
Array containing derivative information the user wants to use at a particular point. EXPERIMENTAL
- derivPtrint, array, size (nDerivPtr)
Array of indices pointing to the index of points in X (or x,y,z), for which the user has supplied a derivative for in
deriv
. EXPERIMENTAL- derivWeightsarray size(nDerivPtr)
Optional array of the weighting to use for derivatives. A value of -1 can be used to exactly constrain a derivative. EXPERIMENTAL
Examples
>>> x = [0, 0.5, 1.0] >>> y = [0, 0.25, 1.0] >>> s = [0., 0.5, 1.0] >>> # Spatial interpolated seg (k=2 makes this a straight line) >>> line_seg = Curve(x=x, y=y, k=2) >>> # With explicit parameter values >>> line_seg = Curve(x=x, y=y, k=2, s=s) >>> #Interpolate parabolic curve >>> parabola = Curve(x=x, y=y, k=3) >>> #Interpolate parabolic curve with parameter values >>> parabola = Curve(x=x, y=y, k=3, s=s)
- calcInterpolatedGrevillePoints()[source]
Compute greville points, but with additional interpolated knots
- 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.
- getDerivative(s)[source]
Evaluate the derivatie of the spline at parametric position, s
- Parameters
- sfloat
Parametric location for derivative
- Returns
- dsarray
The first derivative. This is an array of size nDim
- getLength()[source]
Compute the length of the curve using the Euclidean Norm
- Returns
- lengthfloat
Physical length of curve
- getSecondDerivative(s)[source]
Evaluate the second derivatie of the spline at parametric position, s
- Parameters
- sfloat
Parametric location for derivative
- Returns
- d2sarray
The second derivative. This is an array of size nDim
- getValue(s)[source]
Evaluate the spline at parametric position, s
- Parameters
- sfloat or array
Parametric position(s) at which to evaluate the curve.
- Returns
- valuesarray of size nDim or an array of size (N, 3)
The evaluated points. If a single scalar s was given, the result with be an array of length nDim (or a scalar if nDim=1). If a vector of s values were given it will be an array of size (N, 3) (or size (N) if ndim=1)
- insertKnot(u, r)[source]
Insert at knot in the curve at parametric position u
- Parameters
- ufloat
Parametric position to split at
- rint
Number of time to insert. Should be > 0.
- Returns
- actualRint
The number of times the knot was actually inserted
- breakPtint
Index in the knot vector of the new knot(s)
- projectCurve(inCurve, nIter=25, eps=1e-10, **kwargs)[source]
Find the minimum distance between this curve (self) and a second curve passed in (inCurve)
- Parameters
- inCurvepySpline.curve objet
Other curve to use
- nIterint
Maximum number of Newton iterations to perform.
- epsfloat
Desired parameter tolerance.
- sfloat
Initial guess for curve1 (this curve class)
- tfloat
Initial guess for inCurve (curve passed in )
- Returns
- sfloat
Parametric position on curve1 (this class)
- tfloat
Parametric position on curve2 (inCurve)
- Dfloat
Minimum distance between this curve and inCurve. It is equivalent to ||self(s) - inCurve(t)||_2.
- projectCurveMultiSol(inCurve, nIter=25, eps=1e-10, **kwargs)[source]
Find the minimum distance between this curve (self) and a second curve passed in (inCurve). Try to find as many local solutions as possible
- Parameters
- inCurvepySpline.curve objet
Other curve to use
- nIterint
Maximum number of Newton iterations to perform.
- epsfloat
Desired parameter tolerance.
- sfloat
Initial guess for curve1 (this curve class)
- tfloat
Initial guess for inCurve (curve passed in )
- Returns
- sarray
Parametric position(s) on curve1 (this class)
- tfloat
Parametric position)s_ on curve2 (inCurve)
- Dfloat
Minimum distance(s) between this curve and inCurve. It is equivalent to ||self(s) - inCurve(t)||_2.
- projectPoint(x0, nIter=25, eps=1e-10, **kwargs)[source]
Perform a point inversion algorithm. Attempt to find the closest parameter values 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.
- Returns
- sfloat or array
Solution to the point inversion. s are the parametric locations yielding the minimum distance to points x0
- Dfloat or array
Physical distances between the points and the curve. This is simply ||curve(s) - X0||_2.
- recompute(nIter, computeKnots=True)[source]
Run iterations of Hoscheks Parameter Correction on the current curve
- Parameters
- nIterint
The number of parameter correction iterations to run
- computeKnotsbool
Flag whether or not the knots should be recomputed
- splitCurve(u)[source]
Split the curve at parametric position u. This uses the
insertKnot()
routine- Parameters
- ufloat
Parametric position to insert knot.
- Returns
- curve1pySpline curve object
Curve from s=[0, u]
- curve2pySpline curve object
Curve from s=[u, 1]
Notes
curve1 and curve2 may be None if the parameter u is outside the range of (0, 1)
- windowCurve(uLow, uHigh)[source]
Compute the segment of the curve between the two parameter values
- Parameters
- uLowfloat
Lower bound for the clip
- uHighfloat
Upper bound for the clip
- writeIGES_directory(handle, Dcount, Pcount, twoD=False)[source]
Write the IGES file header information (Directory Entry Section) for this curve.
DO NOT MODIFY ANYTHING HERE UNLESS YOU KNOW EXACTLY WHAT YOU ARE DOING!
- writeIGES_parameters(handle, Pcount, counter)[source]
Write the IGES parameter information for this curve.
DO NOT MODIFY ANYTHING HERE UNLESS YOU KNOW EXACTLY WHAT YOU ARE DOING!
- writeTecplot(fileName, curve=True, coef=True, orig=True)[source]
Write the curve to a tecplot .dat file
- Parameters
- fileNamestr
File name for tecplot file. Should have .dat extension
- curvebool
Flag to write discrete approximation of the actual curve
- coefbool
Flag to write b-spline coefficients
- origbool
Flag to write original data (used for fitting) if it exists