#  SpliPy
This repository contains the SpliPy packages. SpliPy is a pure python library
for the creation, evaluation and manipulation of B-spline and NURBS geometries.
It supports n-variate splines of any dimension, but emphasis is made on the
use of curves, surfaces and volumes. The library is designed primarily for
analysis use, and therefore allows fine-grained control over many aspects which
is not possible to achieve with conventional CAD tools.
## Features
SpliPy allows for the generation of parametric curves, surfaces and volumes in the form of non-uniform rational B-splines (NURBS). It supports traditional curve- and surface-fitting methods such as (but not limited to)
### Curve fitting
* Bezier curves
* Hermite Interpolation
* Cubic Curve Interpolation
* B-spline Interpolation
* Least Square Fit
### Surface operations
* Sweep
* Revolve
* Loft
* Edge_Curves (interior from four edges)
* Extrude
* Structured Point Cloud Interpolation
* Least Square Fit
**Revolve**
**Sweep**
**Loft**
### Volume operations
* Revolve
* Extrude
* Loft
* Structured Point Cloud Interpolation
* Least Square Fit
In addition to these basic building blocks, it also supports a number of primitive shapes such as (but not limited to)
### Primitive shapes
* Cube
* Circle
* Disc
* Cylinder
* Torus
* Teapot
## Examples
### Derivatives of spline curves
``` python
from splipy import *
import numpy as np
n = 250 # number of evaluation points
c = curve_factory.circle() # create the NURBS circle (r=1)
t = np.linspace(c.start(0), c.end(0), n) # parametric evaluation points
x = c(t) # physical (x,y)-coordinates, size (n,2)
v = c.derivative(t, 1) # velocity at all points
a = c.derivative(t, 2) # acceleration at all points
```
### Curve fitting
Lissajous curves are a family of parametric curves of the type
```
x = A sin(at+d)
y = B sin(bt)
```
More info: [https://en.wikipedia.org/wiki/Lissajous_curve](https://en.wikipedia.org/wiki/Lissajous_curve). Stripping the [animation parts of the code](https://github.com/sintefmath/Splipy/blob/master/examples/lissajous.py), one can generate these curves in the following way
``` python
from splipy import *
import numpy as np
from fractions import gcd
def lissajous(a, b, d):
# request a,b integers, so we have closed, periodic curves
n = np.gcd(a,b)
N = (a/n) * (b/n) # number of periods before looping
# compute a set of interpolation points
numb_pts = max(3*N, 100) # using 3N interpolation points is decent enough
t = np.linspace(0,2*np.pi/n, numb_pts)
x = np.array([np.sin(a*t + d), np.sin(b*t)])
# do a cubic curve interpolation with periodic boundary conditions
my_curve = curve_factory.cubic_curve(x.T, curve_factory.Boundary.PERIODIC)
```
Animation of the lissajous curve with a=3, b=4 and d=pi/2
### Surface Sweep
This produces the trefoil knot shown above
``` python
from splipy import *
from numpy import pi,cos,sin,transpose,array,sqrt
# define a parametric representation of the trefoil knot (to be sampled)
def trefoil(u):
x = [41*cos(u) - 18*sin( u) - 83*cos(2*u) - 83*sin(2*u) - 11*cos(3*u) + 27*sin(3*u),
36*cos(u) + 27*sin( u) - 113*cos(2*u) + 30*sin(2*u) + 11*cos(3*u) - 27*sin(3*u),
45*sin(u) - 30*cos(2*u) + 113*sin(2*u) - 11*cos(3*u) + 27*sin(3*u)]
return transpose(array(x))
knot_curve = curve_factory.fit(trefoil, 0, 2*pi) # adaptive curve fit of trefoil knot
square_curve = 15 * curve_factory.n_gon(4) # square cross-section
my_surface = surface_factory.sweep(crv, square) # sweep out the surface
```
### Working with the controlpoints
``` python
>>> from splipy import *
>>> my_curve = curve_factory.circle(r=3)
>>> print(my_curve[0])
[3. 0. 1.]
>>> print(my_curve[1])
[2.12132034 2.12132034 0.70710678]
>>> for controlpoint in my_curve:
... print(controlpoint)
[3. 0. 1.]
[2.12132034 2.12132034 0.70710678]
[0. 3. 1.]
[-2.12132034 2.12132034 0.70710678]
[-3. 0. 1.]
[-2.12132034 -2.12132034 0.70710678]
[ 0. -3. 1.]
[ 2.12132034 -2.12132034 0.70710678]
```
### Creating STL files
STL files are used extensively for 3D representation and is one of the only supported formats for 3D printing.
``` python
from splipy.io import STL
from splipy import surface_factory
# create a NURBS torus
my_torus = surface_factory.torus(minor_r=1, major_r=4)
# STL files are tessellated linear triangles. View with i.e. meshlab
with STL('torus.stl') as my_file:
my_file.write(my_torus, n=(50, 150)) # specify resolution of 50x150 evaluation pts
```
**Torus tessellation as viewed in Meshlab**
## Citations
If you use Splipy in your work, please consider citing
[K. A. Johannessen and E. Fonn 2020 *J. Phys.: Conf. Ser.* **1669** 012032](https://iopscience.iop.org/article/10.1088/1742-6596/1669/1/012032/meta).
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"description": "\n#  SpliPy\n\nThis repository contains the SpliPy packages. SpliPy is a pure python library\nfor the creation, evaluation and manipulation of B-spline and NURBS geometries.\nIt supports n-variate splines of any dimension, but emphasis is made on the\nuse of curves, surfaces and volumes. The library is designed primarily for\nanalysis use, and therefore allows fine-grained control over many aspects which\nis not possible to achieve with conventional CAD tools.\n\n## Features\n\nSpliPy allows for the generation of parametric curves, surfaces and volumes in the form of non-uniform rational B-splines (NURBS). It supports traditional curve- and surface-fitting methods such as (but not limited to)\n\n### Curve fitting\n* Bezier curves\n* Hermite Interpolation\n* Cubic Curve Interpolation\n* B-spline Interpolation\n* Least Square Fit\n\n### Surface operations\n* Sweep\n* Revolve\n* Loft\n* Edge_Curves (interior from four edges)\n* Extrude\n* Structured Point Cloud Interpolation\n* Least Square Fit\n\n**Revolve**\n\n\n**Sweep**\n\n\n**Loft**\n\n\n### Volume operations\n* Revolve\n* Extrude\n* Loft\n* Structured Point Cloud Interpolation\n* Least Square Fit\n\nIn addition to these basic building blocks, it also supports a number of primitive shapes such as (but not limited to)\n\n### Primitive shapes\n* Cube\n* Circle\n* Disc\n* Cylinder\n* Torus\n* Teapot\n\n## Examples\n\n### Derivatives of spline curves\n``` python\n from splipy import *\n import numpy as np\n\n n = 250 # number of evaluation points\n c = curve_factory.circle() # create the NURBS circle (r=1)\n t = np.linspace(c.start(0), c.end(0), n) # parametric evaluation points\n x = c(t) # physical (x,y)-coordinates, size (n,2)\n v = c.derivative(t, 1) # velocity at all points\n a = c.derivative(t, 2) # acceleration at all points\n```\n\n![Missing circle animation](http://i.imgur.com/8MaBiTW.gif \"Circle animation\")\n\n### Curve fitting\nLissajous curves are a family of parametric curves of the type\n\n```\nx = A sin(at+d)\ny = B sin(bt)\n```\n\nMore info: [https://en.wikipedia.org/wiki/Lissajous_curve](https://en.wikipedia.org/wiki/Lissajous_curve). Stripping the [animation parts of the code](https://github.com/sintefmath/Splipy/blob/master/examples/lissajous.py), one can generate these curves in the following way\n\n\n``` python\nfrom splipy import *\nimport numpy as np\nfrom fractions import gcd\n\ndef lissajous(a, b, d):\n # request a,b integers, so we have closed, periodic curves\n n = np.gcd(a,b)\n N = (a/n) * (b/n) # number of periods before looping\n\n # compute a set of interpolation points\n numb_pts = max(3*N, 100) # using 3N interpolation points is decent enough\n t = np.linspace(0,2*np.pi/n, numb_pts)\n x = np.array([np.sin(a*t + d), np.sin(b*t)])\n\n# do a cubic curve interpolation with periodic boundary conditions\nmy_curve = curve_factory.cubic_curve(x.T, curve_factory.Boundary.PERIODIC)\n```\n\n![Missing Lissajous curve animation](http://i.imgur.com/HKr59BT.gif \"lissajous(3,4,pi/2)\")\n\nAnimation of the lissajous curve with a=3, b=4 and d=pi/2\n\n### Surface Sweep\n\nThis produces the trefoil knot shown above\n\n``` python\nfrom splipy import *\nfrom numpy import pi,cos,sin,transpose,array,sqrt\n\n# define a parametric representation of the trefoil knot (to be sampled)\ndef trefoil(u):\n x = [41*cos(u) - 18*sin( u) - 83*cos(2*u) - 83*sin(2*u) - 11*cos(3*u) + 27*sin(3*u),\n 36*cos(u) + 27*sin( u) - 113*cos(2*u) + 30*sin(2*u) + 11*cos(3*u) - 27*sin(3*u),\n 45*sin(u) - 30*cos(2*u) + 113*sin(2*u) - 11*cos(3*u) + 27*sin(3*u)]\n return transpose(array(x))\n\nknot_curve = curve_factory.fit(trefoil, 0, 2*pi) # adaptive curve fit of trefoil knot\nsquare_curve = 15 * curve_factory.n_gon(4) # square cross-section\nmy_surface = surface_factory.sweep(crv, square) # sweep out the surface\n```\n\n### Working with the controlpoints\n\n``` python\n>>> from splipy import *\n>>> my_curve = curve_factory.circle(r=3)\n>>> print(my_curve[0])\n[3. 0. 1.]\n>>> print(my_curve[1])\n[2.12132034 2.12132034 0.70710678]\n>>> for controlpoint in my_curve:\n... print(controlpoint)\n[3. 0. 1.]\n[2.12132034 2.12132034 0.70710678]\n[0. 3. 1.]\n[-2.12132034 2.12132034 0.70710678]\n[-3. 0. 1.]\n[-2.12132034 -2.12132034 0.70710678]\n[ 0. -3. 1.]\n[ 2.12132034 -2.12132034 0.70710678]\n```\n\n### Creating STL files\n\nSTL files are used extensively for 3D representation and is one of the only supported formats for 3D printing.\n\n``` python\nfrom splipy.io import STL\nfrom splipy import surface_factory\n\n# create a NURBS torus\nmy_torus = surface_factory.torus(minor_r=1, major_r=4)\n\n# STL files are tessellated linear triangles. 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