bpf4

bpf4

About

bpf4 is a python library to operate with curves in 2D space.

Curves can be defined via breakpoints (break-point functions, hence the name) or using functions. Moreover, curves can be used to build other curves. bpf4 can be used to perform curve fitting, data analysis, plotting, etc. Its core is programmed in cython for efficiency.

Installation

pip install --upgrade bpf4

Documentation

The documentation is hosted at https://bpf4.readthedocs.io

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Example

Find the intersection between two curves

from bpf4 import bpf  # this imports the api
a = bpf.spline((0, 0), (1, 5), (2, 3), (5, 10))  # each point (x, y)
b = bpf.expon((0, -10), (2,15), (5, 3), exp=3)
a.plot() # uses matplotlib
b.plot() 
zeros = (a - b).zeros()
import pylab
pylab.plot(zeros, a.map(zeros), 'o')

Features

Many interpolation types besides linear:

• spline
• univariate splie
• pchip (hermite)
• cosine
• exponential
• logarithmic
• etc.

With the exception of curve-fitting bpfs (splines), interpolation types can be mixed, so that each segment has a different interpolation. Following from the example above:

c = (a + b).sin().abs()
# plot only the range (1.5, 4)
c[1.5:4].plot()  

Syntax support for shifting, scaling and slicing a bpf

a >> 2        # a shifted to the right
(a * 5) ^ 2   # scale the x coord by 2, scale the y coord by 5
a[2:2.5]      # slice only a portion of the bpf
a[::0.01]     # sample the bpf with an interval of 0.01

Derivation / Integration

from bpf4 import *
a = spline((0, 0), (1, 5), (2, 3), (5, 10))
deriv = a.derivative()
integr = a.integrated()

import matplotlib.pyplot as plt 
fig, axs = plt.subplots(3, 1, sharex=True, figsize=(16, 8), tight_layout=True)
a.plot(axes=axs[0], show=False)
deriv.plot(axes=axs[1], show=False)
integr.plot(axes=axs[2])

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Mathematical operations

Max / Min

a = linear(0, 0, 1, 0.5, 2, 0)
b = expon(0, 0, 2, 1, exp=3)
a.plot(show=False, color="red", linewidth=4, alpha=0.3)
b.plot(show=False, color="blue", linewidth=4, alpha=0.3)
core.Max((a, b)).plot(color="black", linewidth=4, alpha=0.8, linestyle='dotted')

a = linear(0, 0, 1, 0.5, 2, 0)
b = expon(0, 0, 2, 1, exp=3)
a.plot(show=False, color="red", linewidth=4, alpha=0.3)
b.plot(show=False, color="blue", linewidth=4, alpha=0.3)
core.Min((a, b)).plot(color="black", linewidth=4, alpha=0.8, linestyle='dotted')

+, -, *, /

a = linear(0, 0, 1, 0.5, 2, 0)
b = expon(0, 0, 2, 1, exp=3)
a.plot(show=False, color="red", linewidth=4, alpha=0.3)
b.plot(show=False, color="blue", linewidth=4, alpha=0.3)
(a*b).plot(color="black", linewidth=4, alpha=0.8, linestyle='dotted')

a = linear(0, 0, 1, 0.5, 2, 0)
b = expon(0, 0, 2, 1, exp=3)
a.plot(show=False, color="red", linewidth=4, alpha=0.3)
b.plot(show=False, color="blue", linewidth=4, alpha=0.3)
(a**b).plot(color="black", linewidth=4, alpha=0.8, linestyle='dotted')

a = linear(0, 0, 1, 0.5, 2, 0)
b = expon(0, 0, 2, 1, exp=3)
a.plot(show=False, color="red", linewidth=4, alpha=0.3)
b.plot(show=False, color="blue", linewidth=4, alpha=0.3)
((a+b)/2).plot(color="black", linewidth=4, alpha=0.8, linestyle='dotted')

Building functions

A bpf can be used to build complex formulas

Fresnel's Integral: ( S(x) = \int_0^x {sin(t^2)} dt )

t = slope(1)
f = (t**2).sin()[0:10:0.001].integrated()
f.plot()

Polar plots

Any kind of matplotlib plot can be used. For example, polar plots are possible by creating an axes with polar=True

Cardiod: (\rho = 1 + sin(-\theta) )

from math import *
theta = slope(1, bounds=(0, 2*pi))
r = 1 + (-theta).sin()

ax = plt.axes(polar=True)
ax.set_rticks([0.5, 1, 1.5, 2]); ax.set_rlabel_position(38)
r.plot(axes=ax)

Flower 5: (\rho = 3 + cos(5 * \theta) )

theta = core.Slope(1, bounds=(0, 2*pi))
r = 3 + (5*theta).cos()

ax = plt.axes(polar=True)
r.plot(axes=ax)