bpf4

wheels

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

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])

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)

Metadata

Release files for bpf4 1.14.0

For a detailed explanation of source distributions (sdists) and built distributions (wheels), please see the package formats documentation.

Built distributions (wheels)

Table of built distributions (wheels) for bpf4 1.14.0
File	Interpreter	ABI	Platform	Reset
bpf4-1.14.0-cp313-cp313-win_amd64.whl 446.3 kB Apr 29, 2025	CPython 3.13	CPython 3.13	Windows x86-64	Details
bpf4-1.14.0-cp313-cp313-win32.whl 392.1 kB Apr 29, 2025	CPython 3.13	CPython 3.13	Windows x86-32	Details
bpf4-1.14.0-cp313-cp313-manylinux_2_17_x86_64.manylinux2014_x86_64.whl 2.7 MB Apr 29, 2025	CPython 3.13	CPython 3.13	Linux glibc 2.17+ x86-64	Details
bpf4-1.14.0-cp313-cp313-macosx_11_0_arm64.whl 461.8 kB Apr 29, 2025	CPython 3.13	CPython 3.13	macOS 11.0+ ARM64	Details
bpf4-1.14.0-cp313-cp313-macosx_10_13_x86_64.whl 511.0 kB Apr 29, 2025	CPython 3.13	CPython 3.13	macOS 10.13+ x86-64	Details
bpf4-1.14.0-cp312-cp312-win_amd64.whl 446.6 kB Apr 29, 2025	CPython 3.12	CPython 3.12	Windows x86-64	Details
bpf4-1.14.0-cp312-cp312-win32.whl 391.8 kB Apr 29, 2025	CPython 3.12	CPython 3.12	Windows x86-32	Details
bpf4-1.14.0-cp312-cp312-manylinux_2_17_x86_64.manylinux2014_x86_64.whl 2.7 MB Apr 29, 2025	CPython 3.12	CPython 3.12	Linux glibc 2.17+ x86-64	Details
bpf4-1.14.0-cp312-cp312-macosx_11_0_arm64.whl 464.1 kB Apr 29, 2025	CPython 3.12	CPython 3.12	macOS 11.0+ ARM64	Details
bpf4-1.14.0-cp312-cp312-macosx_10_13_x86_64.whl 513.8 kB Apr 29, 2025	CPython 3.12	CPython 3.12	macOS 10.13+ x86-64	Details
bpf4-1.14.0-cp311-cp311-win_amd64.whl 451.3 kB Apr 29, 2025	CPython 3.11	CPython 3.11	Windows x86-64	Details
bpf4-1.14.0-cp311-cp311-win32.whl 397.8 kB Apr 29, 2025	CPython 3.11	CPython 3.11	Windows x86-32	Details
bpf4-1.14.0-cp311-cp311-manylinux_2_17_x86_64.manylinux2014_x86_64.whl 2.8 MB Apr 29, 2025	CPython 3.11	CPython 3.11	Linux glibc 2.17+ x86-64	Details
bpf4-1.14.0-cp311-cp311-macosx_11_0_arm64.whl 462.9 kB Apr 29, 2025	CPython 3.11	CPython 3.11	macOS 11.0+ ARM64	Details
bpf4-1.14.0-cp311-cp311-macosx_10_9_x86_64.whl 512.8 kB Apr 29, 2025	CPython 3.11	CPython 3.11	macOS 10.9+ x86-64	Details
bpf4-1.14.0-cp310-cp310-win_amd64.whl 446.0 kB Apr 29, 2025	CPython 3.10	CPython 3.10	Windows x86-64	Details
bpf4-1.14.0-cp310-cp310-win32.whl 396.5 kB Apr 29, 2025	CPython 3.10	CPython 3.10	Windows x86-32	Details
bpf4-1.14.0-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl 2.6 MB Apr 29, 2025	CPython 3.10	CPython 3.10	Linux glibc 2.17+ x86-64	Details
bpf4-1.14.0-cp310-cp310-macosx_11_0_arm64.whl 460.4 kB Apr 29, 2025	CPython 3.10	CPython 3.10	macOS 11.0+ ARM64	Details
bpf4-1.14.0-cp310-cp310-macosx_10_9_x86_64.whl 509.7 kB Apr 29, 2025	CPython 3.10	CPython 3.10	macOS 10.9+ x86-64	Details

Total release size: 17.9 MB

Release files / bpf4-1.14.0-cp313-cp313-win_amd64.whl

Download URL	bpf4-1.14.0-cp313-cp313-win_amd64.whl
Size	446.3 kB
Tags	CPython 3.13 Windows x86-64
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Release files / bpf4-1.14.0-cp313-cp313-macosx_11_0_arm64.whl

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Size	461.8 kB
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Size	446.6 kB
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Download URL	bpf4-1.14.0-cp312-cp312-macosx_10_13_x86_64.whl
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Release files / bpf4-1.14.0-cp311-cp311-win32.whl

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