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# -*- coding: utf-8 -*-
# input-remapper - GUI for device specific keyboard mappings
# Copyright (C) 2025 sezanzeb <b8x45ygc9@mozmail.com>
#
# This file is part of input-remapper.
#
# input-remapper is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# input-remapper is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with input-remapper. If not, see <https://www.gnu.org/licenses/>.
import math
from typing import Dict, Union
class Transformation:
"""Callable that returns the axis transformation at x."""
def __init__(
self,
# if input values are > max_, the return value will be > 1
max_: Union[int, float],
min_: Union[int, float],
deadzone: float,
gain: float = 1,
expo: float = 0,
) -> None:
self._max = max_
self._min = min_
self._deadzone = deadzone
self._gain = gain
self._expo = expo
self._cache: Dict[float, float] = {}
def __call__(self, /, x: Union[int, float]) -> float:
if x not in self._cache:
y = (
self._calc_qubic(self._flatten_deadzone(self._normalize(x)))
* self._gain
)
self._cache[x] = y
return self._cache[x]
def set_range(self, min_, max_):
# TODO docstring
if min_ != self._min or max_ != self._max:
self._cache = {}
self._min = min_
self._max = max_
def _normalize(self, x: Union[int, float]) -> float:
"""Move and scale x to be between -1 and 1
return: x
"""
if self._min == -1 and self._max == 1:
return x
half_range = (self._max - self._min) / 2
middle = half_range + self._min
return (x - middle) / half_range
def _flatten_deadzone(self, x: float) -> float:
"""
y ^ y ^
| |
1 | / 1 | /
| / | /
| / ==> | ---
| / | /
-1 | / -1 | /
|------------> |------------>
-1 1 x -1 1 x
"""
if abs(x) <= self._deadzone:
return 0
return (x - self._deadzone * x / abs(x)) / (1 - self._deadzone)
def _calc_qubic(self, x: float) -> float:
"""Transforms an x value by applying a qubic function
k = 0 : will yield no transformation f(x) = x
1 > k > 0 : will yield low sensitivity for low x values
and high sensitivity for high x values
-1 < k < 0 : will yield high sensitivity for low x values
and low sensitivity for high x values
see also: https://www.geogebra.org/calculator/mkdqueky
Mathematical definition:
f(x,d) = d * x + (1 - d) * x ** 3 | d = 1 - k | k ∈ [0,1]
the function is designed such that if follows these constraints:
f'(0, d) = d and f(1, d) = 1 and f(-x,d) = -f(x,d)
for k ∈ [-1,0) the above function is mirrored at y = x
and d = 1 + k
"""
k = self._expo
if k == 0 or x == 0:
return x
if 0 < k <= 1:
d = 1 - k
return d * x + (1 - d) * x**3
if -1 <= k < 0:
# calculate return value with the real inverse solution
# of y = b * x + a * x ** 3
# LaTeX for better readability:
#
# y=\frac{{{\left( \sqrt{27 {{x}^{2}}+\frac{4 {{b}^{3}}}{a}}
# +{{3}^{\frac{3}{2}}} x\right) }^{\frac{1}{3}}}}
# {{{2}^{\frac{1}{3}}} \sqrt{3} {{a}^{\frac{1}{3}}}}
# -\frac{{{2}^{\frac{1}{3}}} b}
# {\sqrt{3} {{a}^{\frac{2}{3}}}
# {{\left( \sqrt{27 {{x}^{2}}+\frac{4 {{b}^{3}}}{a}}
# +{{3}^{\frac{3}{2}}} x\right) }^{\frac{1}{3}}}}
sign = x / abs(x)
x = math.fabs(x)
d = 1 + k
a = 1 - d
b = d
c = (math.sqrt(27 * x**2 + (4 * b**3) / a) + 3 ** (3 / 2) * x) ** (1 / 3)
y = c / (2 ** (1 / 3) * math.sqrt(3) * a ** (1 / 3)) - (
2 ** (1 / 3) * b
) / (math.sqrt(3) * a ** (2 / 3) * c)
return y * sign
raise ValueError("k must be between -1 and 1")
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