-
Notifications
You must be signed in to change notification settings - Fork 0
Commit
This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository.
- Loading branch information
Showing
1 changed file
with
157 additions
and
0 deletions.
There are no files selected for viewing
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Original file line number | Diff line number | Diff line change |
---|---|---|
@@ -0,0 +1,157 @@ | ||
import numpy as np | ||
import matplotlib.pyplot as plt | ||
from matplotlib.widgets import Slider | ||
|
||
""" | ||
A simple control interface for sigmoid generation. Control points are on the | ||
derivative of the curve, where indefinite integration results in a sigmoid. | ||
There are 4 control points and 2 shapers. The 4 control points are: | ||
* Head | ||
* Shoulder | ||
* Knee | ||
* Toe | ||
Which control their respective points on the sigmoid. The two shaper functions | ||
control the behavior between the Toe and the Knee, and the Shoulder and Head | ||
respectively. | ||
* tk_exponent | ||
* sh_exponent | ||
These are currently simple exponential, but could be swapped with another | ||
function with other characteristics, especially if you want the second | ||
derivative curve to be smooth. | ||
""" | ||
|
||
|
||
# linear interpolation | ||
def lerp(a, b, t): | ||
return a + (b - a) * t | ||
|
||
|
||
# helper class | ||
class Coordinate(dict): | ||
__getattr__ = dict.get | ||
__setattr__ = dict.__setitem__ | ||
__delattr__ = dict.__delitem__ | ||
|
||
|
||
def sigmoid_gradient(x, toe, knee, tk_exp, shoulder, head, sh_exp): | ||
"""The sigmoid control point function | ||
All functions (once agreed on) could then by symbolically integrated, and | ||
the resultant integrated function could be used instead (with additional | ||
functions to maintain the additional needed constants). | ||
:param x: input value | ||
:param toe: toe control point (x,y) | ||
:param knee: knee control point (x,y) | ||
:param tk_exp: toe-knee exponent | ||
:param shoulder: shoulder control point (x,y) | ||
:param head: head control point (x,y) | ||
:param sh_exp: shoulder-head exponent | ||
:return: output derivative value | ||
""" | ||
|
||
if toe.x <= x <= knee.x: | ||
|
||
return (pow(x / knee.x, tk_exp) + toe.y) * knee.y | ||
|
||
elif knee.x < x <= shoulder.x: | ||
|
||
return lerp(knee.y, shoulder.y, (x - knee.x) / (shoulder.x - knee.x)) | ||
|
||
elif shoulder.x < x <= head.x: | ||
|
||
return (pow( | ||
((head.x - shoulder.x) - (x - shoulder.x)) / (head.x - shoulder.x), | ||
sh_exp) * (shoulder.y - head.y)) + head.y | ||
|
||
else: | ||
return head.y | ||
|
||
|
||
# PLOT ######################################################################## | ||
|
||
# helper function for plotting | ||
def process(x_data, _knee, _knee_x, _shoulder, _shoulder_x, _k_exp, _s_exp): | ||
y_data = np.zeros(np.size(x_data)) | ||
|
||
for idx, x in enumerate(x_data): | ||
toe = Coordinate({"x": 0, "y": 0}) | ||
knee = Coordinate({"x": _knee_x, "y": _knee}) | ||
tk_exp = _k_exp | ||
shoulder = Coordinate({"x": _shoulder_x, "y": _shoulder}) | ||
head = Coordinate({"x": 3.0, "y": 0.05}) | ||
sh_exp = _s_exp | ||
|
||
y_data[idx] = sigmoid_gradient(x, toe, knee, tk_exp, shoulder, head, | ||
sh_exp) | ||
return y_data | ||
|
||
|
||
# helper function for plotting | ||
def process_integrate(x_data, _knee, _knee_x, _shoulder, _shoulder_x, _k_exp, _s_exp): | ||
y_data = process(x_data, _knee, _knee_x, _shoulder, _shoulder_x, _k_exp, _s_exp) | ||
y_data_int = np.cumsum(y_data) | ||
|
||
return y_data_int | ||
|
||
|
||
# initialize | ||
fig = plt.figure() | ||
ax = fig.add_subplot(111) | ||
fig.subplots_adjust(left=0.25, bottom=0.4) | ||
|
||
x_data = np.arange(0, 4, 1.0 / 100) | ||
normalize_data = np.arange(0, 1.0, 1.0 / 100) | ||
|
||
[line1] = ax.plot(x_data, process(x_data, 0.5, 1.0, 0.5, 2.0, 2.2, 2.2) * 200.0, | ||
linewidth=2, color='blue') | ||
[line2] = ax.plot(x_data, process_integrate(x_data, 0.5, 1.0, 0.5, 2.0, 2.2, 2.2), | ||
linewidth=2, color='red') | ||
|
||
# axis | ||
ax.set_xlim([0, 4]) | ||
ax.set_ylim([0, 150]) | ||
|
||
# sliders | ||
body_y_ax = fig.add_axes([0.25, 0.25, 0.65, 0.03]) | ||
body_y_slider = Slider(body_y_ax, 'Body', 0.01, 1.0, valinit=0.5) | ||
|
||
knee_x_ax = fig.add_axes([0.25, 0.2, 0.65, 0.03]) | ||
knee_x_slider = Slider(knee_x_ax, 'Knee X', 0.0, 2.0, valinit=1.0) | ||
|
||
shoulder_x_ax = fig.add_axes([0.25, 0.15, 0.65, 0.03]) | ||
shoulder_x_slider = Slider(shoulder_x_ax, 'Shoulder X', 1.0, 3.0, valinit=2.0) | ||
|
||
knee_exp_ax = fig.add_axes([0.25, 0.1, 0.65, 0.03]) | ||
knee_exp_slider = Slider(knee_exp_ax, 'Knee Exp', 0.0, 10.0, valinit=2.2) | ||
|
||
shoulder_exp_ax = fig.add_axes([0.25, 0.05, 0.65, 0.03]) | ||
shoulder_exp_slider = Slider(shoulder_exp_ax, 'Shoulder Exp', 0.0, 10.0, | ||
valinit=2.2) | ||
|
||
|
||
# action | ||
def sliders_on_changed(val): | ||
line1.set_ydata(process(x_data, body_y_slider.val, knee_x_slider.val, body_y_slider.val, shoulder_x_slider.val, | ||
knee_exp_slider.val, | ||
shoulder_exp_slider.val) * 200.0) | ||
line2.set_ydata( | ||
process_integrate(x_data, body_y_slider.val, knee_x_slider.val, body_y_slider.val, shoulder_x_slider.val, | ||
knee_exp_slider.val, shoulder_exp_slider.val)) | ||
fig.canvas.draw_idle() | ||
|
||
|
||
# update | ||
body_y_slider.on_changed(sliders_on_changed) | ||
knee_x_slider.on_changed(sliders_on_changed) | ||
shoulder_x_slider.on_changed(sliders_on_changed) | ||
knee_exp_slider.on_changed(sliders_on_changed) | ||
shoulder_exp_slider.on_changed(sliders_on_changed) | ||
|
||
# plot | ||
plt.show() |