A rational function to approximate a tanh-like soft clipper - Node.js Geometry

Node.js examples for Geometry:Trigonometric functions

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Description

A rational function to approximate a tanh-like soft clipper

Demo Code


/* ---------------------------------------------------------------------------------------
This jsaSound Code is distributed under LGPL 3
Copyright (C) 2012 National University of Singapore
Inquiries: director@anclab.org/*from w w  w .  j  a  va2 s.c  o m*/

This library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 3 of the License, or any later version.
This library 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 GNULesser General Public License for more details.
You should have received a copy of the GNU General Public License and GNU Lesser General Public License along with this program.  If not, see <http://www.gnu.org/licenses/>
------------------------------------------------------------------------------------------*/
/*
Author: Lonce Wyse
Date: July 2012
*/
/*
This is a rational function to approximate a tanh-like soft clipper. It is based on the pade-approximation of the tanh function with tweaked coefficients.
The function is in the range x=-3..3 and outputs the range y=-1..1. Beyond this range the output must be clamped to -1..1.
The first to derivatives of the function vanish at -3 and 3, so the transition to the hard clipped region is C2-continuous.
http://stackoverflow.com/questions/6118028/fast-hyperbolic-tangent-approximation-in-javascript
*/
function rational_tanh(x) {
    if( x < -3 )
        return -1;
    else if( x > 3 )
        return 1;
    else
        return x * ( 27 + x * x ) / ( 27 + 9 * x * x );
}

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