A Convenient Generalization of Schlick's Bias and Gain Functions

TL;DR

This paper introduces a unified parametric function that generalizes Schlick's bias and gain functions, enabling flexible control over curve shape for inputs in [0, 1], with applications in graphics and data processing.

Contribution

A novel single parametric function that encompasses bias, gain, and other smooth monotonic curves, providing enhanced flexibility and simplicity.

Findings

The function includes bias and gain as special cases.

It can describe a variety of smooth, monotonic curves.

The approach simplifies curve adjustments in practical applications.

Abstract

We present a generalization of Schlick's bias and gain functions -- simple parametric curve-shaped functions for inputs in [0, 1]. Our single function includes both bias and gain as special cases, and is able to describe other smooth and monotonic curves with variable degrees of asymmetry.