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## BLEND: utility for smoothly blending functions or creating piecewise functions

version 1.1.0.0 (2.3 KB) by Sky Sartorius

### Sky Sartorius (view profile)

Returns a function that smoothly blends, with specified location and distance, between two functions

Updated 21 Apr 2016

BLEND uses hyperbolic tangent (tanh) to smoothly blend two functions or smoothly combine a piecewise function into a single function handle.

F = blend(f1,f2,LOC,DIST) returns function handle foo which, when evaluated, will return a smooth blend between functions provided in handles f1 and f2.
The blend is centered around LOC, and most of the smooth blend happens in the region LOC +/- DIST such that F will have value ca. 0.88*f1(x) + 0.12*f2 at LOC - DIST and 0.12*f1(x) + 0.88*f2(x) at LOC + DIST.

For a pure piecewise function, set the blend distance DIST to zero. F will evaluate to NaN at x = LOC. To avoid evaluating to NaN at x = LOC, use eps instead of zero. Default DIST = 0.

Example 1: Make a single function handle for a piecewise function (no smoothing).
foo = blend(@sin, 1, pi/2);
ezplot(foo, [0 pi])

Example 2: Make a smooth function from a discontinuous piecewise function and use vectorization to illustrate the effect of different blending distances.
f1 = @(x) -x;
f2 = @(x) x;
[dist, x] = meshgrid([0 .01 .1 .5 1], -2:.001:4);
foo = blend(f1, f2, 1, dist);
plot(x, foo(x))

### Cite As

Sky Sartorius (2019). BLEND: utility for smoothly blending functions or creating piecewise functions (https://www.mathworks.com/matlabcentral/fileexchange/56530-blend-utility-for-smoothly-blending-functions-or-creating-piecewise-functions), MATLAB Central File Exchange. Retrieved .