Easing and extensions for FFmpeg Xfade filter

Standard easings • CSS easings • transpiled GL Transitions • custom expressions

Summary

This project is a port of standard easing equations, CSS easings and many GL Transitions for use in tandem with easing or alone. The easing expressions can be used for other filters besides xfade.

There are 2 variants:

1. custom ffmpeg build with added xfade easing option
2. custom expressions for use with standard ffmpeg build

Xfade is a FFmpeg video transition filter with many built-in transitions and an expression evaluator for custom effects. But the progress rate is linear. starting and stopping abruptly and proceeding at constant speed, so transitions lack interest. Easing inserts a progress envelope to smooth transitions in a natural way.

Example usage:

• custom ffmpeg: set the new easing option to the easing name, with optional CSS-easing arguments, and the transition option to the transition name, with optional customisation arguments.
  Example (quartic-out,radial):
  xfade=duration=3:offset=10:easing=quartic-out:transition=radial
  Example (CSS,GL):
  xfade=duration=3:offset=10:easing='cubic-bezier(0.12,0.57,0.63,0.21)'
:transition='gl_cube(floating=5,unzoom=0.8)'
• custom expression: set the xfade transition option to custom and the expr option to the concatenation of a standard easing expression and a transition expression (this variant does not support CSS easings).
  Example (quartic-out,radial):
  xfade=duration=3:offset=10:transition=custom:expr='st(0,P^4);
st(1,atan2(X-W/2,Y-H/2)-(ld(0)-0.5)*PI*2.5);st(1,st(1,clip(ld(1),0,1))*ld(1)*(3-2*ld(1)));B*ld(1)+A*(1-ld(1))'
  Pre-generated expressions can be copied verbatim from supplied files.

A CLI wrapper script is provided to generate custom expressions, test videos, visual media sequences and more. It also facilitates generic ffmpeg filter easing – see Easing other filters.

The custom ffmpeg variant is fast with a simple API and no restrictions. Installation involves a few patches to a single ffmpeg C source file, with no dependencies. The custom expression variant is convenient but clunky – see Performance – and runs on plain vanilla ffmpeg but with restrictions: it doesn’t support CSS easing and certain transitions.

At present extended transitions are limited to ported GL Transitions but more effects may be added downstream.

[!NOTE] Coming next

• multiple easings/transitions interspersed in input file list of CLI script, for batch processing with varying transition effects
• audio support

Example

wipedown with cubic easing

CLI command (for custom ffmpeg use)

ffmpeg -i first.mp4 -i second.mp4 -filter_complex "
    xfade=duration=3:offset=1:easing=cubic-in-out:transition=wipedown
    " output.mp4

Easing mode in-out is the default mode; the above is equivalent to easing=cubic.
The default easing is linear (none).

CLI command (for custom expression use)

ffmpeg -i first.mp4 -i second.mp4 -filter_complex_threads 1 -filter_complex "
    xfade=duration=3:offset=1:transition=custom:expr='
        st(0, if(lt(P, 0.5), 4 * P^3, 1 - 4 * (1-P)^3)) ;
        if(gt(Y, H*(1-ld(0))), A, B)
    '" output.mp4

Here, the expr parameter is shown on two lines for clarity.
The first line is the easing expression $e(P)$ (cubic in-out) which stores its calculated progress value in st(0).
The second line is the transition expression $t(e(P))$ (wipedown) which loads its eased progress value from ld(0) instead of P. The semicolon token combines expressions.

[!IMPORTANT] ffmpeg option -filter_complex_threads 1 is required because xfade expression variables (the st() & ld() functions) are shared between slice processing jobs and therefore not thread-safe, consequently processing is much slower

Getting the expressions

In this example you can copy the easing expression from file easings-inline.txt and the transition expression from transitions-rgb24-inline.txt or transitions-yuv420p-inline.txt. Those contain inline expressions for CLI use.

Alternatively use the CLI script:

xfade-easing.sh -t wipedown -e cubic -x -

dumps the xfade expr parameter:

'st(0,if(lt(P,0.5),4*P^3,1-4*(1-P)^3));if(gt(Y,H*(1-ld(0))),A,B)'

Using a script

Some expressions are very long, so using -filter_complex_script keeps things manageable and readable.

For this same example you can copy the easing expression from file easings-script.txt and the transition expression from transitions-rgb24-script.txt or transitions-yuv420p-script.txt. Those contain multiline expressions for script use (but the inline expressions work too).

Alternatively use xfade-easing.sh with expansion specifiers expr='%n%X' (see Usage):

xfade-easing.sh -t wipedown -e cubic -s "xfade=offset=10:duration=5:transition=custom:expr='%n%X'" -x script.txt

writes the complete xfade filter description to file script.txt:

xfade=offset=10:duration=5:transition=custom:expr='
st(0, if(lt(P, 0.5), 4 * P^3, 1 - 4 * (1-P)^3))
;
if(gt(Y, H * (1 - ld(0))), A, B)'

and the command becomes

ffmpeg -i first.mp4 -i second.mp4 -filter_complex_threads 1 -filter_complex_script script.txt output.mp4`

Custom FFmpeg variant

Building ffmpeg

1. check the FFmpeg Compilation Guide for any prerequisites, e.g. macOS requires Xcode
2. get the ffmpeg source tree:
   • for snapshot: git clone https://git.ffmpeg.org/ffmpeg.git ffmpeg
   • for latest stable, Download Source Code then extract the .xz archive:
     tar -xJf ffmpeg-x.x.x.tar.xz or use xz/gunzip/etc.
3. cd ffmpeg and patch libavfilter/vf_xfade.c:
   • download vf_xfade.patch and run git apply vf_xfade.patch
   • or download vf_xfade.c and if necessary patch manually (it’s from libavfilter version 9, June 7 2023), see vf_xfade diff – only 7 changes
4. download xfade-easing.h to libavfilter/
5. run ./configure with any --prefix and other options (drawtext requires --enable-libfreetype --enable-libharfbuzz --enable-libfontconfig); to replicate an existing configuration run ffmpeg -hide_banner -buildconf
6. run make, it takes a while
   the fix for ld: warning: text-based stub file are out of sync warnings is here
7. if required run make install or use ffmpeg in the root source directory
8. test using ffmpeg -hide_banner --help filter=xfade: there should be an easing option under xfade AVOptions

For simplicity, xfade-easing is implemented as static functions in the header file xfade-easing.h and included into vf_xfade.c at an optimal place. As those functions have no external linkage and completely implement an interface that is only visible to the vf_xfade.c compilation unit, this approach is justified IMO, even if unusual, and obviates changing the Makefile. Implementation within header files is not uncommon.

Expressions

Pre-generated easing and transition expressions are in the expr/ subdirectory for mix and match use. The CLI script can produce combined expressions in any syntax using expansion specifiers (like printf).

Inline, for -filter_complex

This format is condensed into a single line stripped of whitespace.

Example: elastic out easing (leaves progress in st(0))

st(0,cos(20*(1-P)*PI/3)/2^(10*(1-P)))

Script, for -filter_complex_script

This format is best for expressions that are too unwieldy for inline ffmpeg commands.

Example: gl_rotate_scale_fade transition (expects progress in ld(0) (cf. rotate_scale_fade.glsl)

st(1, 0.5);
st(2, 0.5);
st(3, 1);
st(4, 8);
st(5, X / W - ld(1));
st(6, 1 - Y / H - ld(2));
st(7, hypot(ld(5), ld(6)));
st(5, ld(5) / ld(7));
st(6, ld(6) / ld(7));
st(3, 2 * PI * ld(3) * (1 - ld(0)));
st(8, 2 * abs(ld(0) - 0.5));
st(8, ld(4) * (1 - ld(8)) + 1 * ld(8));
st(4, ld(5) * cos(ld(3)) - ld(6) * sin(ld(3)));
st(6, ld(5) * sin(ld(3)) + ld(6) * cos(ld(3)));
st(1, ld(1) + ld(4) * ld(7) / ld(8));
st(2, ld(2) + ld(6) * ld(7) / ld(8));
if(between(ld(1), 0, 1) * between(ld(2), 0, 1),
 st(1, ld(1) * W);
 st(2, (1 - ld(2)) * H);
 st(3, ifnot(PLANE, a0(ld(1),ld(2)), if(eq(PLANE,1), a1(ld(1),ld(2)), if(eq(PLANE,2), a2(ld(1),ld(2)), a3(ld(1),ld(2))))));
 st(4, ifnot(PLANE, b0(ld(1),ld(2)), if(eq(PLANE,1), b1(ld(1),ld(2)), if(eq(PLANE,2), b2(ld(1),ld(2)), b3(ld(1),ld(2))))));
 st(5, 1 - ld(0));
 ld(3) * (1 - ld(5)) + ld(4) * ld(5),
 st(1, 0.15);
 if(eq(PLANE,3), 255, ld(1)*255)
)

Uneased, for transitions without easing

These use P directly for progress instead of ld(0). They are especially useful for non-xfade transitions where custom expressions are always needed.

Example: gl_WaterDrop transition (cf. WaterDrop.glsl)

st(1, 30);
st(2, 30);
st(3, 1 - P);
st(4, X / W - 0.5);
st(5, 0.5 - Y / H);
st(6, hypot(ld(4), ld(5)));
st(7, if(lte(ld(6), ld(3)),
 st(1, sin(ld(6) * ld(1) - ld(3) * ld(2)));
 st(4, ld(4) * ld(1));
 st(5, ld(5) * ld(1));
 st(4, X + ld(4) * W);
 st(5, Y - ld(5) * H);
 ifnot(PLANE, a0(ld(4),ld(5)), if(eq(PLANE,1), a1(ld(4),ld(5)), if(eq(PLANE,2), a2(ld(4),ld(5)), a3(ld(4),ld(5))))),
 A
));
ld(7) * (1 - ld(3)) + B * ld(3)

Generic, for easing other filters

These ease ld(0) instead od P - see Easing other filters.

Pixel format

Transitions that affect colour components work differently for RGB than non-RGB colour spaces and for different bit depths. For the custom expression variant, xfade-easing.sh emulates vf_xfade.c function config_output() logic, deducing the RGB signal type AV_PIX_FMT_FLAG_RGB from the -f option format name (rgb/bgr/etc. see pixdesc.c) and the bit depth from ffmpeg -pix_fmts data. It can then set the black, white and mid plane values correctly. See How does FFmpeg identify color spaces? for details.

The expression files in expr/ cater for RGB and YUV formats with 8-bit component depth. For faster processing of greyscale media use xfade-easing.sh -f gray. Greyscale is not RGB therefore it is processed as a luma plane.

If in doubt, check with ffmpeg -pix_fmts or use the xfade-easing.sh -f option.

Transparency

The expression files in expr/ also cater for RGBA and YUVA formats with 4 planes.

For lossless intermediate video content with alpha channel support use the xfade-easing.sh -f -v options with an alpha format, e.g. rgba/yuva420p, and .mkv filename extension. For lossy video with alpha use an alpha format and the .webm extension.

Example: overlaid transparent gl_RotateScaleVanish transition with quadratic-in easing

xfade-easing.sh -f rgba -e quadratic-in -t 'gl_RotateScaleVanish(FadeInSecond=0,ReverseEffect=1,trkMat=1)' -v alpha.mkv -z 250x skaro.png tardis.png
ffmpeg -filter_complex 'movie=gallifrey.png,scale=250:-2[bg]; movie=alpha.mkv[fg]; [bg][fg]overlay' drwho.mp4

This demonstrates the additional trkMat option which tracks the Tardis alpha value to expose Skaro behind then Gallifrey’s Citadel when the transition ends, both planets being opaque images.
(trkMat is only availble in the custom ffmpeg variant)

Easing expressions

Standard easings (Robert Penner)

This implementation derives from Michael Pohoreski’s single argument version of Robert Penner’s easing functions, further optimised by me for the peculiarities of xfade.

• quadratic
• cubic
• quartic
• quintic
• sinusoidal
• exponential
• circular
• elastic
• back
• bounce

Supplementary easings

• squareroot
• cuberoot

The squareroot and cuberoot easings focus more on the middle regions and less on the extremes, opposite to quadratic and cubic respectively:

All standard and supplementary easings

Here are all the above easings superimposed using the Desmos Graphing Calculator:

CSS easings

The custom ffmpeg variant supports CSS Easing Functions Level 2 which are too complex for custom expressions:

• linear linear()
• ease ease-in ease-out ease-in-out cubic-bezier()
• step-start step-end steps()

Linear easing

The new CSS linear() function can approximate any progress contour by interpolating between adjacent points, documented at W3C here. There’s a CSS Linear() Generator online by its pioneer Jake Archibald to convert easings expressed in JavaScript or SVG to linear().

Cubic Bézier easing

There are 4 fixed CSS smoothing curves and a general cubic-bezier() easing function documented at W3C here. See also the CSS Cubic Bezier Generator to craft your own. The implementation used here is transpiled from Apple’s open-source Webkit.

Step easing

The CSS steps() staircase function is for transitions that jump a constant amount, documented at W3C here.

Overshoots

The elastic and back easings overshoot and undershoot, causing many transitions to clip and others to show colour distortion. Therefore they are quite useless for xfade (but see Easing other filters). CSS easings linear() and cubic-bezier() can also overshoot.

Rendering expressions can only access the two frames of data available. A wrapping overshoot strategy might work for simple horizontal/vertical effects whereby fetching X & Y pixel data is intercepted but at present eased progress outside the range 0 to 1 yields unpredictable results.

Easing other filters

The easing expressions are useful for filters other than xfade, e.g. blend, drawtext, geq, overlay, rotate, zoompan, etc. – anywhere an ffmpeg expr is used to calculate filter options.

For this purpose the CLI script includes text expansion codes %g & %G to generate generic easing expressions for the value in ld(0) (instead of P for xfade), leaving the result in ld(0). You can also copy generic easing expressions from file generic-easings-inline.txt for inline -filter_complex use, or generic-easings-script.txt for -filter_complex_script scripts.

To ease other filters, store a normalised input value in st(0,…), append the easing expression, then scale the eased result left in ld(0).

Example: zoompan filter with elastic-out zooming

Here’s the zoom option expression for the zoompan filter:

zoom='st(0, clip((time - 1) / 3, 0, 1));
        st(0, 1 - cos(20 * ld(0) * PI / 3) / 2^(10 * ld(0)));
      lerp(1, 3, ld(0))'

The first line stores a 3 second duration delayed by 1 second normalised to a value between 0 and 1.
The last line scales the result to zoom between 1x and 3x.
The middle line performs elastic-out easing, obtained from generic-easings-script.txt, or
xfade-easing.sh -e elastic-out -s %G -x -

The zoompan filter can produce impressive Ken Burns effects when zoom, x & y are all dynamic. Adding easing can take the illusion of motion even further. I have another FFmpeg project on the go that does just that.

Example: zoompan with back zooming and drawtext with squareroot scrolling

The initial zoom here is 1.2x to accommodate the 10% undershoot that back easing produces. So the zoompan zoom expression, with back expr from generic-easings-inline.txt, is:

z='st(0, clip((time - 1) / 3, 0, 1));
     st(0,if(lt(ld(0),0.5),2*ld(0)*ld(0)*(2*ld(0)*3.59491-2.59491),1-2*(1-ld(0))^2*(4.59491-2*ld(0)*3.59491)));
   lerp(1.2, 3.1, ld(0))'

And the drawtext y expression with squareroot easing is:

y='st(0, clip((t - 1) / 3, 0, 1));
     st(0, if(lt(ld(0), 0.5), sqrt(2 * ld(0)), 2 - sqrt(2 * (1 - ld(0)))) / 2);
   lerp(line_h + 3, h - line_h * 2 + 5, ld(0))'

Transition expressions

Xfade transitions

The custom ffmpeg variant eases the built-in xfade transitions; these are provided for custom expression use. They are converted from C-code in vf_xfade.c to custom expressions for use with easing. Omitted transitions are distance and hblur which perform aggregation, so cannot be computed efficiently on a per plane-pixel basis.

• fade fadefast fadeslow
• fadeblack fadewhite fadegrays
• wipeleft wiperight wipeup wipedown
• wipetl wipetr wipebl wipebr
• slideleft slideright slideup slidedown
• smoothleft smoothright smoothup smoothdown
• circlecrop rectcrop
• circleopen circleclose
• vertopen vertclose horzopen horzclose
• diagtl diagtr diagbl diagbr
• hlslice hrslice vuslice vdslice
• radial zoomin
• dissolve pixelize
• squeezeh squeezev
• hlwind hrwind vuwind vdwind
• coverleft coverright coverup coverdown
• revealleft revealright revealup revealdown

Gallery

Here are the xfade transitions processed using custom expressions instead of the built-in transitions (for testing), without easing – see also the FFmpeg Wiki Xfade page:

GL Transitions

The open collection of GL Transitions initiative lead by Gaëtan Renaudeau (gre) “aims to establish an universal collection of transitions that various softwares can use” released under a Free License.

Many of the simpler GLSL transitions at gl-transitions, many of them customisable, have been converted to native C transitions (for custom ffmpeg variant) and custom expressions (for custom expression variant) for use with or without easing:

• gl_angular [args: startingAngle,clockwise; default: (90,0)] (by: Fernando Kuteken)
• gl_BookFlip (by: hong)
• gl_Bounce [args: shadow_alpha,shadow_height,bounces,direction; default: (0.6,0.075,3,0)] (by: Adrian Purser)
• gl_BowTie [args: vertical; default: (0)] (by: huynx)
• gl_cannabisleaf (by: Flexi23)
• gl_CrazyParametricFun [args: a,b,amplitude,smoothness; default: (4,1,120,0.1)] (by: mandubian)
• gl_crosshatch [args: center.x,center.y,threshold,fadeEdge; default: (0.5,0.5,3,0.1)] (by: pthrasher)
• gl_crosswarp (by: Eke Péter)
• gl_cube [args: persp,unzoom,reflection,floating,bgBkWhTr; default: (0.7,0.3,0.4,3,0)] (by: gre)
• gl_DirectionalScaled [args: direction.x,direction.y,scale,bgBkWhTr; default: (0,1,0.7,0)] (by: Thibaut Foussard)
• gl_directionalwarp [args: smoothness,direction.x,direction.y; default: (0.1,-1,1)] (by: pschroen)
• gl_doorway [args: reflection,perspective,depth,bgBkWhTr; default: (0.4,0.4,3,0)] (by: gre)
• gl_Dreamy (by: mikolalysenko)
• gl_Exponential_Swish [args: zoom,angle,offset,exponent,wrap.x,wrap.y,blur,bgBkWhTr; default: (0.8,0,0,4,2,2,0,0)] (by: Boundless)
• gl_GridFlip [args: size.x,size.y,pause,dividerWidth,randomness,bgBkWhTr; default: (4,4,0.1,0.05,0.1,0)] (by: TimDonselaar)
• gl_heart (by: gre)
• gl_hexagonalize [args: steps,horizontalHexagons; default: (50,20)] (by: Fernando Kuteken)
• gl_InvertedPageCurl (by: Hewlett-Packard)
• gl_kaleidoscope [args: speed,angle,power; default: (1,1,1.5)] (by: nwoeanhinnogaehr)
• gl_Mosaic [args: endx,endy; default: (2,-1)] (by: Xaychru)
• gl_perlin [args: scale,smoothness; default: (4,0.01)] (by: Rich Harris)
• gl_pinwheel [args: speed; default: (2)] (by: Mr Speaker)
• gl_polar_function [args: segments; default: (5)] (by: Fernando Kuteken)
• gl_PolkaDotsCurtain [args: dots,centre.x,centre.y; default: (20,0,0)] (by: bobylito)
• gl_powerKaleido [args: scale,z,speed; default: (2,1.5,5)] (by: Boundless)
• gl_randomNoisex (by: towrabbit)
• gl_randomsquares [args: size.x,size.y,smoothness; default: (10,10,0.5)] (by: gre)
• gl_ripple [args: amplitude,speed; default: (100,50)] (by: gre)
• gl_Rolls [args: type,RotDown; default: (0,0)] (by: Mark Craig)
• gl_RotateScaleVanish [args: FadeInSecond,ReverseEffect,ReverseRotation,bgBkWhTr,trkMat; default: (1,0,0,0)] (by: Mark Craig)
• gl_rotateTransition (by: haiyoucuv)
• gl_rotate_scale_fade [args: centre.x,centre.y,rotations,scale,backGray; default: (0.5,0.5,1,8,0.15)] (by: Fernando Kuteken)
• gl_Slides [args: type,In; default: (0,0)] (by: Mark Craig)
• gl_squareswire [args: squares.h,squares.v,direction.x,direction.y,smoothness; default: (10,10,1.0,-0.5,1.6)] (by: gre)
• gl_static_wipe [args: u_transitionUpToDown,u_max_static_span; default: (1,0.5)] (by: Ben Lucas)
• gl_Stripe_Wipe [args: nlayers,layerSpread,color1,color2,shadowIntensity,shadowSpread,angle; default: (3,0.5,0x3319CCFF,0x66CCFFFF,0.7,0,0)] (by: Boundless)
• gl_swap [args: reflection,perspective,depth,bgBkWhTr; default: (0.4,0.2,3,0)] (by: gre)
• gl_Swirl (by: Sergey Kosarevsky)
• gl_WaterDrop [args: amplitude,speed; default: (30,30)] (by: Paweł Płóciennik)
• gl_windowblinds (by: Fabien Benetou)

Gallery

Here are the ported GL Transitions with default parameters and no easing – see also the GL Transitions Gallery (which lacks many recent contributor transitions):

With easing

GL Transitions can also be eased, although easing is integral with some:

Example: Swirl transition with bounce easing

Customisation parameters

Many GL Transitions accept parameters to customise the transition effect. The parameters and default values are shown above.

Example: two pinwheel speeds: -t 'gl_pinwheel(0.5)' and -t 'gl_pinwheel(10)'

Parameters are appended to the transition name as CSVs within parenthesis.

For the custom ffmpeg variant the parameters may be name=value pairs in any order, e.g. gl_WaterDrop(speed=20,amplitude=50), or they may be indexed values, as follows.

For the custom expression variant the parameters must be indexed values only but empty values assume defaults, e.g. gl_GridFlip(5,3,,0.1,,1) arguments are size.x=5,size.y=3,dividerWidth=0.1,bgBkWhTr=1 with default values for other parameters.

Custom expressions can also be amended directly: parameters are specified using store functions st(p,v) where p is the parameter number and v its value. So for gl_pinwheel with a speed value 10, change the first line of its expr below to st(1, 10);.

st(1, 2);
st(2, 1 - ld(0));
st(1, atan2(0.5 - Y / H, X / W - 0.5) + ld(2) * ld(1));
st(1, mod(ld(1), PI / 4));
if(lte(ld(2), ld(1)), A, B)

Similarly, gl_directionalwarp takes 3 parameters: smoothness, direction.x, direction.y (from xfade-easing.sh -L) and its expr starts with 3 corresponding st() (store) functions which may be changed from their default values:

st(1, 0.1);
st(2, -1);
st(3, 1);
st(4, hypot(ld(2), ld(3)));
etc.

Colour parameters

Colour values follow ffmpeg rules at Color) (custom ffmpeg variant only),
e.g. gl_Stripe_Wipe(color1=DeepSkyBlue,color2=ffd700)

Altered GL Transitions

• gl_angular has an additional clockwise parameter
• gl_Bounce has an additional direction parameter to control bounce direction: 0=south, 1=west, 2=north, 3=east
• gl_BowTie combines BowTieHorizontal and BowTieVertical using parameter vertical
• gl_RotateScaleVanish has an additional trkMat parameter (track matte, custom ffmpeg only) which treats the moving image/video as a variable-transparency overlay (I might add this feature to other transitions)
• gl_Exponential_Swish option blur default was originally 0.5 but blurring makes it unacceptably slow
• several GL Transitions show a black background during their transition, e.g. gl_cube and gl_doorway, but this implementation provides an additional bgBkWhTr parameter to control the background: 0=black (default), 1=white, -1=transparent

Porting

GLSL shader code runs on the GPU in real time. However GL Transition and Xfade APIs are broadly similar and non-complex algorithms are easily ported using vector resolution.

To make the transpiled code easier to follow, original variable names from the GLSL and xfade source code are replicated in xfade-easing.sh and xfade-easing.h. The script uses pseudo functions to emulate real functions, expanding them inline later.

Example: porting transition gl_randomsquares

randomsquares.glsl:

uniform ivec2 size; // = ivec2(10, 10)
uniform float smoothness; // = 0.5

float rand (vec2 co) {
    return fract(sin(dot(co.xy ,vec2(12.9898,78.233))) * 43758.5453);
}

vec4 transition(vec2 p) {
    float r = rand(floor(vec2(size) * p));
    float m = smoothstep(0.0, -smoothness, r - (progress * (1.0 + smoothness)));
    return mix(getFromColor(p), getToColor(p), m);
}

xfade-easing.sh (custom expression variant):

gl_randomsquares) # (case)
    _make "st(1, ${a[0]-10});" # size.x
    _make "st(2, ${a[1]-10});" # size.y
    _make "st(3, ${a[2]-0.5});" # smoothness
    _make 'st(1, floor(ld(1) * X / W));'
    _make 'st(2, floor(ld(2) * (1 - Y / H)));'
    _make 'st(4, frand(ld(1), ld(2), 4));' # r
    _make 'st(4, ld(4) - ((1 - P) * (1 + ld(3))));'
    _make 'st(4, smoothstep(0, -ld(3), ld(4), 4));' # m
    _make 'mix(A, B, ld(4))'
    ;;

Here, frand(), smoothstep() and mix() are pseudo functions. Customizable parameters are generally stored first. _make is just an expression string builder function.

xfade-easing.h (custom ffmpeg variant):

static vec4 gl_randomsquares(const XTransition *e)
{
    PARAM_BEGIN
    PARAM_2(ivec2, size, 10, 10)
    PARAM_1(float, smoothness, 0.5)
    PARAM_END
    float r = frand2(floor2(mul2(vec2i(size), e->p)));
    float m = smoothstep(0, -smoothness, r - e->progress * (1 + smoothness));
    return mix4(e->a, e->b, m);
}

Here, vec4 and ivec2 simulate GLSL vector types and XTransition encapsulates all data pertaining to a transition:

typedef struct { // modelled on GL Transition Specification v1
    const float progress; // transition progress, moves from 0.0 to 1.0 (cf. P)
    const float ratio; // viewport width / height (cf. W / H)
    vec2 p; // pixel position in slice, .y==0 is bottom (cf. X, Y)
    vec4 a, b; // plane data at p (cf. A, B)
    ...
} XTransition;

Custom expression performance

FFmpeg expr strings initially get parsed into an expression tree of AVExpr nodes in libavutil/eval.c. That expression is then executed for every pixel in each plane, which obviously incurs a performance hit, considerably exacerbated by disabling slice threading in order to use the st() and ld() functions. So custom transition expressions are not fast.

The following times are based on empirical timings scaled by benchmark scores (the Geekbench Mac Benchmark Chart). They are rough estimates in seconds to process a 3-second transition of HD720 (1280x720) 3-plane media (rgb24) through a null muxer at Mac benchmark midpoints. For greyscale (single plane), subtract two thirds. For an alpha plane, add a third. Mac model performance varies enormously so the Mac vintage dates are only approximate. Windows performance has not been measured.

The slowest supported transition gl_powerKaleido is clearly impractical for most purposes! The most complex transition is gl_InvertedPageCurl which involved considerable refactoring; it omits anti-aliasing for simplicity. See xfade-easing.h for the transpiled GLSL-C code that helped to optimize the custom expressions.

Using the custom ffmpeg build on M2 Macs, the slowest transition takes just 4 seconds for the same task. However gl_Exponential_Swish with blurring can take 3 minutes! While much slower than a GPU, CPU processing is at least tolerable. Unlike built-in xfade transitions the custom ffmpeg C code in xfade-easing.h deploys a single pixel iterator for all extended transition functions which in turn operate on all planes at once. And it does not require -filter_complex_threads 1.

Performance-wise, custom expressions are slower by a factor of 41 (median), 47 (mean) with a huge standard deviation of 26!

Other faster ways to use GL Transitions with FFmpeg are:

• gl-transition-scripts includes a Node.js CLI script gl-transition-render which can render multiple GL Transitions and images for FFmpeg processing
• ffmpeg-concat is a Node.js package which requires installation and a lot of temporary storage
• ffmpeg-gl-transition is a native FFmpeg filter which requires building ffmpeg from source

CLI script

xfade-easing.sh is a Bash 4 shell wrapper for ffmpeg. It can:

• generate custom easing and transition expressions for the xfade expr parameter
• generate easing graphs via gnuplot (especially useful for CSS easings)
• create demo videos for testing
• concenate visual media with eased transitions for presentations and slideshows.

Usage

FFmpeg XFade easing and extensions version 2.1.2 by Raymond Luckhurst, https://scriptit.uk
Generates custom expressions for rendering eased transitions and easing in other filters,
also creates easing graphs, demo videos, presentations and slideshows
See https://github.com/scriptituk/xfade-easing
Usage: xfade-easing.sh [options] [image/video inputs]
Options:
    -f pixel format (default: rgb24): use ffmpeg -pix_fmts for list
    -t transition name and arguments, if any (default: fade); use -L for list
       args in parenthesis as CSV, e.g.: 'gl_perlin(5,0.1)'
    -e easing function and arguments, if any (default: linear)
       CSS args in parenthesis as CSV, e.g.: 'cubic-bezier(0.17,0.67,0.83,0.67)'
    -x expr output filename (default: no expr), accepts expansions, - for stdout
    -a append to expr output file
    -s expr output format string with text expansion (default: '%x')
       %f expands to pixel format, %F to format in upper case
       %e expands to the easing name
       %t expands to the transition name
       %E, %T upper case expansions of %e, %t
       %c expands to the CSS easing arguments
       %a expands to the GL transition arguments; %A to the default arguments (if any)
       %x expands to the generated expr, condensed, intended for inline filterchains
       %X uncondensed version of %x, intended for -filter_complex_script files
       %p expands to the progress easing expression, condensed, for inline filterchains
       %g expands to the generic easing expression (for other filters), condensed
       %z expands to the eased transition expression only, condensed
          for the uneased transition expression only, omit -e option and use %x or %X
       %P, %G, %Z, uncondensed versions of %p, %g, %z, for -filter_complex_script files
       %n inserts a newline
    -p easing plot filename (default: no plot), accepts expansions
       formats: gif, jpg, png, svg, pdf, eps, html <canvas>, from file extension
    -m multiple easings to plot on one graph (default: the -e easing)
       CSV easings with optional legend prefix, e.g. in=cubic-in,out=cubic-out,in-out=cubic
    -q plot title (default: easing name, or Easings for multiple plots)
    -c canvas size for easing plot (default: 640x480, scaled to inches for PDF/EPS)
       format: WxH; omitting W or H keeps aspect ratio, e.g. -z x300 scales W
    -v video output filename (default: no video), accepts expansions
       formats: animated gif, mp4 (x264), webm, mkv (FFV1 lossless), from file extension
       if - then format is the null muxer (no output)
       if -f format has alpha then webm and mkv generate transparent video output
       if gifsicle is available then gifs will be optimised
    -z video size (default: input 1 size)
       format: WxH; omitting W or H keeps aspect ratio, e.g. -z 400x scales H
    -d video transition duration (default: 3s, minimum: 0) (see note after -l)
    -i time between video transitions (default: 1s, minimum: 0) (see note after -l)
    -l video length (default: 5s)
       note: options -d, -i, -l are interdependent: l=ni+(n-1)d for n inputs
       given -t & -l, d is calculated; else given -l, t is calculated; else l is calculated
    -j allow input videos to play within transitions (default: no)
       normally videos only play during the -i time but this sets them playing throughout
    -r video framerate (default: 25fps)
    -n show effect name on video as text (requires the libfreetype library)
    -u video text font size multiplier (default: 1.0)
    -k video stack orientation,gap,colour,padding (default: ,0,white,0), e.g. h,2,red,1
       stacks uneased and eased videos horizontally (h), vertically (v) or auto (a)
       auto selects the orientation that displays easing to best effect
       also stacks transitions with default and custom parameters, eased or not
       videos are only stacked if they are different (nonlinear-eased or customised)
       unstacked videos can be padded using orientation=1, e.g. 1,0,blue,5
    -L list all transitions and easings
    -H show this usage text
    -V show this script version
    -X use custom expressions, not the xfade API that supports xfade-easing natively
       by default native support is detected automatically using ffmpeg --help filter=xfade
       the native API adds an easing option and runs much faster
       e.g. xfade=duration=4:offset=1:easing=quintic-out:transition=wiperight
       e.g. xfade=duration=5:offset=2.5:easing='cubic-bezier(.17,.67,.83,.67)' \
            transition='gl_swap(depth=5,reflection=0.7,perspective=0.6)' (see repo README)
    -I set ffmpeg loglevel to info for -v (default: warning)
    -D dump debug messages to stderr and set ffmpeg loglevel to debug for -v
    -P log xfade progress percentage using custom expression print() function (implies -I)
    -T temporary file directory (default: /tmp)
    -K keep temporary files if temporary directory is not /tmp
Notes:
    1. point the shebang path to a bash4 location (defaults to MacPorts install)
    2. this script requires Bash 4 (2009), ffmpeg, gawk, gsed, seq, also gnuplot for plots
    3. use ffmpeg option -filter_complex_threads 1 (slower!) because xfade expression
       vars used by st() & ld() are shared across slices, therefore not thread-safe
       (the custom ffmpeg build works without -filter_complex_threads 1)
    4. CSS easings are supported in the custom ffmpeg build but not as custom expressions
    4. certain xfade transitions are not implemented as custom expressions because
       they perform aggregation (distance, hblur)
    5. many GL Transitions are also ported, some of which take customisation parameters
       to override defaults append parameters in parenthesis (see -X above)
    6. some GL Transitions are only available in the custom ffmpeg build
    7. many transitions do not lend themselves well to easing, others have easing built in
       easings that overshoot (back & elastic) may cause weird effects!

Generating expr code

Expr code is generated using the -x option and customised with the -s,-a options.

• xfade-easing.sh -t slideright -e quadratic -x -
  prints expr for slideright transition with quadratic-in-out easing to stdout
• xfade-easing.sh -t coverup -e quartic-in -x coverup_quartic-in.txt
  prints expr for coverup transition with quartic-in easing to file coverup_quartic-in.txt
• xfade-easing.sh -t coverup -e quartic-in -x %t_%e.txt
  ditto, using expansion specifiers in file name
• xfade-easing.sh -t rectcrop -e exponential-out -s "\$expr['%t_%e'] = '%n%X';" -x exprs.php -a
  appends the following to file exprs.php:

$expr['rectcrop_exponential-out'] = '
st(0, if(eq(P, 0), 0, 2^(-10 * (1 - P))))
;
st(1, abs(ld(0) - 0.5));
if(lt(abs(X - W / 2), ld(1) * W) * lt(abs(Y - H / 2), ld(1) * H),
 if(lt(ld(0), 0.5), B, A),
 if(lt(PLANE,3), 0, 255)
)';

• xfade-easing.sh -t gl_polar_function -s "expr='%n%X'" -x fc-script.txt
  This is not eased, therefore the expr written to fc-script.txt uses progress P directly:

expr='
st(1, 5);
st(2, X / W - 0.5);
st(3, 0.5 - Y / H);
st(4, atan2(ld(3), ld(2)) - PI / 2);
st(4, cos(ld(1) * ld(4)) / 4 + 1);
st(1, hypot(ld(2), ld(3)));
if(gt(ld(1), ld(4) * (1 - P)), A, B)'

Generating test plots

Plots are generated using the -p option and customised with the -m,-q,-c options.

Plot data is logged using the print function of the ffmpeg expression evaluator for the first plane and first pixel as xfade progress P goes from 1 to 0 at 100fps.

• xfade-easing.sh -e elastic -p plot-%e.pdf
  creates a PDF file plot-elastic.pdf of elastic easing
• xfade-easing.sh -q 'Bounce Easing' -m in=bounce-in,out=bounce-out,in-out=bounce -p %e.png -c 500x
  creates image file bounce.png of the bounce easing scaled to 500px wide with title and legends:

The plots above in Standard easings show test plots for all standard easings and all three modes (in, out and in-out).

Generating demo videos

Videos are generated using the -v option and customised with the -z,-d,-i,-l,-j,-r,-n,-u,-k options.

[!NOTE] all transition effect demos on this page are animated GIFs regardless of the commands shown

Timing

Input media is serialised according to the expression $L=NI+(N-1)D$ where L is the total video length (option -l); I is the individual display time (option -i); D is the transition duration (option -d); N is the number of inputs. Transition offsets are spaced accordingly. Depending on option -j and the input media length, pre and post padding is added by frame cloning to ensure enough frames are available for transition processing. See Usage for the precedence of options -l, -i, -d.

Examples

• xfade-easing.sh -t hlwind -e quintic-in -v windy.gif creates an animated GIF image of the hlwind transition with quintic-in easing using default built-in images
  

• xfade-easing.sh -t fadeblack -e circular -v maths.mp4 dot.png cross.png creates a MP4 video of the fadeblack transition with circular easing using specified inputs
  

• xfade-easing.sh -t coverdown -e bounce-out -v %t-%e.mp4 wallace.png shaun.png creates a video of the coverdown transition with bounce-out easing using expansion specifiers for the output file name
  

• xfade-easing.sh -t 'gl_polar_function(25)' -v paradise.mkv -n -u 1.2 islands.png rainbow.png creates a lossless (FFV1) video (e.g. for further processing) of an uneased polar_function GL transition with 25 segments annotated in enlarged text
  

• xfade-easing.sh -t 'gl_angular(270,1)' -e exponential -v multiple.mp4 -n -k h -l 20 street.png road.png flowers.png bird.png barley.png creates a video of the angular GL transition with parameter startingAngle=270 (south) and clockwise=1 (an added parameter) for 5 inputs with fast exponential easing
  

• xfade-easing.sh -t gl_BookFlip -e quartic-out -v book.mp4 -f gray -z 248x -n -k h,2,black,1 alice12.png alice34.png creates a simple greyscale page turn with quartic-out easing for a more realistic effect.
  

• xfade-easing.sh -t circlecrop -e sinusoidal -v home-away.mp4 -l 10 -d 8 -z 246x -k h,4,LightSkyBlue,2 -n phone.png beach.png creates a 10s video with a slow 8s circlecrop xfade transition with sinusoidal easing, horizontally stacked with a 4px LightSkyBlue gap (see Color) and 2px padding
  

• xfade-easing.sh -t gl_InvertedPageCurl -e cubic-in -v score.mp4 -f gray -i 2 -d 3 -z 480x -k 1,0,0xD8D8D8,10 fugue1.png fugue2.png fugue3.png a 3s page curl effect, static for 2s, with cubic-in easing using greyscale format (-k 1,0,colour,padding creates a border)
  
  🎹 I play this Bach fugue on my YouTube channel digitallegro but the GL InvertedPageCurl there was generated by ffmpeg-concat

• xfade-easing.sh -t 'gl_PolkaDotsCurtain(10,0.5,0)' -e 'cubic-bezier(0.4,1.2,0.6,-1.1)' -v life.mp4 -l 7 -d 5 -z 500x -f yuv420p -r 30 balloons.png fruits.png a GL transition with arguments and cubic-bezier easing, running at 30fps for 7 seconds, processing in YUV (Y'CbCr) colour space throughout
  

See also

• FFmpeg Xfade filter reference documentation
• FFmpeg Wiki Xfade page with gallery
• FFmpeg Expression Evaluation reference documentation
• Robert Penner’s Easing Functions the original, from 2001
• Michael Pohoreski’s Easing Functions single oarameter versions of Penner’s Functions
• CSS Easing Functions Level 2 W3C Editor’s Draft
• GL Transitions homepage and Gallery and Editor
• GL Transitions repository on GitHub
• GLSL Data Types and OpenGL Reference Pages
• GLSL Vector and Matrix Operations GLSL specific built-in data types and functions
• The Book of Shaders a guide through the universe of Fragment Shaders
• libavfilter/vf_xfade.c xfade source code
• libavutil/eval.c expr source code
• ffmpeg-concat Node.js package, concats videos with GL Transitions
• ffmpeg-gl-transition native FFmpeg GL Transitions filter
• gl-transition-render Node.js script to render GL Transitions with images on the CLI
• Editly Node.js CLI tool for assembling videos from clips or images or JSON spec.