    MILKDROP preset authoring guide
       return to milkdrop.html

    * * *
    Note that there is another, quite comprehensive, Preset Authoring Guide
    available on the web at http://www.milkdrop.co.uk/, which is continually
    updated and expanded through the hard work of a few dedicated preset
    authors.  Whereas this guide (the one you are currently viewing) gives the bare
    technical specifications for writing your own presets, the guide at milkdrop.co.uk
    'starts at the beginning' and walks you through all of the mathematics and subtleties
    of 'rolling your own', explaining things in great detail.  The guide at milkdrop.co.uk
    is very highly recommended to anyone who wishes to learn more about creating their
    own presets.
    * * *

    Section Listing
    -----------------------
    1. about presets
    2. preset authoring - basic
    3. preset authoring - advanced
        a. per-frame equations
        b. per-pixel equations
        c. preset initialization code and q1-q8
        d. custom shapes & waves
        e. quality assurance
        f. debugging
        g. function reference

    1. About Presets
    -----------------------
        A 'preset' is a collection of parameters that tell MilkDrop how to
        draw the wave, how to warp the image around, and so on.  MilkDrop
        ships with around ~100 built-in presets, each one having a distinct
        look and feel to it.

        Using MilkDrop's built-in "preset-editing menu", you can edit presets
        on the fly, from within the program.  You can make slight adjustments
        to existing presets, then save over them; or you can change lots of
        things, so the preset doesn't look anything like the original, and
        then save it under a new name.  You can even write insane new
        mathematical equations, of your own imagination, into your preset
        files and come up with things that MilkDrop has never done before!

        Each preset is saved as a file with the ".milk" extension, so you can
        easily send them to your friends or post them on the web.  You can also
        go to http://www.nullsoft.com/free/milkdrop and then jump to the
        "preset sharing forum" to see what other people have come up with,
        or post your own cool, new presets.

    2. Preset Authoring - Basic
    -----------------------

        You can edit the properties of the current preset by hitting 'M',
        which brings up the "preset-editing menu".  From this menu you
        can use the up and down arrow keys to select an item.  Press
        the RIGHT arrow key to move forward through the menu and select
        the item (note: you can also hit SPACE or RETURN to do this);
        ***press the LEFT arrow key to go back to the previous menu.***

        Pressing 'M' while the menu is already showing will hide the menu;
        pressing ESCAPE will do the same thing.  Press 'M' again to bring
        the menu back.

        Once you've reached an item on the menu whose value can be edited,
        use the UP and DOWN arrow keys to increase or decrease its value,
        respectively.  Changes will register immediately.  Use PAGE UP and
        PAGE DOWN to increase the value more quickly.  Hold down SHIFT
        and use the UP/DOWN arrow keys to change the value very slowly.
        Hit RETURN To keep the new value, or ESC to abort the change.

        If the item you're editing is a text string, you can use the
        arrow keys to move around.  The Insert key can be used to toggle
        between insert and overtype modes.  You can hold shift and use
        the arrow keys (home, end, left, right) to make a selection,
        which will be identified by brackets [].  You can then use CTRL-C
        or CTRL-X to copy or cut text.  CTRL-P pastes.  When finished
        editing, hit RETURN To keep the new string, or ESC to abort the
        change.

        You'll want to get into the habit of using SCROLL LOCK whenever
        you're making changes to a preset that you intend to save;
        otherwise, the preset is sure to keep randomly changing on you.
        You might ask me, "why don't you just automatically lock the
        preset while the menu is up?"  I will answer you, "because in
        the instant between exiting the menu and going to save the preset,
        the preset might then switch, and you'd lose your changes."  Then
        you might ask me, "then why don't you just leave it locked
        whenever the user makes a change from the menu?" and I will say
        to you, "because I hate it when programs do things like that.  You
        have an idea in your brain about the state of the Scroll Lock key,
        because you're the one setting that state.  I want your mind to
        always be up-to-date."  And you might then ask me: "how large is
        large?"  And I will tell you: "thirty."

        There are also some hotkeys that will allow you to change certain
        common parameters to the current preset.  These are listed below.

        MOTION
            i/I - zoom in/out
            [ / ] - push motion to the left/right (dx)
            { / } - push motion up/down (dy)
            < / > - rotate left/right (rot)
            o/O - shrink/grow the amplitude of the warp effect

        WAVEFORM
            W - cycle through waveforms
            j/J - scale waveform down/up
            e/E - make the waveform more transparent/more solid

        BRIGHTNESS
            d/D - decrease, increase decay (fades image to black over time)
            g/G - decrease, increase gamma (brightness)

        VIDEO ECHO effect
            q/Q - scale 2nd graphics layer down/up
            a/A - decrease/increase alpha of 2nd graphics layer
            F - flip 2nd graphics layer (cycles through 4 fixed orientations)

    3. Preset Authoring - Advanced
    -----------------------

        This section describes how to use the 'per-frame' and 'per-pixel'
        equations to develop unique new presets.

        a. PER-FRAME EQUATIONS
        ----------------------

        When you hit 'm' to show the preset-editing menu, several items
        show up.  If you explore the sub-menus, you'll see that
        all of the properties that make up the preset you're currently
        viewing are there.  The values you can specify here (such as
        zoom amount, rotation amount, wave color, etc.) are all static
        values, meaning that they don't change in time.  For example,
        take the 'zoom amount' option under the 'motion' submenu.
        If this value is 1.0, there is no zoom.  If the value is 1.01,
        the image zooms in 1% every frame.  If the value is 1.10, the
        image zooms in 10% every frame.  If the value is 0.9, the image
        zooms out 10% every frame; and so on.

        However, presets get far more interesting if you can take these
        parameters (such as the zoom amount) and animate them (make them
        change over time).  For example, if you could take the 'zoom
        amount' parameter and make it oscillate (vary) between 0.9 and
        1.1 over time, the image would cyclically zoom in and out, in
        time.

        You can do this - by writing 'per-frame' and 'per-pixel'
        equations.  Let's start with 'per-frame' equations.  These are
        executed once per frame.  So, if you were to type the following
        equation in:

            zoom = zoom + 0.1*sin(time);

        ...then the zoom amount would oscillate between 0.9 and 1.1
        over time.  (Recall from your geometry classes that sin()
        returns a value between -1 and 1.)  The equation says: "take
        the static value of 'zoom', then replace it with that value,
        plus some variation."  This particular equation would oscillate
        (cycle) every 6.28 seconds, since the sin() function's
        period is 6.28 (PI*2) seconds.  If you wanted it to make it
        cycle every 2 seconds, you could use:

            zoom = zoom + 0.1*sin(time*3.14);

        Now, let's say you wanted to make the color of the waveform
        (sound wave) that gets plotted on the screen vary through time.
        The color is defined by three values, one for each of the main
        color components (red, green, and blue), each in the range 0 to 1
        (0 is dark, 1 is full intensity).  You could use something like this:

            wave_r = wave_r + 0.5*sin(time*1.13);
            wave_g = wave_g + 0.5*sin(time*1.23);
            wave_b = wave_b + 0.5*sin(time*1.33);

        It's nice to stagger the frequencies (1.13, 1.23, and 1.33) of
        the sine functions for the red, green, and blue color components
        of the wave so that they cycle at different rates, to avoid them
        always being all the same (which would create a greyscale wave).

        Here is a full list of the variables available for writing per-frame
        equations:

        NAME       WRITABLE?  RANGE  DESCRIPTION
        ----       ---------  -----  -----------
        zoom           yes    >0     controls inward/outward motion.  0.9=zoom out 10% per frame, 1.0=no zoom, 1.1=zoom in 10%
        zoomexp        yes    >0     controls the curvature of the zoom; 1=normal
        rot            yes           controls the amount of rotation.  0=none, 0.1=slightly right, -0.1=slightly clockwise, 0.1=CCW
        warp           yes    >0     controls the magnitude of the warping; 0=none, 1=normal, 2=major warping...
        cx             yes    0..1   controls where the center of rotation and stretching is, horizontally.  0=left, 0.5=center, 1=right
        cy             yes    0..1   controls where the center of rotation and stretching is, vertically.  0=top, 0.5=center, 1=bottom
        dx             yes           controls amount of constant horizontal motion; -0.01 = move left 1% per frame, 0=none, 0.01 = move right 1%
        dy             yes           controls amount of constant vertical motion; -0.01 = move up 1% per frame, 0=none, 0.01 = move down 1%
        sx             yes    >0     controls amount of constant horizontal stretching; 0.99=shrink 1%, 1=normal, 1.01=stretch 1%
        sy             yes    >0     controls amount of constant vertical stretching; 0.99=shrink 1%, 1=normal, 1.01=stretch 1%
        wave_mode      yes    0,1,2,3,4,5,6,7  controls which of the 8 types of waveform is drawn
        wave_x         yes    0..1   position of the waveform: 0 = far left edge of screen, 0.5 = center, 1 = far right
        wave_y         yes    0..1   position of the waveform: 0 = very bottom of screen, 0.5 = center, 1 = top
        wave_r         yes    0..1   amount of red color in the wave (0..1),
        wave_g         yes    0..1   amount of green color in the wave (0..1)
        wave_b         yes    0..1   amount of blue color in the wave (0..1)
        wave_a         yes    0..1   opacity of the wave (0..1) [0=transparent, 1=opaque]
        wave_mystery   yes    -1..1  what this parameter does is a mystery.  (honestly, though, this value does different things for each waveform; for example, it could control angle at which the waveform was drawn.)
    	wave_usedots   yes    0/1    if 1, the waveform is drawn as dots (instead of lines)
        wave_thick     yes    0/1    if 1, the waveform's lines (or dots) are drawn with double thickness
        wave_additive  yes    0/1    if 1, the wave is drawn additively, saturating the image at white
        wave_brighten  yes    0/1    if 1, all 3 r/g/b colors will be scaled up until at least one reaches 1.0
        ob_size        yes    0..0.5 thickness of the outer border drawn at the edges of the screen every frame
        ob_r           yes    0..1   amount of red color in the outer border
        ob_g           yes    0..1   amount of green color in the outer border
        ob_b           yes    0..1   amount of blue color in the outer border
        ob_a           yes    0..1   opacity of the outer border (0=transparent, 1=opaque)
        ib_size        yes    0..0.5 thickness of the inner border drawn at the edges of the screen every frame
        ib_r           yes    0..1   amount of red color in the inner border
        ib_g           yes    0..1   amount of green color in the inner border
        ib_b           yes    0..1   amount of blue color in the inner border
        ib_a           yes    0..1   opacity of the inner border (0=transparent, 1=opaque)
        mv_r           yes    0..1   amount of red color in the motion vectors
        mv_g           yes    0..1   amount of green color in the motion vectors
        mv_b           yes    0..1   amount of blue color in the motion vectors
        mv_a           yes    0..1   opacity of the motion vectors (0=transparent, 1=opaque)
        mv_x           yes    0..64  the number of motion vectors in the X direction
        mv_y           yes    0..48  the number of motion vectors in the Y direction
        mv_l           yes    0..5   the length of the motion vectors (0=no trail, 1=normal, 2=double...)
        mv_dx          yes    -1..1  horizontal placement offset of the motion vectors
        mv_dy          yes    -1..1  vertical placement offset of the motion vectors
        decay          yes    0..1   controls the eventual fade to black; 1=no fade, 0.9=strong fade, 0.98=recommended
        gamma          yes    >0     controls display brightness; 1=normal, 2=double, 3=triple, etc.
        echo_zoom      yes    >0     controls the size of the second graphics layer
        echo_alpha     yes    >0     controls the opacity of the second graphics layer; 0=transparent (off), 0.5=half-mix, 1=opaque
        echo_orient    yes    0,1,2,3 selects an orientation for the second graphics layer.  0=normal, 1=flip on x, 2=flip on y, 3=flip on both
        darken_center  yes    0/1    if 1, help keeps the image from getting too bright by continually dimming the center point
        wrap           yes    0/1    sets whether or not screen elements can drift off of one side and onto the other
        invert         yes    0/1    inverts the colors in the image
        brighten       yes    0/1    brightens the darker parts of the image (nonlinear; square root filter)
        darken         yes    0/1    darkens the brighter parts of the image (nonlinear; squaring filter)
        solarize       yes    0/1    emphasizes mid-range colors
        monitor        yes    any    set this value for debugging your preset code; if you hit the 'N' key,
                                        the value of 'monitor' will be posted in the upper-right corner of milkdrop.
                                        for example, setting "monitor = q3;" would let you keep an eye on q3's value.

        time       NO         >0       retrieves the current time, in seconds, since MilkDrop started running
        fps        NO         >0       retrieves the current framerate, in frames per second.
        frame      NO                  retrieves the number of frames of animation elapsed since the program started
        progress   NO         0..1     progress through the current preset; if preset was just loaded, this is closer to 0; if preset is about to end, this is closer to 1.
                                         -note that if Scroll Lock is on, 'progress' will freeze!

        bass       NO         >0       retrieves the current amount of bass.  1 is normal; below ~0.7 is quiet; above ~1.3 is loud bass
        mid        NO         >0         -same, but for mids (middle frequencies)
        treb       NO         >0         -same, but for treble (high) frequencies
        bass_att   NO         >0       retrieves an attenuated reading on the bass, meaning that it is damped in time and doesn't change so rapidly.
        mid_att    NO         >0         -same, but for mids (middle frequencies)
        treb_att   NO         >0         -same, but for treble (high) frequencies

        meshx          NO     8-128  tells you the user's mesh size in the X direction.  always an integer value.
        meshy          NO     6-96   tells you the user's mesh size in the Y direction.  always an integer value.

        q1             yes    any    }
        q2             yes    any    }
        q3             yes    any    }
        q4             yes    any    } Used to carry information between the per-frame code
        q5             yes    any    }  and the per-pixel code; see below.
        q6             yes    any    }
        q7             yes    any    }
        q8             yes    any    }

        Some of the variables are read-only, meaning that you shouldn't change
        their values them through the equations.  You can; it won't stop you;
        but the results are unpredictable.

        You can also make up to 30 of your own variables.  For example:

            my_volume = (bass + mid + treb)/3;
            zoom = zoom + 0.1*(my_volume - 1);

        This would make the zoom amount increase when the music is loud,
        and decrease when the music is quiet.

        HOWEVER, custom variables do not carry over from per-frame equations
        to per-pixel equations; if you set a custom variable's value in the
        per-frame equations, and try to read it in the per-pixel equations,
        you will not get the correct value.  Instead, you have to "bridge the
        gap" using 8 special variables: q1 through q8.  This is usually only
        used when you want to precompute some custom values in the per-frame
        equations for later use in the per-pixel equations.  For a good
        example of this, see the 'dynamic swirls' preset.  See below for
        more information on q1-q8.

        b. PER-PIXEL EQUATIONS
        -----------------------

        So far we've discussed only how to change parameters based on
        time.  What if you wanted to also vary a parameter, such as the
        zoom amount, in different ways, for different locations on the
        screen?  For example, normally, the result of the 'zoom' parameter
        is to just do a flat zoom.  This doesn't look very realistic,
        because you don't see any perspective in the zoom.  It would be
        better if we could give a unique zoom amount to each pixel on
        the screen; we could make the pixels far away from the center
        zoom more, and this would give it more perspective.  In order
        to do this, we use "per-pixel" equations, instead of per-frame
        equations.

        The code for this per-pixel equation is simple:

            zoom = zoom + rad*0.1;

        Where 'rad' is the radius of the pixel if it were cast into
        polar coordinates; from another perspective, 'rad' is the distance
        of the pixel from the center of the screen.  'rad is zero at the
        center, and 1 at the corners.  So if we run the above code,
        the image will be zoomed into 10% more at the edges of the screen
        than at the center.

        The per-pixel equations are really just like the per-frame equations,
        except for a variables.  The following variables are available
        exclusively to per-pixel equations (and not to per-frame equations):

        NAME       WRITABLE?  RANGE    DESCRIPTION
        ----       ---------  -----    -----------
        x          NO         0..1     retrieves the x-position of the current pixel.  At the very left edge of the screen this would be 0; in the middle, 0.5; and at the right, 1.
        y          NO         0..1     retrieves the y-position of the current pixel.  At the very top edge of the screen this would be 0; in the middle, 0.5; and at the bottom, 1.
        rad        NO         0..1     retrives the distance of the pixel from the center of the screen.  At the center of the screen this will be zero, and at the corners, 1.
                                          (The middle of the edges will be 0.707 (half of the square root of 2).
        ang        NO         0..6.28  retrieves the angle of the current pixel, with respect to the center of the screen.
                                          If the point is to the right of the center, this is zero; above it, it is PI/2 (1.57); to the left, it is PI (3.14); and below, it is 4.71 (PI*3/2).
                                          If it is just a dab below being directly to the right of the center of the screen, the value will approach 6.28 (PI*2).
                                          (note: this is simply the arctangent of y over x, precomputed for you.)

        zoom       yes        >0       controls inward/outward motion.  0.9=zoom out 10% per frame, 1.0=no zoom, 1.1=zoom in 10%
        zoomexp    yes        >0       controls the curvature of the zoom; 1=normal
        rot        yes                 controls the amount of rotation.  0=none, 0.1=slightly right, -0.1=slightly clockwise, 0.1=CCW
        warp       yes        >0       controls the magnitude of the warping; 0=none, 1=normal, 2=major warping...
        cx         yes        0..1     controls where the center of rotation and stretching is, horizontally.  0=left, 0.5=center, 1=right
        cy         yes        0..1     controls where the center of rotation and stretching is, vertically.  0=top, 0.5=center, 1=bottom
        dx         yes                 controls amount of constant horizontal motion; -0.01 = move left 1% per frame, 0=none, 0.01 = move right 1%
        dy         yes                 controls amount of constant vertical motion; -0.01 = move up 1% per frame, 0=none, 0.01 = move down 1%
        sx         yes        >0       controls amount of constant horizontal stretching; 0.99=shrink 1%, 1=normal, 1.01=stretch 1%
        sy         yes        >0       controls amount of constant vertical stretching; 0.99=shrink 1%, 1=normal, 1.01=stretch 1%

        time       NO         >0       retrieves the current time, in seconds, since MilkDrop started running
        fps        NO         >0       retrieves the current framerate, in frames per second.
        frame      NO                  retrieves the number of frames of animation elapsed since the program started
        progress   NO         0..1     progress through the current preset; if preset was just loaded, this is closer to 0; if preset is about to end, this is closer to 1.
                                         -note that if Scroll Lock is on, 'progress' will freeze!

        bass       NO         >0       retrieves the current amount of bass.  1 is normal; below ~0.7 is quiet; above ~1.3 is loud bass
        mid        NO         >0         -same, but for mids (middle frequencies)
        treb       NO         >0         -same, but for treble (high) frequencies
        bass_att   NO         >0       retrieves an attenuated reading on the bass, meaning that it is damped in time and doesn't change so rapidly.
        mid_att    NO         >0         -same, but for mids (middle frequencies)
        treb_att   NO         >0         -same, but for treble (high) frequencies

        meshx      NO         8-128    tells you the user's mesh size in the X direction.  always an integer value.
        meshy      NO         6-96     tells you the user's mesh size in the Y direction.  always an integer value.

        q1         yes        any      }
        q2         yes        any      }
        q3         yes        any      }
        q4         yes        any      } Used to carry information between the per-frame code
        q5         yes        any      }  and the per-pixel code; see below.
        q6         yes        any      }
        q7         yes        any      }
        q8         yes        any      }

        The main reason for distinction between per-frame and per-pixel equations
        is simple: SPEED.  If you have a per-pixel equation that doesn't make use
        of the x, y, rad, or ang variables, then there's no reason for it to be
        executed per-pixel; it could be executed once per frame, and the result
        would be the same.  So, here's a maxim to write on the wall:

            "If a per-pixel equation doesn't use at least one of the variables
             { x, y, rad, ang }, then it should be actually be a per-frame
             equation."

        You might be wondering how on earth all these formulas could be computed
        for every pixel on the screen, every frame, and still yield a high frame
        rate.  Well, that's the magic of the hamster.  And the fact that it really
        does the processing only at certain points on the screen, then interpolates
        the results across the space between the points.  In the config panel,
        the "mesh size" option defines how many points (in X and Y) there are at
        which the per-pixel equations are actually computed.  When you crank this
        option up, you start eating up CPU cycles rather quickly.

        c. PRESET INITIALIZATION CODE AND q1-q8
        -----------------------
        In MilkDrop 1.03 and later, you can write code that is executed only
        once, at the start of a preset.  This code allows you to set the initial
        value of your own (user-defined) variables (such as 'my_variable'), as well
        as the q1..q8 variables.  Any variable that is accessible in the per-frame
        equations is also accessible here, for reading; however, most of them will not
        be affected if you change them here, because they are overwritten by the base
        variable values of the preset at the start of each frame! (i.e. the values
        of the variables are reset to the values from the menus at the beginning of
        each frame.)  In effect, most of these variables are treated as 'read-only'
        in the initialization code.  If you do read (access) their values, you will
        get the base values - the ones baked into the preset (via the menu system).

        The variables that are writable include only q1..q8, and
        any custom variables that you want to create & initialize for later use.

        If you write to the values of q1..q8, these will become the new 'base values'
        to which q1..q8 are initialized at the start of each frame, for the per-frame
        code.  So when you access (read) q1-q8 in the per-frame code, you'll get the
        values that were set at the end of the preset init code.  You can then
        modify them (or not) in the per-frame code, and they will then be readable by
        the per-pixel code; but they will not persist to the next frame; they will be
        reset again, at the start of the next frame, to the values they had at the
        end of the preset init code.  See the q_and_t_vars.gif image for a diagram
        of the flow of the values of the q1-q8 varibles.

        In the per-pixel code, the q1-q8 values start (for the first pixel in any frame)
        as the values they had at the end of the per-frame code.  If you modify q1-q8
        in the per-pixel code, those modified values will carry over from pixel to
        pixel.  Next frame, they will be reset to whatever value they had at the end
        of the [next frame's execution of the] per-frame code.  (It's all in the diagram.)

        If you declare & assign values to your own new variables here, however, these
        values are 'sticky' like q1-q8; they can be modified by the per-frame code,
        and they will retain their (modified) values from frame to frame.

        One final note: when you edit the preset init code and apply it (by hitting
        CTRL+ENTER), the init code will re-execute immediately.  However, when you
        edit the regular per-frame/per-pixel code and hit CTRL+ENTER, the preset init
        code will NOT be re-executed; the results of the last execution will persist.
        If you change per-frame/per-pixel code and want to re-execute the initialization
        code (i.e. to randomize it or reset the preset), you'll have to save it and re-
        load it.

        d. CUSTOM SHAPES AND WAVES
        ----------------------
        As of MilkDrop 1.04, two new features are available: custom shapes, and custom
        waves.  A preset can have up to 4 of each.

        With custom shapes, you can draw an n-sided shape (with 3-100 sides) anywhere
        on the screen, at any angle and size, in any color, and at any opacity.  You
        even have the option to map the previous frame's image onto the shape, which
        makes for some incredible possibilities (such as realtime hardware fractals -
        see the 'Geiss - Feedback' preset).  You can also write per-frame code to
        control all of these things about the shape(s).  This way, they can react to
        the audio or change over time - whatever you can imagine.

        With custom waves, you can draw the waveform (or the frequency spectrum)
        wherever, whenever, and however you want; a great addition since MilkDrop
        1.03, where only the built-in waveforms were possible.  With custom waves
        you can also write per-frame code to control the waves, and per-point code
        to place every point (or line segment) on the wave exactly where you want,
        and in exactly the color you want, and so on.

        Remember those q1-q8 variables that were committed at the end of the preset
        initialization code, then reset (to those values) at the beginning of each
        frame, and then (potentially) modified in the preset per-frame code?  Those
        (potentially modified) values of q1-q8 - as they were at the end of the
        preset's per-frame code, each frame - are piped into the custom wave & custom
        shape per-frame code.  So if you read 'q3' in the custom wave per-frame
        code, what you're really reading is the value of 'q3' as it was left at the
        end of this frame's per-frame code.  Again, see the q_and_t_vars.gif image
        for a diagram of the flow of the values of the q1-q8 varibles.

        For custom waves, you can modify q1-q8 and that value will get passed on
        to the per-point code.  If you then modify q1-q8 in the per-point code,
        the modified values will pass on to the next point, much like the per-pixel
        code for the preset.

        There are, however, 8 additional variables available for custom waves
        and shapes: t1-t8.  These are very similar to q1-q8, but they exist only
        for custom waves & shapes.  Recall that q1-q8 exist so that you can carry
        custom data (values) from the preset init code and per-frame code, to the
        preset's per-pixel code (which uses a different pool of variables).
        Likewise, t1-t8 exist so that you can pass custom values from the custom
        wave/shape init code, on to the custom wave/shape per-frame code, and
        then (in the case of custom waves) on to the per-point code.  q1-q8 are
        also used to bridge another gap: to carry values from the preset init/per-
        frame code, to the custom wave/shape code.  Again, see the diagram; it's
        probably easier to understand than all of this explanation.

        CUSTOM SHAPE PER-FRAME VARIABLES
        ----------------------
            NAME       WRITABLE?  RANGE    DESCRIPTION
            ----       ---------  -----    -----------
            sides      yes        3-100    the default number of sides that make up the polygonal shape
            thick      yes        0/1      if ON, the border will be overdrawn 4X to make it thicker, bolder, and more visible
            additive   yes        0/1      if ON, the shape will add color to sature the image toward white; otherwise, it will replace what's there.
    	    x          yes        0..1     default x position of the shape (0..1; 0=left side, 1=right side)
    	    y          yes        0..1     default y position of the shape (0..1; 0=bottom, 1=top of screen)
    	    rad        yes        0+       default radius of the shape (0+)
    	    ang        yes        0..6.28  default rotation angle of the shape (0...2*pi)
            textured   yes        0/1      if ON, the shape will be textured with the image from the previous frame
            tex_zoom   yes        >0       the portion of the previous frame's image to use with the shape
            tex_ang    yes        0..6.28  the angle at which to rotate the previous frame's image before applying it to the shape
    	    r          yes        0..1     default amount of red color toward the center of the shape (0..1)
    	    g          yes        0..1     default amount of green color toward the center of the shape (0..1)
    	    b          yes        0..1     default amount of blue color toward the center of the shape (0..1)
    	    a          yes        0..1     default opacity of the center of the shape; 0=transparent, 1=opaque
    	    r2         yes        0..1     default amount of red color toward the outer edge of the shape (0..1)
    	    g2         yes        0..1     default amount of green color toward the outer edge of the shape (0..1)
    	    b2         yes        0..1     default amount of blue color toward the outer edge of the shape (0..1)
    	    a2         yes        0..1     default opacity of the outer edge of the shape; 0=transparent, 1=opaque
    	    border_r   yes        0..1     default amount of red color in the shape's border (0..1)
    	    border_g   yes        0..1     default amount of green color in the shape's border (0..1)
    	    border_b   yes        0..1     default amount of blue color in the shape's border (0..1)
    	    border_a   yes        0..1     default opacity of the shape's border; 0=transparent, 1=opaque

            time       NO         >0       retrieves the current time, in seconds, since MilkDrop started running
            fps        NO         >0       retrieves the current framerate, in frames per second.
            frame      NO                  retrieves the number of frames of animation elapsed since the program started
            progress   NO         0..1     progress through the current preset; if preset was just loaded, this is closer to 0; if preset is about to end, this is closer to 1.
                                             -note that if Scroll Lock is on, 'progress' will freeze!

            bass       NO         >0       retrieves the current amount of bass.  1 is normal; below ~0.7 is quiet; above ~1.3 is loud bass
            mid        NO         >0         -same, but for mids (middle frequencies)
            treb       NO         >0         -same, but for treble (high) frequencies
            bass_att   NO         >0       retrieves an attenuated reading on the bass, meaning that it is damped in time and doesn't change so rapidly.
            mid_att    NO         >0         -same, but for mids (middle frequencies)
            treb_att   NO         >0         -same, but for treble (high) frequencies

            q1         yes        any      }
            q2         yes        any      }
            q3         yes        any      } Used to carry information
            q4         yes        any      }  from the preset per-frame code
            q5         yes        any      }  to the custom shape/wave per-frame code.
            q6         yes        any      }  see q_and_t_vars.gif
            q7         yes        any      }
            q8         yes        any      }

            t1         yes        any      }
            t2         yes        any      }
            t3         yes        any      } Used to carry information
            t4         yes        any      }  from the custom shape init code
            t5         yes        any      }  to the custom shape per-frame code.
            t6         yes        any      }  see q_and_t_vars.gif
            t7         yes        any      }
            t8         yes        any      }

        CUSTOM WAVE PER-FRAME VARIABLES
        ---------------------
            NAME       WRITABLE?  RANGE    DESCRIPTION
            ----       ---------  -----    -----------
    	    r          yes        0..1     base amount of red color in the wave (0..1)
    	    g          yes        0..1     base amount of green color in the wave (0..1)
    	    b          yes        0..1     base amount of blue color in the wave (0..1)
    	    a          yes        0..1     base opacity of the waveform; 0=transparent, 1=opaque

            time       NO         >0       retrieves the current time, in seconds, since MilkDrop started running
            fps        NO         >0       retrieves the current framerate, in frames per second.
            frame      NO                  retrieves the number of frames of animation elapsed since the program started
            progress   NO         0..1     progress through the current preset; if preset was just loaded, this is closer to 0; if preset is about to end, this is closer to 1.
                                             -note that if Scroll Lock is on, 'progress' will freeze!

            bass       NO         >0       retrieves the current amount of bass.  1 is normal; below ~0.7 is quiet; above ~1.3 is loud bass
            mid        NO         >0         -same, but for mids (middle frequencies)
            treb       NO         >0         -same, but for treble (high) frequencies
            bass_att   NO         >0       retrieves an attenuated reading on the bass, meaning that it is damped in time and doesn't change so rapidly.
            mid_att    NO         >0         -same, but for mids (middle frequencies)
            treb_att   NO         >0         -same, but for treble (high) frequencies

            q1         yes        any      }
            q2         yes        any      }
            q3         yes        any      } Used to carry information
            q4         yes        any      }  from the preset per-frame code
            q5         yes        any      }  to the custom shape/wave per-frame code.
            q6         yes        any      }  see q_and_t_vars.gif
            q7         yes        any      }
            q8         yes        any      }

            t1         yes        any      }
            t2         yes        any      }
            t3         yes        any      } Used to carry information
            t4         yes        any      }  from the custom wave init code,
            t5         yes        any      }  to the custom wave per-frame code,
            t6         yes        any      }  and on to the custom wave per-point code.
            t7         yes        any      }  see q_and_t_vars.gif
            t8         yes        any      }

        CUSTOM WAVE PER-POINT VARIABLES
        ---------------------
            NAME       WRITABLE?  RANGE    DESCRIPTION
            ----       ---------  -----    -----------
    	    x          yes        0..1     the x position of this point that makes up the wave (0=left, 1=right)
    	    y          yes        0..1     the y position of this point that makes up the wave (0=bottom, 1=top)
            sample     no         0..1     how far along we are, through the samples that make up the waveform: 0=first sample, 0.5 = half-way through; 1=last sample.
            value1     no         any      the value of the Left audio channel sample at this point in the waveform (or freq. spectrum).
            value2     no         any      the value of the Right audio channel sample at this point in the waveform (or freq. spectrum).
    	    r          yes        0..1     amount of red color in this point of the wave (0..1)
    	    g          yes        0..1     amount of green color in this point of the wave (0..1)
    	    b          yes        0..1     amount of blue color in this point of the wave (0..1)
    	    a          yes        0..1     opacity of this point of the waveform; 0=transparent, 1=opaque

            time       NO         >0       retrieves the current time, in seconds, since MilkDrop started running
            fps        NO         >0       retrieves the current framerate, in frames per second.
            frame      NO                  retrieves the number of frames of animation elapsed since the program started
            progress   NO         0..1     progress through the current preset; if preset was just loaded, this is closer to 0; if preset is about to end, this is closer to 1.
                                             -note that if Scroll Lock is on, 'progress' will freeze!

            bass       NO         >0       retrieves the current amount of bass.  1 is normal; below ~0.7 is quiet; above ~1.3 is loud bass
            mid        NO         >0         -same, but for mids (middle frequencies)
            treb       NO         >0         -same, but for treble (high) frequencies
            bass_att   NO         >0       retrieves an attenuated reading on the bass, meaning that it is damped in time and doesn't change so rapidly.
            mid_att    NO         >0         -same, but for mids (middle frequencies)
            treb_att   NO         >0         -same, but for treble (high) frequencies

            q1         yes        any      }
            q2         yes        any      }
            q3         yes        any      } Used to carry information
            q4         yes        any      }  from the preset per-frame code
            q5         yes        any      }  to the custom wave per-frame code
            q6         yes        any      }  and on to the custom wave per-point code.
            q7         yes        any      }  see q_and_t_vars.gif
            q8         yes        any      }

            t1         yes        any      }
            t2         yes        any      }
            t3         yes        any      } Used to carry information
            t4         yes        any      }  from the custom wave init code,
            t5         yes        any      }  to the custom wave per-frame code,
            t6         yes        any      }  and on to the custom wave per-point code.
            t7         yes        any      }  see q_and_t_vars.gif
            t8         yes        any      }

        e. QUALITY ASSURANCE
        ----------------------
        In order to make sure the presets you create work well on other systems,
        keep the following in mind:

             1. Design your presets using the default mesh size (32x24) option
            from the config panel, or at least check, before you distribute them,
            to make sure they look correct at the default mesh size.  If your
            mesh is too coarse (small), then a viewer with the default mesh size
            might see unexpected "bonus" effects that you might not have intended,
            and might mess up your preset.  If your mesh is too fine, then a
            viewer with the default might not see all the detail you intended,
            and it might look bad.

             2. Keep your presets fast.  There's nothing to spoil the mood like
            a preset popping up that chokes at 10 fps.  Since division is 11
            times slower than multiplication (or addition/subtraction), if you
            divide a bunch of values by one other value, pre-divide that value
            ("inv = 1/myval;") and then multiply those other values by that
            inverse.  Also, never put computations in the per-pixel code that
            are the same for every pixel; move these into the per-frame code,
            and carry the results to the per-pixel code using the q1-q8 variables.
            Remember that maxim: "If a per-pixel equation doesn't use at least
            one of the variables { x, y, rad, ang }, then it should be actually
            be a per-frame equation."

             2. Try to design your presets in a 32-bit video mode, so that its
            brightness levels are standard.  The thing to really watch out
            for is designing your presets in 16-bit color when the "fix pink/
            white color saturation artifact" checkbox is checked.  This
            checkbox keeps the image extra dark to avoid color saturation,
            which is only necessary on some cards, in 16-bit color.  If this
            is the case for you, and you write a preset, then when you run
            it on another machine, it might appear insanely bright.

             3. Don't underestimate the power of the 'dx' and 'dy' parameters.  Some
            of the best presets a based on using these.  If you strip everything
            out of a preset so that there's no motion at all, then you can use the
            dx and dy parameters to have precise manual control over the motion.
            Basically, all the other effects (zoom, warp, rot, etc.) are just
            complicated abstractions; they could all be simulated by using only
            { x, y, rad, ang } and { dx, dy }.

             4. If you use the 'progress' variable in a preset, make sure you
            try the preset out with several values for 'Time Between Auto
            Preset Changes'.  The biggest thing to avoid is using something
            like sin(progress), since the rate at which 'progress' increases
            can vary drastically from system to system, dependong on the user's
            setting for 'Time Between Auto Preset Changes'.

        f. DEBUGGING
        -----------------------
        One feature that preset authors should definitely be aware of is the
        variable monitoring feature, which lets you monitor (watch) the value
        of any per-frame variable you like.  First, hit the 'N' key to show
        the monitor value, which will probably display zero.  Then all you
        have to do is add a line like this to the per-frame equations:

            monitor = x;

        where 'x' is the variable or expression you want to monitor.  Once you
        hit CTRL+ENTER to accept the changes, you should see the value of the
        per-frame variable or expression in the upper-right corner of the
        screen!

        Once again, note that it only works for *per-frame* equations, and NOT
        for per-pixel equations.

        g. FUNCTION REFERENCE
        -----------------------
        Following is a list of the functions supported by the expression evaluator.
        The list was blatently ripped from the help box of Justin Frankels' AVS
        plug-in, since MilkDrop uses the expression evaluator that he wrote.

            Format your expressions using a semicolon (;) to delimit between statements.
            Use parenthesis ['(' and ')'] to denote precedence if you are unsure.
            The following operators are available:
                = : assign
                +,-,/,* : plus, minus, divide, multiply
                | : convert to integer, and do bitwise or
                & : convert to integer, and do bitwise and
                % : convert to integer, and get remainder
            The following functions are available:
                int(var)   :  returns the integer value of 'var' (rounds toward zero)
                abs(var)   :  returns the absolute value of var
                sin(var)   :  returns the sine of the angle var (expressed in radians)
                cos(var)   :  returns the cosine of the angle var
                tan(var)   :  returns the tangent of the angle var
                asin(var)  :  returns the arcsine of var
                acos(var)  :  returns the arccosine of var
                atan(var)  :  returns the arctangent of var
                sqr(var)   :  returns the square of var
                sqrt(var)  :  returns the square root of var
                pow(var,var2) : returns var to the power of var2
                log(var)      : returns the log base e of var
                log10(var)    : returns the log base 10 of var
                sign(var)     : returns the sign of var or 0
                min(var,var2) : returns the smalest value
                max(var,var2) : returns the greatest value
                sigmoid(var,var2) : returns sigmoid function value of x=var (var2=constraint)
                rand(var)     : returns a random integer modulo 'var'; e.g. rand(4) will return 0, 1, 2, or 3.
                bor(var,var2) : boolean or, returns 1 if var or var2 is != 0
                bnot(var)  : boolean not, returns 1 if var == 0 or 0 if var != 0
                if(cond,vartrue,varfalse) : if condition is nonzero, returns valtrue, otherwise returns valfalse
                equal(var,var2) : returns 1 if var = var2, else 0
                above(var,var2) : returns 1 if var > var2, else 0
                below(var,var2) : returns 1 if var < var2, else 0

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