Water

[spritus]

Water is a really nice effect, one of the better tricks around. Its also
pretty simple to code, should take no more than an afternoons work to get a
good water routine.

First thing you'll need is 2 buffers, for the water. This needs to be an
array of ints, same size as destination buffer. Arrange these in a 2-element
array, to ease the flipping. Clear these to zero, and you're ready to start.

Calculate The New Water
Calculating the new water is pretty simple. You'll need a loop that
execute from 1 to height-1, then 1 to width - 1. At each element for the
water, you'll need to sum the North, South, East, West points from the
current water, and divide by 2 Not 4, 2. Then subtract the new water
for [y]

• from this. This is your basic smooth function. Now you need to

add the 'harmonic motion' to it. Take the new-water[y]

• , shift it right

x places (x could be 4) and subtract it from the new-water[y]

• .

Pseudo-code for this might look like:

for y := 1 to height - 1
    for x := 1 to width - 1
        new-water[y]

• = ((old-water[y-1]
• +

                  old-water[y+1]

• +

                  old-water[y][x-1] +
                  old-water[y][x+1]) / 2) -
                  new-water[y]

• )

        new-water[y]

• -= new-water[y]
• shr x

    end
end

Not too hard to make into working code. Because there are 2 pages, and we are
flipping between them, the references to what seem like uncalculated water
( - new-water[y]

• ) are ok, because they come around and feed back. This is

all it takes to calculate the water! You may also want a part where you set
the 1 pixel wide frame around the water to 0, just to be safe.

Paint The Water
Water is also pretty straightforward to paint. In fact some of the
techniques here, you will see later on in the bump-mapping. Back to the task
in hand. We will again need a loop for every pixel on the screen. What we
need to do is calculate a kind-of normal at each pixel. This is simply:

offsetx = water[y]

• - water[y+1]

offsety = water[y]

• - water[y][x+1]

Which measures changes in X and Y. 'Colour' is then calculated by
128 - offsetx. Clip colour to the 0..255 range. Divide both offsetx and
offsety by 8, and add them to x and y. Now for the tricky bit. You'll need a
background image (or perhaps you can do without ...). You need to light
the background image by the water. This is done by:

offsetx /= 3;
offsety /= 8;
indexu = offsetx + x;
indexv = offsety + y;
MulTable[backdrop[indexv*256+indexu]*256+colour];

MulTable is another handy lookup table. It simply takes the value of
(row*col) >> 8.

Pseudo code for this would be :

For y := 1 to height - 1
    For x := 1 to width - 1
        offsetx = water[y]

• - water[y+1]

        offsety = water[y]

• - water[y][x+1]

        colour = 128 - offsetx
        trim colour to 0..255
        divide offsetx and offsety by 8
        add offsetx to x giving indexu
        add offsety to y giving indexv
        Plot (backdrop*colour) >> 8, lookup in table
    End
End


What we are effectively doing here is applying fake lighting to the water,
then mixing the colours. There are plenty of variations on calculating the
normals. Plenty of room for exploration there.

The Water Loop
Note it makes a difference what order you do calculations in. Its pretty
simple though. You need to:

Draw to the water
Paint it
Calculate new water
Page flip the water

If you stick to that, you can't go wrong. If you really want to be smart,
you'll use the texturemap lighting info on this page to do make logos and so
on ripple. I've even seen it combined with bump-mapping. Water is a very
rewarding effect, well worth coding.