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Water

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Introduction

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.
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Basics

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.

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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][x]
from this. This is your basic smooth function. Now you need to add the
'harmonic motion' to it. Take the new-water[y][x], shift it right x places
(x could be 4) and subtract it from the new-water[y][x]. Pseudo-code for
this might look like:

for y := 1 to height - 1
        for x := 1 to width - 1
                new-water[y][x] = ((old-water[y-1][x] +
                                    old-water[y+1][x] +
                                    old-water[y][x-1] +
                                    old-water[y][x+1]) / 2) -
                                    new-water[y][x])
                new-water[y][x] -= new-water[y][x] 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][x]) 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.

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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][x] - water[y+1][x]
offsety = water[y][x] - 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][x] - water[y+1][x]
                offsety = water[y][x] - 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.

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The Water Loop

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

  1. Draw to the water
  2. Paint it
  3. Calculate new water
  4. 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.

Tom Hammersley,tomh@globalnet.co.uk

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