Gouraud



                              Gouraud shading

Warning: some knowledge about vectors required

Types of shading

Shading is the change in saturation on a surface because of reflection.
Shading depends on the properties of the surface and the angle between
surface, light source and your eyes There are three types of shading which
are commonly used in computer graphic programs.

Flat shading

This type of shading is very simple and fast. The object you are to shade
is divided in a lot of flat surfaces. You take the normal on a surface (a
normal is a vector perpendicular on the surface) and you compute the angle
between the light source vector (the direction in which the light shines)
and the normal. This angle is then translated to a shade. So every surface
has one shade. For example when you have 16 shades, 0 being the dullest and
16 the brightest, you divide them between 0 and x degrees. x is an angle
between 0 and 90 degrees. Why 90? Because light can't go around a corner. A
smaller x means a smaller spot of light (hotspot).

Phong shading

Phong shading produces the best results but is real slow. What you do is,
you calculate the normal on every point of the surface. Now you will
ask:"How am I supposed to calculate the normal of a point?". Well, that's
impossible. But you can make a plane consisting of adjacent points and take
the normal of that plane. Next you shade all points the same way as with
flat shading. Of course there are a lot of methods to make it faster, but I
haven't looked at them yet.

Gouraud shading

After flat and before phong comes gouraud shading. With gouraud shading you
divide the object into flat triangles. Each triangle has of course three
vertices. From each vertex you take the normal. Same problem: how do you
calculate the normal of a point. Not. In this case you take the average
direction of the triangle normals of the triangles of which the vertex is a
part. After you did that, you shade the vertices and you interpolate the
shading over the triangle. The easiest and fastest way of doing this is:

   * Trace the edges. You know where the edges begin and end. You also know
     the light intensity of those points, so it's easy to calculate dY/dX
     and dI/dX of the edges and calculate the edge and the colors along the
     edge.
   * Trace the scanlines. By tracing the edges, you have acquired all
     starting points, ending points, starting intensities and ending
     intensities of the triangles scanlines. So all you have to do is fill
     up the lines between the edges.

Tracing the scanlines can be a problem. When you use a floating-point
divide per scanline, it'll run like a snail. To overcome this, you can use
Bresenham, DDA or setup a DIV-table.

   * Bresenham uses no DIVs at all, but the time it takes to draw one pixel
     is longer than the other methods. See some code.
   * Digital Differential Analyser. DDA uses IDIVs, but as you might know
     IDIVs are much faster than DIVs or FDIVs. This technique is called
     fixed point. It means that you give a pre-determined amount of bits to
     the integer and the fraction of the number.
     Example:
          Take 10 bits and divide them between integer and fraction:
          111111.1111 e.g. 0000010100 makes 1.25.

     Converting from floating point to fixed is just a matter of
     multiplying with 2number of fraction bits and casting it into an
     integer. But beware of the fact that you have less bits for the
     integer part.
     From fixed point to normal integer is done by adding 2(number of
     fraction bits)-1 and shifting the bits fraction places to the right.
     Code is available.
   * Division table. This is essentially the same as DDA, but now you don't
     do the division. Instead you look it up in an array. Only to be used
     on a processor that doesn't divide faster than it does a memory
     lookup.

Soon: MMX Code!
Download render.zip. This is a gouraud shaded and texture mapped vector
engine. It was made by Peter Zijlstra (peter@mcs.nl) and me. x86, FPU and
VESA 1.2 required.
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This page was made by Marijn Meijles
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Date this article was posted to GameDev.net: 7/16/1999
(Note that this date does not necessarily correspond to the date the article was written)
See Also:
Lighting and Shading