Topic : Sub-pixel accuracy
Author : Paul Nettle
Page : 1

Sub-Pixel Accuracy
by Paul Nettle

Sub-pixel accuracy is used to clean up rendering quality, and solve other accuracy problems (such as gaps between adjacent polygons).

Sub-pixel accuracy is roughly defined as: "Only pixels whose center-points lie inside a given polygon are lit." To achieve sub-pixel accuracy, it is not necessary to adhere to this definition exactly. For real-time applications, any point inside the pixel (i.e. the lower right corner) may be used rather than the center. The only side-effect of this is that the entire screen is shifted down/right by exactly 0.5 pixels. Our example uses this corner. If this isn't clear, it will be soon.

To better understand this, consider a piece of graph paper made up of large blocks. Inside each block is a small point at the very center. Upon this page, is the outline of a triangle that almost fills the page. Also, consider that the lines making up the outline of the triangle as well as the points the designate the center of each grid point are infinitely thin. This is important since we're referring to a mathematical model of a triangle, not a physical triangle rendered in pixels or with a pen which has a width.

From this simple diagram, sub-pixel accuracy is easy to understand. Each block of the grid is a pixel. And only those pixels whose center-points lie inside the triangle will be lit with the color of the triangle.

This isn't nearly as hard to implement as this description may make it sound. The implementation of this is actually very simple, and a minimal speed hit.

Sub-pixel accuracy is only necessary due to the nature of our digital (i.e. pixel) displays. As the pixels become smaller and smaller, sub-pixel accuracy becomes less important. When the pixels become infinitely small (i.e. "real life" then sub-pixel accuracy is no longer necessary). However, even with high-resolution displays (1280x1024) the differences of sub-pixel accuracy can be perceived.

One major problem with drawing polygons onto a digital display (i.e. pixels) is that we're forced to make a decision whether or not to turn a pixel on or off. Without sub-pixel accuracy, we'll simply light any pixel that touches the polygon. This isn't good enough.

Consider a polygon with a nearly horizontal top edge. The top two vertices are very close to the 100th scan-line. One is slightly above the scan-line (i.e. y = 99.9) and the second vertex is slightly below the scan-line (i.e. y = 100.1). Without sub-pixel accuracy, the top edge might be a horizontal line, with an extra lit pixel above the vertex at one end. This SHOULD be drawn as a horizontal line with a break at the mid-point, where the edge continues on, yet one scan-line lower.

Sub-pixel accuracy also gives our polygons a smooth feel as they animate very slowly on- screen.

Now that I've filled you with all that technical information, let me simplify the process by simply saying that all this can be achieved by simply "sliding" our polygons into place to align on pixel boundaries before we draw. That's all there is to it.

The simplest polygon routine (a triangle scan-converter) usually starts by finding the top-most point, and scan-converting downward until it hits the next vertex. From there, one edge changes direction, and the scan-conversion process continues until the bottom of the polygon is reached.

In this model, at the top of each edge a starting X is calculated as well as a delta X. The starting X is interpolated along the edge of the polygon using the delta X. Using this model, consider the following code fragment:

start_x += delta_x * (1.0 - (ceil(start_y) - start_y));

What this does is to simply "slide" the starting X coordinate along its edge by the distance that the starting Y is from the bottom of its scan-line.

This process must be done for each value that gets interpolated along the edges (i.e. any U/V for texturing or Gouraud color values, etc.)

If used, the ceil() function can cause a dramatic slowdown on many systems. I use an the Intel processor for the majority of my work. This is an inline routine I use to replace portions of the line above for more speed:

inline  float   SUB_PIX(const float input)
  float   retCode;

  __asm   fld     input
  __asm   fld     input
  __asm   fsub    dword ptr half
  __asm   frndint
  __asm   fsubp   st(1), st
  __asm   fld1
  __asm   fsubrp  st(1), st
  __asm   fstp    retCode

  return retCode;

In the above code sample, `half' is a 32-bit floating point memory variable containing the value 0.5f.

This reduces our sub-pixel correction to:

start_x += delta_x * SUB_PIX(start_y);

This is sub-pixel accuracy. To test your modifications, try rotating a 3D cube VERY slowly (i.e. 1/256th degree increments).

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