FreeType Glyph Conventions

1. FreeType outline description and structure

a. Outline curve decomposition

An outline is described as a series of closed contours in the 2D plane. Each contour is made of a series of line segments and Bézier arcs. Depending on the file format, these can be second-order or third-order polynomials. The former are also called quadratic or conic arcs, and they are used in the TrueType format. The latter are called cubic arcs and are mostly used in the Type 1 format.

Each arc is described through a series of start, end, and control points. Each point of the outline has a specific tag which indicates whether it is used to describe a line segment or an arc. The tags can take the following values:

The following rules are applied to decompose the contour's points into segments and arcs:

• Two successive "on" points indicate a line segment joining them.
• One conic "off" point amidst two "on" points indicates a conic Bézier arc, the "off" point being the control point, and the "on" ones the start and end points.
• Two successive cubic "off" points amidst two "on" points indicate a cubic Bézier arc. There must be exactly two cubic control points and two "on" points for each cubic arc (using a single cubic "off" point between two "on" points is forbidden, for example).
• Finally, two successive conic "off" points forces the rasterizer to create (during the scan-line conversion process exclusively) a virtual "on" point amidst them, at their exact middle. This greatly facilitates the definition of successive conic Bézier arcs. Moreover, it is the way outlines are described in the TrueType specification.

Note that it is possible to mix conic and cubic arcs in a single contour, even though no current font driver produces such outlines.

b. Outline descriptor

A FreeType outline is described through a simple structure, called FT_Outline, which fields are:

Here, points is a pointer to an array of FT_Vector records, used to store the vectorial coordinates of each outline point. These are expressed in 1/64th of a pixel, which is also known as the 26.6 fixed float format.

contours is an array of point indices used to delimit contours in the outline. For example, the first contour always starts at point 0, and ends at point contours[0]. The second contour starts at point contours[0]+1 and ends at contours[1], etc.

Note that each contour is closed, and that n_points should be equal to contours[n_contours-1]+1 for a valid outline.

Finally, tags is an array of bytes, used to store each outline point's tag.

3. Coordinates, scaling and grid-fitting

An outline point's vectorial coordinates are expressed in the 26.6 format, i.e. in 1/64th of a pixel, hence coordinates (1.0,-2.5) is stored as the integer pair (x:64,y:-192).

After a master glyph outline is scaled from the EM grid to the current character dimensions, the hinter or grid-fitter is in charge of aligning important outline points (mainly edge delimiters) to the pixel grid. Even though this process is much too complex to be described in a few lines, its purpose is mainly to round point positions, while trying to preserve important properties like widths, stems, etc.

The following operations can be used to round vectorial distances in the 26.6 format to the grid:

    round( x )   == ( x + 32 ) & -64
    floor( x )   ==          x & -64
    ceiling( x ) == ( x + 63 ) & -64

Once a glyph outline is grid-fitted or transformed, it often is interesting to compute the glyph image's pixel dimensions before rendering it. To do so, one has to consider the following:

The scan-line converter draws all the pixels whose centers fall inside the glyph shape. It can also detect drop-outs, i.e. discontinuities coming from extremely thin shape fragments, in order to draw the "missing" pixels. These new pixels are always located at a distance less than half of a pixel but it is not easy to predict where they will appear before rendering.

This leads to the following computations:

• compute the bbox

• grid-fit the bounding box with the following:

      xmin = floor( bbox.xMin )
      xmax = ceiling( bbox.xMax )
      ymin = floor( bbox.yMin )
      ymax = ceiling( bbox.yMax )

• return pixel dimensions, i.e.

      width = (xmax - xmin)/64

  and

      height = (ymax - ymin)/64

By grid-fitting the bounding box, it is guaranteed that all the pixel centers that are to be drawn, including those coming from drop-out control, will be within the adjusted box. Then the box's dimensions in pixels can be computed.

Note also that, when translating a grid-fitted outline, one should always use integer distances to move an outline in the 2D plane. Otherwise, glyph edges won't be aligned on the pixel grid anymore, and the hinter's work will be lost, producing very low quality bitmaps and pixmaps.