The semantics of Vg

The following notations and definitions give precise meaning to images and their combinators.


The semantics of colors is the one ascribed to Gg.color: colors are in a linearized sRGBA space.

Color stops

A value of type Gg.Color.stops specifies a color at each point of the 1D unit space. It is defined by a list of pairs (ti, ci) where ti is a value from 0 to 1 and ci the corresponding color at that value. Colors at points between ti and ti+1 are linearly interpolated between ci and ci+1. If ti lies outside 0 to 1 or if ti-1 >= ti the semantics is undefined.

Given a stops value stops = [(t0, c0); (t1,c1); ... (tn, cn)] and any point t of 1D space, the semantic function:

[] : Gg.Color.stops -> float -> Gg.color

maps them to a color value written [stops]t as follows.


Values of type Vg.image represent maps from the infinite 2D euclidian space to colors. Given an image i and a point pt of the plane the semantic function

[]: image -> Gg.p2 -> Gg.color

maps them to a color value written [i]pt representing the image's color at this point.

Paths and areas

A value of type Vg.path is a list of subpaths. A subpath is a list of directed and connected curved segments. Subpaths are disconnected from each other and may (self-)intersect.

A path and an area specification of type Vg.P.area define a finite area of the 2D euclidian space. Given an area specification a, a path p and a point pt, the semantic function:

[]: P.area -> path -> Gg.p2 -> bool

maps them to a boolean value written [a, p]pt that indicates whether pt belongs to the area or not.

The semantics of area rules is as follows:

Outline areas

The outline area of a path specified by a value o of type Vg.P.outline is the union of its subpaths outline areas.

A subpath outline area is inside the parallel curves at a distance o.width / 2 of its path segments that are joined accoring to the join style o.join (see below) and closed at the subpath end points with a cap style o.cap (see below). The outline area of a subpath can also be chopped at regular intervals according to the o.dashes parameter (see below).

Segment jointures

The shape of subpath segment jointures is specified in o.join by a value of type Vg.P.join. From left to right:

Subpath caps

The shape of subpath (or dashes) end points is specified in o.cap by a value of type Vg.P.cap. From left to right:

Outline dashes

The path outline area can be chopped at regular intervals by specifying a value (off, pat) of type Vg.P.dashes in o.dashes.

The dash pattern pat is a list of lengths that specify the length of alternating dashes and gaps (starting with dashes). The dash offset off is a positive offset that indicates where to start in the dash pattern at the beginning of a subpath.