Safe Haskell	None

Geom2D.CubicBezier.MetaPath

Description

This module implements an extension to paths as used in D.E.Knuth's Metafont. Metafont gives a more intuitive method to specify paths than bezier curves. I'll give a brief overview of the metafont curves. For a more in depth explanation look at The MetafontBook.

Each spline has a tension parameter, which is a relative measure of the length of the curve. You can specify the tension for the left side and the right side of the spline separately. By default metafont gives a tension of 1, which gives a good looking curve. Tensions shouldn't be less than 3/4, but this implementation doesn't check for it. If you want to avoid points of inflection on the spline, you can use TensionAtLeast instead of Tension, which will adjust the length of the control points so they fall into the bounding triangle, if such a triangle exist.

You can either give directions for each node, or let metafont find them. Metafont will solve a set of equations to find the directions. You can also let metafont find directions at corner points by setting the curl, which is how much the point curls at that point. At endpoints a curl of 1 is implied when it is not given.

Metafont will then find the control points from the path for you. You can also specify the control points explicitly.

Here is an example path from the metafont program text:

 z0..z1..tension atleast 1..{curl 2}z2..z3{-1,-2}..tension 3 and 4..z4..controls z45 and z54..z5

This path is equivalent to:

 z0{curl 1}..tension atleast 1 and atleast 1..{curl 2}z2{curl 2}..tension 1 and 1..
 {-1,-2}z3{-1,-2}..tension 3 and 4..z4..controls z45 and z54..z5

This path can be used with the following datatype:

 OpenMetaPath [ (z0, MetaJoin Open (Tension 1) (Tension 1) Open)
              , (z1, MetaJoin Open (TensionAtLeast 1) (TensionAtLeast 1) (Curl 2))
              , (z2, MetaJoin Open (Tension 1) (Tension 1) Open)
              , (z3, MetaJoin (Direction (Point (-1) (-2))) (Tension 3) (Tension 4) Open)
              , (z4, Controls z45 z54)
              ] z5

Cyclic paths are similar, but use the CyclicMetaPath contructor. There is no ending point, since the ending point will be the same as the first point.

Synopsis

Documentation

unmeta :: MetaPath -> Path Source

Create a normal path from a metapath.

data MetaPath Source

Constructors

OpenMetaPath [(Point, MetaJoin)] Point
CyclicMetaPath [(Point, MetaJoin)]

Instances

Show MetaPath

data MetaJoin Source

Constructors

MetaJoin
Fields metaTypeL :: MetaNodeType tensionL :: Tension tensionR :: Tension metaTypeR :: MetaNodeType
Controls Point Point

Instances

Show MetaJoin

data MetaNodeType Source

Constructors

Open
Curl
Fields curlgamma :: Double
Direction
Fields nodedir :: Point

Instances

Show MetaNodeType

data Tension Source

Constructors

Tension
Fields tensionValue :: Double
TensionAtLeast
Fields tensionValue :: Double

Instances

Eq Tension
Show Tension