Polygons and shapes

ngon(x, y, radius, sides=5, orientation=0, action=:nothing;
    vertices=false, reversepath=false)

Find the vertices of a regular n-sided polygon centred at x, y:

ngon() draws the shapes: if you just want the raw points, use keyword argument vertices=true, which returns the array of points instead. Compare:

ngon(0, 0, 4, 4, 0, vertices=true) # returns the polygon's points:

    4-element Array{Luxor.Point,1}:
    Luxor.Point(2.4492935982947064e-16,4.0)
    Luxor.Point(-4.0,4.898587196589413e-16)
    Luxor.Point(-7.347880794884119e-16,-4.0)
    Luxor.Point(4.0,-9.797174393178826e-16)

whereas

ngon(0, 0, 4, 4, 0, :close) # draws a polygon

ngon(centerpos, radius, sides=5, orientation=0, action=:nothing;
    vertices=false,
    reversepath=false)

Draw a regular polygon centred at point p:

star(xcenter, ycenter, radius, npoints=5, ratio=0.5, orientation=0, action=:nothing;
    vertices = false,
    reversepath=false)

Make a star. ratio specifies the height of the smaller radius of the star relative to the larger.

Use vertices=true to return the vertices of a star instead of drawing it.

star(center, radius, npoints=5, ratio=0.5, orientation=0, action=:nothing;
    vertices = false, reversepath=false)

Draw a star centered at a position:

Draw a polygon.

poly(pointlist::Array, action = :nothing;
    close=false,
    reversepath=false)

A polygon is an Array of Points. By default poly() doesn't close or fill the polygon, to allow for clipping.

prettypoly(points, action=:nothing, vertexfunction=() -> circle(O, 1, :fill);
    close=false,
    reversepath=false,
    vertexlabels = (n, l) -> ()
    )

Draw the polygon defined by points, possibly closing and reversing it, using the current parameters, and then evaluate the vertexfunction function at every vertex of the polygon. For example, you can mark each vertex of a polygon with a randomly colored filled circle.

p = star(O, 70, 7, 0.6, 0, vertices=true)
prettypoly(p, :fill, () ->
    begin
        randomhue()
        circle(O, 10, :fill)
    end,
    close=true)

The optional keyword argument vertexlabels lets you supply a function with two arguments that can access the current vertex number and the total number of vertices at each vertex. For example, you can label the vertices of a triangle "1 of 3", "2 of 3", and "3 of 3" using:

prettypoly(triangle, :stroke,
    vertexlabels = (n, l) -> (text(string(n, " of ", l))))

Simplify a polygon:

simplify(pointlist::Array, detail=0.1)

detail is the smallest permitted distance between two points in pixels.

isinside(p, pol)

Is a point p inside a polygon pol? Returns true or false.

This is an implementation of the Hormann-Agathos (2001) Point in Polygon algorithm

randompoint(lowpt, highpt)

Return a random point somewhere inside the rectangle defined by the two points.

randompoint(lowx, lowy, highx, highy)

Return a random point somewhere inside a rectangle defined by the four values.

randompointarray(lowpt, highpt, n)

Return an array of n random points somewhere inside the rectangle defined by two points.

randompointarray(lowx, lowy, highx, highy, n)

Return an array of n random points somewhere inside the rectangle defined by the four coordinates.

polysplit(p, p1, p2)

Split a polygon into two where it intersects with a line. It returns two polygons:

(poly1, poly2)

This doesn't always work, of course. For example, a polygon the shape of the letter "E" might end up being divided into more than two parts.

Sort a polygon by finding the nearest point to the starting point, then the nearest point to that, and so on.

polysortbydistance(p, starting::Point)

You can end up with convex (self-intersecting) polygons, unfortunately.

Sort the points of a polygon into order. Points are sorted according to the angle they make with a specified point.

polysortbyangle(pointlist::Array, refpoint=minimum(pointlist))

The refpoint can be chosen, but the minimum point is usually OK too:

polysortbyangle(parray, polycentroid(parray))

Find the centroid of simple polygon.

polycentroid(pointlist)

Returns a point. This only works for simple (non-intersecting) polygons.

You could test the point using isinside().

polysmooth(points, radius, action=:action; debug=false)

Make a closed path from the points and round the corners by making them arcs with the given radius. Execute the action when finished.

The arcs are sometimes different sizes: if the given radius is bigger than the length of the shortest side, the arc can't be drawn at its full radius and is therefore drawn as large as possible (as large as the shortest side allows).

The debug option also draws the construction circles at each corner.

offsetpoly(path::Array, d)

Return a polygon that is offset from a polygon by d units.

The incoming set of points path is treated as a polygon, and another set of points is created, which form a polygon lying d units away from the source poly.

Polygon offsetting is a topic on which people have written PhD theses and published academic papers, so this short brain-dead routine will give good results for simple polygons up to a point (!). There are a number of issues to be aware of:

• very short lines tend to make the algorithm 'flip' and produce larger lines

• small polygons that are counterclockwise and larger offsets may make the new polygon appear the wrong side of the original

• very sharp vertices will produce even sharper offsets, as the calculated intersection point veers off to infinity

polyfit(plist::Array, npoints=30)

Build a polygon that constructs a B-spine approximation to it. The resulting list of points makes a smooth path that runs between the first and last points.