# Simple graphics

In Luxor, there are different ways of working with graphical items. Some, such as lines, rectangles and circles, are drawn immediately (ie placed on the drawing and then "forgotten"). Others can be constructed and then converted to lists of points for further processing. For these, watch out for a `vertices=true`

option.

## Rectangles and boxes

The simple rectangle and box shapes can be made in different ways.

```
axes()
sethue("red")
rect(O, 100, 100, :stroke)
sethue("blue")
box(O, 100, 100, :stroke)
```

Whereas `rect()`

rectangles are positioned at one corner, a box made with `box()`

can either be defined by its center and dimensions, or by two opposite corners.

If you want the coordinates of the corners of a box, use this form of `box()`

:

`box(centerpoint, width, height, vertices=true)`

`Luxor.rect`

— Function.`rect(xmin, ymin, w, h, action)`

Create a rectangle with one corner at (`xmin`

/`ymin`

) with width `w`

and height `h`

and then do an action.

See `box()`

for more ways to do similar things, such as supplying two opposite corners, placing by centerpoint and dimensions.

`rect(cornerpoint, w, h, action)`

Create a rectangle with one corner at `cornerpoint`

with width `w`

and height `h`

and do an action.

`Luxor.box`

— Function.`box(cornerpoint1, cornerpoint2, action=:nothing)`

Create a rectangle between two points and do an action.

`box(points::AbstractArray, action=:nothing)`

Create a box/rectangle using the first two points of an array of Points to defined opposite corners.

`box(pt::Point, width, height, action=:nothing; vertices=false)`

Create a box/rectangle centered at point `pt`

with width and height. Use `vertices=true`

to return an array of the four corner points rather than draw the box.

`box(x, y, width, height, action=:nothing)`

Create a box/rectangle centered at point `x/y`

with width and height.

`box(x, y, width, height, cornerradius, action=:nothing)`

Create a box/rectangle centered at point `x/y`

with `width`

and `height`

. Round each corner by `cornerradius`

.

`Luxor.polybbox`

— Function.Find the bounding box of a polygon (array of points).

`polybbox(pointlist::AbstractArray)`

Return the two opposite corners (suitable for `box()`

, for example).

For regular polygons, see the next section on Polygons.

## Circles and ellipses

There are various ways to make circles, including by center and radius, or passing through two points:

```
p1 = O
p2 = Point(100, 0)
sethue("red")
circle(p1, 40, :fill)
sethue("green")
circle(p1, p2, :stroke)
sethue("black")
arrow(O, Point(0, -40))
map(p -> circle(p, 4, :fill), [p1, p2])
```

Or passing through three points. The `center3pts()`

function returns the center position and radius of a circle passing through three points:

```
sethue("black")
p1 = Point(0, -50)
p2 = Point(100, 0)
p3 = Point(0, 65)
map(p -> circle(p, 4, :fill), [p1, p2, p3])
circle(center3pts(p1, p2, p3)..., :stroke)
```

With `ellipse()`

you can place ellipses (and circles) by defining the center point and the width and height.

```
tiles = Tiler(500, 300, 5, 5)
width = 20
height = 25
for (pos, n) in tiles
randomhue()
ellipse(pos, width, height, :fill)
sethue("black")
label = string(round(width/height, 2))
textcentered(label, pos.x, pos.y + 25)
width += 2
end
```

It's also possible to construct polygons that are approximations to ellipses with two focal points and a distance.

```
f1 = Point(-100, 0)
f2 = Point(100, 0)
ellipsepoly = ellipse(f1, f2, 170, :none, vertices=true)
[ begin
setgray(rescale(c, 150, 1, 0, 1))
poly(offsetpoly(ellipsepoly, c), close=true, :fill);
rotate(pi/20)
end
for c in 150:-10:1 ]
```

`Luxor.circle`

— Function.`circle(x, y, r, action=:nothing)`

Make a circle of radius `r`

centered at `x`

/`y`

.

`action`

is one of the actions applied by `do_action`

, defaulting to `:nothing`

. You can also use `ellipse()`

to draw circles and place them by their centerpoint.

`circle(pt, r, action)`

Make a circle centered at `pt`

.

`circle(pt1::Point, pt2::Point, action=:nothing)`

Make a circle that passes through two points that define the diameter:

`Luxor.ellipse`

— Function.`ellipse(xc, yc, w, h, action=:none)`

Make an ellipse, centered at `xc/yc`

, fitting in a box of width `w`

and height `h`

.

`ellipse(cpt, w, h, action=:none)`

Make an ellipse, centered at point `c`

, with width `w`

, and height `h`

.

```
ellipse(focus1::Point, focus2::Point, k, action=:none;
stepvalue=pi/100,
vertices=false,
reversepath=false)
```

Build a polygon approximation to an ellipse, given two points and a distance, `k`

, which is the sum of the distances to the focii of any points on the ellipse (or the shortest length of string required to go from one focus to the perimeter and on to the other focus).

`circlepath()`

constructs a circular path from Bézier curves, which allows you to use circles as paths.

```
setline(4)
tiles = Tiler(600, 250, 1, 5)
for (pos, n) in tiles
randomhue()
circlepath(pos, tiles.tilewidth/2, :path)
newsubpath()
circlepath(pos, rand(5:tiles.tilewidth/2 - 1), :fill, reversepath=true)
end
```

`Luxor.circlepath`

— Function.```
circlepath(center::Point, radius, action=:none;
reversepath=false,
kappa = 0.5522847)
```

Draw a circle using Bézier curves.

## More curved shapes: sectors, spirals, and squircles

A sector (technically an "annular sector") has an inner and outer radius, as well as start and end angles.

```
sethue("tomato")
sector(50, 90, pi/2, 0, :fill)
sethue("olive")
sector(Point(O.x + 200, O.y), 50, 90, 0, pi/2, :fill)
```

You can also supply a value for a corner radius. The same sector is drawn but with rounded corners.

```
sethue("tomato")
sector(50, 90, pi/2, 0, 15, :fill)
sethue("olive")
sector(Point(O.x + 200, O.y), 50, 90, 0, pi/2, 15, :fill)
```

`Luxor.sector`

— Function.`sector(centerpoint::Point, innerradius, outerradius, startangle, endangle, action:none)`

Draw an annular sector centered at `centerpoint`

.

```
sector(innerradius::Real, outerradius::Real, startangle::Real, endangle::Real,
action::Symbol=:none)
```

Draw an annular sector centered at the origin.

```
sector(centerpoint::Point, innerradius, outerradius, startangle, endangle,
cornerradius, action:none)
```

Draw an annular sector with rounded corners, basically a bent sausage shape, centered at `centerpoint`

.

TODO: The results aren't 100% accurate at the moment. There are small discontinuities where the curves join.

The cornerradius is reduced from the supplied value if neceesary to prevent overshoots.

```
sector(innerradius::Real, outerradius::Real, startangle::Real, endangle::Real,
cornerradius::Real, action::Symbol=:none)
```

Draw an annular sector with rounded corners, centered at the current origin.

A pie (or wedge) has start and end angles.

`pie(0, 0, 100, pi/2, pi, :fill)`

`Luxor.pie`

— Function.`pie(x, y, radius, startangle, endangle, action=:none)`

Draw a pie shape centered at `x`

/`y`

. Angles start at the positive x-axis and are measured clockwise.

`pie(centerpoint, radius, startangle, endangle, action=:none)`

Draw a pie shape centered at `centerpoint`

.

Angles start at the positive x-axis and are measured clockwise.

`pie(radius, startangle, endangle, action=:none)`

Draw a pie shape centered at the origin

To construct spirals, use the `spiral()`

function. These can be drawn directly, or used as polygons. The default is to draw Archimedes (non-logarithmic) spirals.

```
sp = spiral(4, 1, stepby=pi/24, period=12pi, vertices=true)
for i in 1:10
setgray(i/10)
setline(22-2i)
poly(sp, :stroke)
end
```

Use the `log=true`

option to draw logarithmic spirals.

```
sp = spiral(2, .12, log=true, stepby=pi/24, period=12pi, vertices=true)
for i in 1:10
setgray(i/10)
setline(22-2i)
poly(sp, :stroke)
end
```

`Luxor.spiral`

— Function.```
spiral(a, b, action::Symbol=:none;
stepby = 0.01,
period = 4pi,
vertices = false,
log=false)
```

Make a spiral. The two primary parameters `a`

and `b`

determine the start radius, and the tightness.

For linear spirals (`log=false`

), `b`

values are:

```
lituus: -2
hyperbolic spiral: -1
Archimedes' spiral: 1
Fermat's spiral: 2
```

For logarithmic spirals (`log=true`

):

`golden spiral: b = ln(phi)/ (pi/2) (about 0.30)`

Values of `b`

around 0.1 produce tighter, staircase-like spirals.

A *squircle* is a cross between a square and a circle. You can adjust the squariness and circularity of it to taste by supplying a value for keyword `rt`

:

```
setline(2)
tiles = Tiler(600, 250, 1, 3)
for (pos, n) in tiles
sethue("lavender")
squircle(pos, 80, 80, rt=[0.3, 0.5, 0.7][n], :fillpreserve)
sethue("grey20")
strokepath()
textcentered("rt = $([0.3, 0.5, 0.7][n])", pos)
end
```

`Luxor.squircle`

— Function.```
squircle(center::Point, hradius, vradius, action=:none;
rt = 0.5, stepby = pi/40, vertices=false)
```

Make a squircle (basically a rectangle with rounded corners). Specify the center position, horizontal radius (distance from center to a side), and vertical radius (distance from center to top or bottom):

The `rt`

option defaults to 0.5, and gives an intermediate shape. Values less than 0.5 make the shape more square. Values above make the shape more round.

To draw a simple rounded rectangle, supply a corner radius:

```
setline(4)
box(O, 200, 150, 10, :stroke)
```

Or you could smooth the corners of a box, like so:

```
setline(4)
polysmooth(box(O, 200, 150, vertices=true), 10, :stroke)
```

## Paths and positions

A path is a sequence of lines and curves. You can add lines and curves to the current path, then use `closepath()`

to join the last point to the first.

A path can have subpaths, created with`newsubpath()`

, which can form holes.

There is a 'current position' which you can set with `move()`

, and can use implicitly in functions like `line()`

, `text()`

, `arc()`

and `curve()`

.

`Luxor.move`

— Function.```
move(x, y)
move(pt)
```

Move to a point.

`Luxor.rmove`

— Function.`rmove(x, y)`

Move by an amount from the current point. Move relative to current position by `x`

and `y`

:

Move relative to current position by the `pt`

's x and y:

`rmove(pt)`

`Luxor.newpath`

— Function.`newpath()`

Create a new path. This is Cairo's `new_path()`

function.

`Luxor.newsubpath`

— Function.`newsubpath()`

Add a new subpath to the current path. This is Cairo's `new_sub_path()`

function. It can be used for example to make holes in shapes.

`Luxor.closepath`

— Function.`closepath()`

Close the current path. This is Cairo's `close_path()`

function.

## Lines

Use `line()`

and `rline()`

to draw straight lines.

`Luxor.line`

— Function.```
line(x, y)
line(x, y, :action)
line(pt)
```

Create a line from the current position to the `x/y`

position and optionally apply an action:

`line(pt1::Point, pt2::Point, action=:nothing)`

Make a line between two points, `pt1`

and `pt2`

and do an action.

`Luxor.rline`

— Function.```
rline(x, y)
rline(x, y, :action)
rline(pt)
```

Create a line relative to the current position to the `x/y`

position and optionally apply an action:

You can use `rule()`

to draw a line across the entire drawing through a point, at an angle to the current x-axis.

```
y = 10
for x in logspace(0, 2.75, 40)
circle(Point(x, y), 2, :fill)
rule(Point(x, y), -pi/2)
y += 2
end
```

`Luxor.rule`

— Function.`rule(pos::Point, theta=0.0)`

Draw a line across the entire drawing passing through `pos`

, at an angle of `theta`

to the x-axis. Returns the two points.

The end points are not calculated exactly, they're just a long way apart.

## Arcs and curves

There are a few standard arc-drawing commands, such as `curve()`

, `arc()`

, `carc()`

, and `arc2r()`

.

`curve()`

constructs Bézier curves from control points:

```
setline(.5)
pt1 = Point(0, -125)
pt2 = Point(200, 125)
pt3 = Point(200, -125)
sethue("red")
map(p -> circle(p, 4, :fill), [O, pt1, pt2, pt3])
line(O, pt1, :stroke)
line(pt2, pt3, :stroke)
sethue("black")
setline(3)
move(O)
curve(pt1, pt2, pt3)
strokepath()
```

`arc2r()`

draws a circular arc that joins two points:

```
tiles = Tiler(700, 200, 1, 6)
for (pos, n) in tiles
c1, pt2, pt3 = ngon(pos, rand(10:50), 3, rand(0:pi/12:2pi), vertices=true)
sethue("black")
map(pt -> circle(pt, 4, :fill), [c1, pt3])
sethue("red")
circle(pt2, 4, :fill)
randomhue()
arc2r(c1, pt2, pt3, :stroke)
end
```

`Luxor.arc`

— Function.`arc(xc, yc, radius, angle1, angle2, action=:nothing)`

Add an arc to the current path from `angle1`

to `angle2`

going clockwise, centered at xc, yc.

Angles are defined relative to the x-axis, positive clockwise.

`arc(centerpoint::Point, radius, angle1, angle2, action=:nothing)`

Add an arc to the current path from `angle1`

to `angle2`

going clockwise, centered at `centerpoint`

.

`Luxor.arc2r`

— Function.` arc2r(c1::Point, p2::Point, p3::Point, action=:nothing)`

Make a circular arc centered at `c1`

that starts at `p2`

and ends at `p3`

, going clockwise.

`c1`

-`p2`

really determines the radius. If `p3`

doesn't lie on the circular path, it will be used only as an indication of the arc's length, rather than its position.

`Luxor.carc`

— Function.`carc(xc, yc, radius, angle1, angle2, action=:nothing)`

Add an arc to the current path from `angle1`

to `angle2`

going counterclockwise, centered at `xc`

/`yc`

.

Angles are defined relative to the x-axis, positive clockwise.

`carc(centerpoint::Point, radius, angle1, angle2, action=:nothing)`

Add an arc centered at `centerpoint`

to the current path from `angle1`

to `angle2`

, going counterclockwise.

`Luxor.carc2r`

— Function.`carc2r(c1::Point, p2::Point, p3::Point, action=:nothing)`

Make a circular arc centered at `c1`

that starts at `p2`

and ends at `p3`

, going counterclockwise.

`c1`

-`p2`

really determines the radius. If `p3`

doesn't lie on the circular path, it will be used only as an indication of the arc's length, rather than its position.

`Luxor.curve`

— Function.```
curve(x1, y1, x2, y2, x3, y3)
curve(p1, p2, p3)
```

Add a Bézier curve.

The spline starts at the current position, finishing at `x3/y3`

(`p3`

), following two control points `x1/y1`

(`p1`

) and `x2/y2`

(`p2`

).

## Geometry tools

You can find the midpoint between two points using `midpoint()`

.

The following code places a small pentagon (using `ngon()`

) at the midpoint of each side of a larger pentagon:

```
sethue("red")
ngon(O, 100, 5, 0, :stroke)
sethue("darkgreen")
p5 = ngon(O, 100, 5, 0, vertices=true)
for i in eachindex(p5)
pt1 = p5[mod1(i, 5)]
pt2 = p5[mod1(i + 1, 5)]
ngon(midpoint(pt1, pt2), 20, 5, 0, :fill)
end
```

A more general function, `between()`

, finds for a value `x`

between 0 and 1 the corresponding point on a line defined by two points. So `midpoint(p1, p2)`

and `between(p1, p2, 0.5)`

should return the same point.

```
sethue("red")
p1 = Point(-150, 0)
p2 = Point(150, 40)
line(p1, p2)
strokepath()
for i in -0.5:0.1:1.5
randomhue()
circle(between(p1, p2, i), 5, :fill)
end
```

Values less than 0.0 and greater than 1.0 appear to work well too, placing the point on the line if extended.

`Luxor.midpoint`

— Function.`midpoint(p1, p2)`

Find the midpoint between two points.

`midpoint(a)`

Find midpoint between the first two elements of an array of points.

`Luxor.between`

— Function.```
between(p1::Point, p2::Point, x)
between((p1::Point, p2::Point), x)
```

Find the point between point `p1`

and point `p2`

for `x`

, where `x`

is typically between 0 and 1, so these two should be equivalent:

`between(p1, p2, 0.5)`

and

`midpoint(p1, p2)`

`center3pts()`

finds the radius and center point of a circle passing through three points which you can then use with functions such as `circle()`

or `arc2r()`

.

`Luxor.center3pts`

— Function.`center3pts(a::Point, b::Point, c::Point)`

Find the radius and center point for three points lying on a circle.

returns `(centerpoint, radius)`

of a circle. Then you can use `circle()`

to place a circle, or `arc()`

to draw an arc passing through those points.

If there's no such circle, then you'll see an error message in the console and the function returns `(Point(0,0), 0)`

.

`intersection()`

finds the intersection of two lines.

```
pt1, pt2, pt3, pt4 = ngon(O, 100, 5, vertices=true)
text.(["pt 1", "pt 2", "pt 3", "pt 4"], [pt1, pt2, pt3, pt4])
line(pt1, pt2, :stroke)
line(pt4, pt3, :stroke)
flag, ip = intersection(pt1, pt2, pt4, pt3)
if flag
circle(ip, 5, :fill)
end
```

`intersectionlinecircle()`

finds the intersection of a line and a circle. There can be 0, 1, or 2 intersection points.

```
l1 = Point(-100.0, -75.0)
l2 = Point(300.0, 100.0)
rad = 100
cpoint = Point(0, 0)
line(l1, l2, :stroke)
circle(cpoint, rad, :stroke)
nints, ip1, ip2 = intersectionlinecircle(l1, l2, cpoint, rad)
sethue("black")
if nints == 2
circle(ip1, 8, :stroke)
circle(ip2, 8, :stroke)
end
```

`intersection2circles()`

finds the area of the intersection of two circles, and `intersectioncirclecircle() finds the points where they cross.

This example shows the areas of two circles, and the area of their intersection.

```
c1 = (O, 150)
c2 = (O + (100, 0), 150)
circle(c1... , :stroke)
circle(c2... , :stroke)
sethue("purple")
circle(c1... , :clip)
circle(c2... , :fill)
clipreset()
sethue("black")
text(string(150^2 * pi |> round), c1[1] - (125, 0))
text(string(150^2 * pi |> round), c2[1] + (100, 0))
sethue("white")
text(string(intersection2circles(c1..., c2...) |> round),
midpoint(c1[1], c2[1]), halign=:center)
sethue("red")
flag, C, D = intersectioncirclecircle(c1..., c2...)
if flag
circle.([C, D], 2, :fill)
end
```

`Luxor.intersection`

— Function.```
intersection(p1::Point, p2::Point, p3::Point, p4::Point;
commonendpoints = false,
crossingonly = false,
collinearintersect = false)
```

Find intersection of two lines `p1`

-`p2`

and `p3`

-`p4`

This returns a tuple: `(boolean, point(x, y))`

.

Keyword options and default values:

`crossingonly = false`

If `crossingonly = true`

, lines must actually cross. The function returns `(false, intersectionpoint)`

if the lines don't actually cross, but would eventually intersect at `intersectionpoint`

if continued beyond their current endpoints.

If `false`

, the function returns `(true, Point(x, y))`

if the lines intersect somewhere eventually at `intersectionpoint`

.

`commonendpoints = false`

If `commonendpoints= true`

, will return `(false, Point(0, 0))`

if the lines share a common end point (because that's not so much an intersection, more a meeting).

Function returns `(false, Point(0, 0))`

if the lines are undefined.

If you want collinear points to be considered to intersect, set `collinearintersect`

to `true`

, although it defaults to `false`

.

`Luxor.intersectionlinecircle`

— Function.`intersectionlinecircle(p1::Point, p2::Point, cpoint::Point, r)`

Find the intersection points of a line (extended through points `p1`

and `p2`

) and a circle.

Return a tuple of `(n, pt1, pt2)`

where

`n`

is the number of intersections,`0`

,`1`

, or`2`

`pt1`

is first intersection point, or`Point(0, 0)`

if none`pt2`

is the second intersection point, or`Point(0, 0)`

if none

The calculated intersection points won't necessarily lie on the line segment between `p1`

and `p2`

.

`Luxor.intersection2circles`

— Function.`intersection2circles(pt1, r1, pt2, r2)`

Find the area of intersection between two circles, the first centered at `pt1`

with radius `r1`

, the second centered at `pt2`

with radius `r2`

.

`Luxor.intersectioncirclecircle`

— Function.`intersectioncirclecircle(cp1, r1, cp2, r2)`

Find the two points where two circles intersect, if they do. The first circle is centered at `cp1`

with radius `r1`

, and the second is centered at `cp1`

with radius `r1`

.

Returns

`(flag, ip1, ip2)`

where `flag`

is a Boolean `true`

if the circles intersect at the points `ip1`

and `ip2`

. If the circles don't intersect at all, or one is completely inside the other, `flag`

is `false`

and the points are both Point(0, 0).

Use `intersection2circles()`

to find the area of two overlapping circles.

In the pure world of maths, it must be possible that two circles 'kissing' only have a single intersection point. At present, this unromantic function reports that two kissing circles have no intersection points.

`Luxor.bboxesintersect`

— Function.`bboxesintersect(acorner1::Point, acorner2::Point, bcorner1::Point, bcorner2::Point)`

Return true if the two bounding boxes defined by acorner1:acorner2 and bcorner1:bcorner2 intersect.

Each pair of points is assumed to define the two opposite corners of a bounding box.

`getnearestpointonline()`

finds perpendiculars.

```
end1, end2, pt3 = ngon(O, 100, 3, vertices=true)
map(pt -> circle(pt, 5, :fill), [end1, end2, pt3])
line(end1, end2, :stroke)
arrow(pt3, getnearestpointonline(end1, end2, pt3))
```

`Luxor.getnearestpointonline`

— Function.`getnearestpointonline(pt1::Point, pt2::Point, startpt::Point)`

Given a line from `pt1`

to `pt2`

, and `startpt`

is the start of a perpendicular heading to meet the line, at what point does it hit the line?

`Luxor.pointlinedistance`

— Function.`pointlinedistance(p::Point, a::Point, b::Point)`

Find the distance between a point `p`

and a line between two points `a`

and `b`

.

`Luxor.slope`

— Function.`slope(pointA::Point, pointB::Point)`

Find angle of a line starting at `pointA`

and ending at `pointB`

.

Return a value between 0 and 2pi. Value will be relative to the current axes.

```
slope(O, Point(0, 100)) |> rad2deg # y is positive down the page
90.0
slope(Point(0, 100), O) |> rad2deg
270.0
```

`Luxor.perpendicular`

— Function.`perpendicular(p::Point)`

Returns point `Point(p.y, -p.x)`

.

`Luxor.@polar`

— Macro.`@polar (p)`

Convert a tuple of two numbers to a Point of x, y Cartesian coordinates.

```
@polar (10, pi/4)
@polar [10, pi/4]
```

produces

`Luxor.Point(7.0710678118654755,7.071067811865475)`

`Luxor.polar`

— Function.`polar(r, theta)`

Convert point in polar form (radius and angle) to a Point.

`polar(10, pi/4)`

produces

`Luxor.Point(7.071067811865475,7.0710678118654755)`

## Arrows

You can draw lines or arcs with arrows at the end with `arrow()`

. For straight arrows, supply the start and end points. For arrows as circular arcs, you provide center, radius, and start and finish angles. You can optionally provide dimensions for the `arrowheadlength`

and `arrowheadangle`

of the tip of the arrow (angle in radians between side and center). The default line weight is 1.0, equivalent to `setline(1)`

), but you can specify another.

```
arrow(O, Point(0, -65))
arrow(O, Point(100, -65), arrowheadlength=20, arrowheadangle=pi/4, linewidth=.3)
arrow(O, 100, pi, pi/2, arrowheadlength=25, arrowheadangle=pi/12, linewidth=1.25)
```

`Luxor.arrow`

— Function.```
arrow(startpoint::Point, endpoint::Point;
linewidth = 1.0,
arrowheadlength = 10,
arrowheadangle = pi/8)
```

Draw a line between two points and add an arrowhead at the end. The arrowhead length will be the length of the side of the arrow's head, and the arrowhead angle is the angle between the sloping side of the arrowhead and the arrow's shaft.

Arrows don't use the current linewidth setting (`setline()`

), and defaults to 1, but you can specify another value. It doesn't need stroking/filling, the shaft is stroked and the head filled with the current color.

```
arrow(centerpos::Point, radius, startangle, endangle;
linewidth = 1.0,
arrowheadlength = 10,
arrowheadangle = pi/8)
```

Draw a curved arrow, an arc centered at `centerpos`

starting at `startangle`

and ending at `endangle`

with an arrowhead at the end. Angles are measured clockwise from the positive x-axis.

Arrows don't use the current linewidth setting (`setline()`

); you can specify the linewidth.

## Julia graphics

A couple of functions in Luxor provide you with instant access to the Julia logo, and the three colored circles:

```
for (pos, n) in Tiler(750, 250, 1, 2)
gsave()
translate(pos - Point(150, 100))
if n == 1
julialogo()
elseif n == 2
julialogo(action=:clip)
for i in 1:500
gsave()
translate(rand(0:400), rand(0:250))
juliacircles(10)
grestore()
end
clipreset()
end
grestore()
end
```

`Luxor.julialogo`

— Function.`julialogo(;action=:fill, color=true)`

Draw the Julia logo. The default action is to fill the logo and use the colors:

`julialogo()`

If `color`

is `false`

, the logo will use the current color, and the dots won't be colored in the usual way.

The logo's dimensions are about 330 wide and 240 high, and the `0/0`

point is at the bottom left corner. To place the logo by locating its center, do this:

```
gsave()
translate(-165, -120)
julialogo() # locate center at 0/0
grestore()
```

To use the logo as a clipping mask:

`julialogo(action=:clip)`

(In this case the `color`

setting is automatically ignored.)

`Luxor.juliacircles`

— Function.`juliacircles(radius=100)`

Draw the three Julia circles in color centered at the origin.

The distance of the centers of the circles from the origin is `radius`

. The optional keyword arguments `outercircleratio`

(default 0.75) and `innercircleratio`

(default 0.65) control the radius of the individual colored circles relative to the `radius`

. So you can get relatively smaller or larger circles by adjusting the ratios.

## Miscellaneous

### Hypotrochoids

`hypotrochoid()`

makes hypotrochoids. The result is a polygon. You can either draw it directly, or pass it on for further polygon fun, as here, which uses `offsetpoly()`

to trace round it a few times.

```
origin()
background("grey15")
sethue("antiquewhite")
setline(1)
p = hypotrochoid(100, 25, 55, :stroke, stepby=0.01, vertices=true)
for i in 0:3:15
poly(offsetpoly(p, i), :stroke, close=true)
end
```

There's a matching `epitrochoid()`

function.

`Luxor.hypotrochoid`

— Function.```
hypotrochoid(R, r, d, action=:none;
stepby=0.01,
period=0,
vertices=false)
```

Make a hypotrochoid with short line segments. (Like a Spirograph.) The curve is traced by a point attached to a circle of radius `r`

rolling around the inside of a fixed circle of radius `R`

, where the point is a distance `d`

from the center of the interior circle. Things get interesting if you supply non-integral values.

Special cases include the hypocycloid, if `d`

= `r`

, and an ellipse, if `R`

= `2r`

.

`stepby`

, the angular step value, controls the amount of detail, ie the smoothness of the polygon,

If `period`

is not supplied, or 0, the lowest period is calculated for you.

The function can return a polygon (a list of points), or draw the points directly using the supplied `action`

. If the points are drawn, the function returns a tuple showing how many points were drawn and what the period was (as a multiple of `pi`

).

`Luxor.epitrochoid`

— Function.```
epitrochoid(R, r, d, action=:none;
stepby=0.01,
period=0,
vertices=false)
```

Make a epitrochoid with short line segments. (Like a Spirograph.) The curve is traced by a point attached to a circle of radius `r`

rolling around the outside of a fixed circle of radius `R`

, where the point is a distance `d`

from the center of the circle. Things get interesting if you supply non-integral values.

`stepby`

, the angular step value, controls the amount of detail, ie the smoothness of the polygon.

If `period`

is not supplied, or 0, the lowest period is calculated for you.

The function can return a polygon (a list of points), or draw the points directly using the supplied `action`

. If the points are drawn, the function returns a tuple showing how many points were drawn and what the period was (as a multiple of `pi`

).

### Grids

If you have to position items regularly, you might find a use for a grid. Luxor provides a simple grid utility. Grids are lazy: they'll supply the next point on the grid when you ask for it.

Define a rectangular grid with `GridRect`

, and a hexagonal grid with `GridHex`

. Get the next grid point from a grid with `nextgridpoint(grid)`

.

```
grid = GridRect(O, 40, 80, (10 - 1) * 40)
for i in 1:20
randomhue()
p = nextgridpoint(grid)
squircle(p, 20, 20, :fill)
sethue("white")
text(string(i), p, halign=:center)
end
```

```
radius = 70
grid = GridHex(O, radius, 600)
for i in 1:15
randomhue()
p = nextgridpoint(grid)
ngon(p, radius-5, 6, pi/2, :fillstroke)
sethue("white")
text(string(i), p, halign=:center)
end
```

`Luxor.GridRect`

— Type.`GridRect(startpoint, xspacing, yspacing, width, height)`

Define a rectangular grid, to start at `startpoint`

and proceed along the x-axis in steps of `xspacing`

, then along the y-axis in steps of `yspacing`

.

`GridRect(startpoint, xspacing=100.0, yspacing=100.0, width=1200.0, height=1200.0)`

For a column, set the `xspacing`

to 0:

`grid = GridRect(O, 0, 40)`

To get points from the grid, use `nextgridpoint(g::Grid)`

.

```
julia> grid = GridRect(O, 0, 40);
julia> nextgridpoint(grid)
Luxor.Point(0.0,0.0)
julia> nextgridpoint(grid)
Luxor.Point(0.0,40.0)
```

When you run out of grid points, you'll wrap round and start again.

`Luxor.GridHex`

— Type.`GridHex(startpoint, radius, width=1200.0, height=1200.0)`

Define a hexagonal grid, to start at `startpoint`

and proceed along the x-axis and then along the y-axis, `radius`

is the radius of a circle that encloses each hexagon. The distance in `x`

between the centers of successive hexagons is:

To get the next point from the grid, use `nextgridpoint(g::Grid)`

.

When you run out of grid points, you'll wrap round and start again.

`Luxor.nextgridpoint`

— Function.`nextgridpoint(g::GridRect)`

Returns the next available (or even the first) grid point of a grid.

`nextgridpoint(g::GridHex)`

Returns the next available grid point of a hexagonal grid.

### Cropmarks

If you want cropmarks (aka trim marks), use the `cropmarks()`

function, supplying the centerpoint, followed by the width and height:

```
cropmarks(O, 1200, 1600)
cropmarks(O, paper_sizes["A0"]...)
```

```
sethue("red")
box(O, 150, 150, :stroke)
cropmarks(O, 150, 150)
```

`Luxor.cropmarks`

— Function.`cropmarks(center, width, height)`

Draw cropmarks (also known as trim marks).

### Bars

For simple bars, use the `bars()`

function, supplying an array of numbers:

```
fontsize(7)
sethue("black")
v = rand(-100:100, 25)
bars(v)
```

To change the way the bars and labels are drawn, define some functions and pass them as keyword arguments to `bars()`

:

```
function mybarfunction(low::Point, high::Point, value;
extremes=[0, 1], barnumber=0, bartotal=0)
@layer begin
sethue(Colors.HSB(rescale(value, extremes[1], extremes[2], 0, 360), 1.0, 0.5))
csize = rescale(value, extremes[1], extremes[2], 5, 25)
circle(high, csize, :fill)
setline(1)
sethue("blue")
line(Point(low.x, 0), high + (0, csize), :stroke)
sethue("white")
text(string(value), high, halign=:center, valign=:middle)
end
end
function mylabelfunction(low::Point, high::Point, value;
extremes=[0, 1], barnumber=0, bartotal=0)
@layer begin
translate(low)
text(string(value), O + (0, 10), halign=:center, valign=:middle)
end
end
v = rand(1:100, 25)
bars(v, xwidth=25, barfunction=mybarfunction, labelfunction=mylabelfunction)
```

`Luxor.bars`

— Function.```
bars(values::AbstractArray;
yheight = 200,
xwidth = 25,
labels = true,
barfunction = f,
labelfunction = f,
)
```

Draw some bars where each bar is the height of a value in the array. The bars will fit in a box `yheight`

high (even if there are negative values).

To control the drawing of the text and bars, define functions that process the end points:

`mybarfunction(bottom::Point, top::Point, value; extremes=[a, b], barnumber=0, bartotal=0)`

`mylabelfunction(bottom::Point, top::Point, value; extremes=[a, b], barnumber=0, bartotal=0)`

and pass them like this:

```
bars(v, yheight=10, xwidth=10, barfunction=mybarfunction)
bars(v, xwidth=15, yheight=10, labelfunction=mylabelfunction)
```

To suppress the text labels, use optional keyword `labels=false`

.