Simple graphics

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.

box(cornerpoint1, cornerpoint2, action=:nothing)

Create a rectangle between two points and do an action.

box(points::Array, 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.

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

polybbox(pointlist::Array)

Return the two opposite corners (suitable for box(), for example).

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:

Make an ellipse, centered at xc/yc, fitting in a box of width w and height h.

ellipse(xc, yc, w, h, action=:none)

Make an ellipse, centered at point c, with width w, and height h.

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

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(center::Point, radius, action=:none;
    reversepath=false,
    kappa = 0.5522847)

Draw a circle using Bézier curves.

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

Draw an annular sector centered at centerpoint.

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.

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

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.

Draw a pie shape centered at the origin

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.

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):

squircle(center::Point, hradius, vradius, action=:none; rt = 0.5, vertices=false)

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.

move(x, y)
move(pt)

Move to a point.

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)

newpath()

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

closepath()

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

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:

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.

Add an arc to the current path from angle1 to angle2 going clockwise.

arc(xc, yc, radius, angle1, angle2, action=:nothing)

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

Arc with centerpoint.

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

  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.

Add an arc to the current path from angle1 to angle2 going counterclockwise.

carc(xc, yc, radius, angle1, angle2, action=:nothing)

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

Add an arc centered at centerpoint to the current path from angle1 to angle2 going counterclockwise.

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.

Add a Bézier curve.

 curve(x1, y1, x2, y2, x3, y3)
 curve(p1, p2, p3)

The spline starts at the current position, finishing at x3/y3 (p3), following two control points x1/y1 (p1) and x2/y2 (p2)

midpoint(p1, p2)

Find the midpoint between two points.

midpoint(a)

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

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(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(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.

intersection_line_circle(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.

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.

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?

pointlinedistance(p::Point, a::Point, b::Point)

Find the distance between a point p and a line between two points a and b.

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

perpendicular(p::Point)

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

@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)

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)

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.

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.)

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.

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).

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).

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.

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.

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(center, width, height)

Draw cropmarks (also known as trim marks).

bars(values::Array;
        yscale = 100,
        xwidth = 10,
        labels = true,
        barfunction = f,
        labelfunction = f,
    )

Draw some bars where each bar is the height of a value in the array.

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])

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

and pass them like this:

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

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