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; vertices=false)

Create a rectangle between two points and do an action. Use vertices=true to return an array of the four corner points rather than draw the box.

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.

box(t::Table, r::Int, c::Int, action::Symbol=:nothing)

Draw a box in table t at row r and column c.

box(t::Table, cellnumber::Int, action::Symbol=:nothing; vertices=false)

Draw box cellnumber in table t.

box(bbox::BoundingBox, :action)

Make a box using the bounds in bbox.

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=:nothing)

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:

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).

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(center::Point, radius, action=:none;
    reversepath=false,
    kappa = 0.5522847498307936)

Draw a circle using Bézier curves.

The magic value, kappa, is 4.0 * (sqrt(2.0) - 1.0) / 3.0.

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.

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

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.

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

Make a squircle or superellipse (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 root (rt) option defaults to 0.5, and gives an intermediate shape. Values less than 0.5 make the shape more rectangular. Values above make the shape more round. The horizontal and vertical radii can be different.

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)
line(pt)

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

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)
rline(pt)

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

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.

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.

  arc2r(c1::Point, p2::Point, p3::Point, action=:nothing)

Add a circular arc centered at c1 that starts at p2 and ends at p3, going clockwise, to the current path.

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.

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.

carc2r(c1::Point, p2::Point, p3::Point, action=:nothing)

Add a circular arc centered at c1 that starts at p2 and ends at p3, going counterclockwise, to the current path.

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.

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).

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)

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.

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.

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.

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.

boundingboxesintersect(bbox1::BoundingBox, bbox2::BoundingBox)

Return true if the two bounding boxes intersect.

ispointonline(pt::Point, pt1::Point, pt2::Point;
    extended = false,
    atol = 10E-5)

Return true if the point pt lies on a straight line between pt1 and pt2.

If extended is false (the default) the point must lie on the line segment between pt1 and pt2. If extended is true, the point lies on the line if extended in either direction.

distance(p1::Point, p2::Point)

Find the distance between two points (two argument form).

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(p1, p2, k)

Return a point p3 that is k units away from p1, such that a line p1 p3 is perpendicular to p1 p2.

Convention? to the right?

perpendicular(p::Point)

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

dotproduct(a::Point, b::Point)

Return the scalar dot product of the two points.

@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.

The BoundingBox type holds two Points, corner1 and corner2.

BoundingBox(;centered=true) # the bounding box of the Drawing
BoundingBox(s::String)      # the bounding box of a text string
BoundingBox(pt::Array)      # the bounding box of a polygon

boxaspectratio(bb::BoundingBox)

Return the aspect ratio (the height divided by the width) of bounding box bb.

boxdiagonal(bb::BoundingBox)

Return the length of the diagonal of bounding box bb.

boxwidth(bb::BoundingBox)

Return the width of bounding box bb.

boxheight(bb::BoundingBox)

Return the height of bounding box bb.

intersectionboundingboxes(bb1::BoundingBox, bb2::BoundingBox)

Returns a bounding box intersection.

boxtop(bb::BoundingBox)

Return the top center point of bounding box bb.

boxbottom(bb::BoundingBox)

Return the top center point of bounding box bb.

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).

cropmarks(center, width, height)

Draw cropmarks (also known as trim marks).

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.