The PrairieDraw library (PrairieDraw.js) is a figure-drawing library which allows dynamic figures to be rendered through the pl-prairiedraw-figure element (see here).

Any parameters passed to the script from the params-names option in the pl-prairiedraw-figure element can be accessed with this.params.get([parameter])

Sylvester.js library and selected methods

PrairieDraw uses the Sylvester.Vector class to specify positions and directions for drawing; any Vector-type arguments listed below are of this type.

Below is an incomplete selection of useful operations on Vector; the complete documentation is found here.

Sylvester.Vector.create(elements) Creates and returns a new Vector from the array elements. It is often useful to alias this command in your script as var $V = Sylvester.Vector.create so you can write $V([x,y]) later on.

add(vector) Returns a new Vector which is the sum of the receiver and the argument.

subtract(vector) Returns a new Vector which is the difference between the receiver and argument; i.e., a.subtract(b) returns the vector difference a-b.

multiply(scalar) or x(scalar) Returns a new Vector which is the receiver scaled by the argument. a.multiply(k) and a.x(k) are equivalent.

dot(vector) Returns the scalar product of the receiver and argument.

cross(vector) Returns a new Vector which is the cross product in left-to-right order; i.e., A.cross(B) returns A x B.

modulus() Returns the (2)-norm of the vector.

toUnitVector() Returns a new Vector which is the receiver scaled to have modulus one.

rotate(angle, axis) Returns a new Vector formed by rotating the receiver counterclockwise through angle (in radians), using the Vector axis as a center point. E.g.,

a = $V([10,5]);
b = $V([5,5]);
c = a.rotate(Math.PI / 2, b) // c = [5, 10]

PrairieDraw.js library

The script provided by script_name may access the PrairieDraw figure via this.pd. The operations below allow for changing the orientation or scaling of the figure, as well as adding drawing elements to it.

In general, drawing objects are opaque, so the order in which items are added affects the final appearance of the figure.

Below is an incomplete list of operations available from PrairieDraw; the library source code can be found here.

Constants provided by PrairieDraw

goldenRatio Returns the golden ratio; useful for creating pleasantly-proportioned figures in the arguments to setUnits.

milesPerKilometer Returns a conversion factor of 0.621371

Setting and changing the coordinate system

setUnits(xSize, ySize [, canvasWidth, preserveCanvasSize]) Sets the size of the canvas in drawing units, with the origin at the center of the drawing. The optional canvasWidth argument specifies (in pixels) the width of the figure, while preserveCanvasSize prevents reshaping the canvas to match the coordinate ratio.

scale(factor) Scale drawing coordinates by the given factor (i.e., the relationship between coordinates and pixels).

translate(offset) Translate the origin of the coordinate system by the Vector offset.

rotate(angle) Rotate the coordinate system counterclockwise by angle radians.

transformByPoints(old1, old2, new1, new2) Perform a combination of scale, translate, and rotate such that Vector points old1 and old2 are mapped to new1 and new2.

Drawing object options

Some drawing objects below have the optional type argument to specify a physical meaning for the line/arrow. When specified, a corresponding color is chosen for the object based on the TAM 2XX style guide here.

Type Color
grid rgb(200,200,200)
position rgb(0,0,255)
angle rgb(0,100,180)
velocity rgb(0,200,0)
angVel rgb(100,180,0)
acceleration rgb(255,0,255)
rotation rgb(150,0,150)
angAcc rgb(100,0,180)
angMom rgb(255,0,0)
force rgb(210,105,30)
moment rbg(255,102,80)

The optional filled argument (default is false) is a boolean to specify if the shape should be shaded.

Drawing points and lines

point(vector) Draw a point at the coordinates given by vector.

line(start, end [, type]) Draw a line segment from Vector position start to stop.

polyline(points [, closed, filled]) Draw a series of line segments connecting the array of points. The optional arguments (defaulting to false) determine if the polyLine should be closed by a line connecting the first and last elements of points.

arc(center, radius, startAngle, endAngle [, filled, aspect]) Draw an arc of a circle centered at center, with radius radius, from angle startAngle to endAngle (in radians). When aspect is provided, the arc is drawn for an ellipse with major axis radius and minor axis radius / aspect (i.e., aspect is major / minor).

circle(center, radius [, filled]) Draws a circle centered at center with radius radius.

rectangle(width, height [, center, angle, filled]) Draw a rectangle (aligned to the axes) of the given width and height. When not specified, center is assumed to be the origin. An angle to rotate can also be given.

rectangleGeneric(bottomLeft, bottomRight, height) Draw a rectangle with one side connecting bottomLeft and bottomRight of the given height. The rectangle extends perpendicular (counter-clockwise) to this line.

Drawing vector arrows

arrow(start, end [, type]) Draw an arrow from start to stop (with arrowhead at stop).

arrowFrom(start, offset [, type]) Draw an arrow from start to start.add(offset).

arrowTo(end, offset [, type]) Draw an arrow from end.subtract(offset) to end.

arrowOutOfPage(vector [, type]) Draw an arrow out of the screen (circle with center dot) at vector.

arrowIntoPage(vector [, type]) Draw an arrow into the screen (circle with center x) at vector.

circleArrow(center, radius, startAngle, endAngle [, type, fixedRad, idealSegmentSize]) Draw an arrow arc centerd at center, with radius radius, from startAngle to endAngle (in radians). The fixedRad option (default false) specifies if a constant radius should be used (as opposed to curling in the beginning/end).

circleArrowCentered(center, radius, centerAngle, extentAngle [, type, fixedRad]) Draw an arrow arc centered at center, with radius radius, centerd at centerAngle and spanning extentAngle (in radians).

triangularDistributedLoad(start, end, startSize, endSize, startLabel, endLabel, arrowToLine, arrowDown) This creates a (trapezoidal) distributed load acting on the line between start and end, with height startSize at one side and endSize at the other and corresponding labels startLabel and endLabel. arrowToLine is true if the arrowheads point towards the line between start and end, and false otherwise. arrowDown is true if the arrowheads point down (negative y direction) and false otherwise. These last two options determine whether arrows appear above or below the line.

This function assumes the line from start to end is horizontal, and has unexpected behaviors when it does not.

Drawing mechanical shapes

rod(start, end, width) Draws a rod with endpoint pins at start and end. The rounded ends of the rod will extend slightly beyond these points.

LshapeRod(start, middle, end, width) Draws an L-shaped rod with endpoints start and end and corner at middle.

TshapeRod(start, center, end, centerEnd, width) Draws a T-shaped rod with hinges at the four points listed. To draw a well-formed rod with three arms, let center be the intersection of the arms and the order start, end, centerEnd represent the clockwise ordering of the three endpoints.

pivot(baseCenter, center, width) Creates a pivot base with hinge point at center and other end at baseCenter. When combined with ground below, baseCenter is usually the midpoint of the ground element.

ground(baseCenter, normal, width) Draws a (shaded) ground element centered at baseCenter and width width. The direction of normal is perpendicular to and away from the ground.

arcGround(center, radius, startAngle, endAngle, outside) Draws a curved ground element with arguments similar to the arc command above. outside is true if the shading goes on the outside of the curve, and false otherwise.

Drawing text and/or LaTex labels

See below for instructions on formatting the text argument in these commands.

text(position, anchor, text [, boxed, angle]) Draws text at the given position. anchor is a Vector with components from (-1,0,1) specifying alignment; i.e., $V([-1,-1]) corresponds to "left" and "bottom" alignment for the text; $V([1,1]) corresponds to "right" and "above". Optional boxed frames the text, and angle rotates it in place.

labelLine(start, end, pos, text [, anchor]) Places text along the line between start and end. pos takes values in local coordinates from (-1,1) specifying the position along and above/below the line. The optional anchor uses the same pattern as above.

labelCircleLine(center, radius, startAngle, endAngle, pos, text) Places text along the arc specified by center, radius, startAngle, and endAngle. pos takes values in local coordinates from (-1,1) along and above/below the curve.

Generating LaTeX labels on figures

When using PrairieDraw.js to draw figures in questions, figure labels can be included using either plain text, like pd.text(..., "label"), or with LaTeX, like pd.text(..., "TEX:$x$"). If you are using LaTeX labels then they have to be rendered into image files before they can be displayed. This is done by running the command:

docker run -it --rm -v PATH_TO_MY_COURSE:/course prairielearn/prairielearn /PrairieLearn/tools/

Replace PATH_TO_MY_COURSE above with your local course path directory, such as /Users/mwest/git/pl-tam212 or C:/GitHub/pl-tam212.

LaTeX labels are searched for by looking for strings of the form "TEX:..." or 'TEX:...' (note the different quote types). Use the "" form if you want to have ' characters in the string itself, and vice versa.

The above command needs to be repeated after any LaTeX labels are added or changed in questions.

The LaTeX label images will be filenames that look like:


These files should be committed to the git repository and pushed to the live server so that they are available along with the question.

Advanced: Running without Docker

If you want to generate LaTeX label images without docker then you will need to install Python, ImageMagick, and LaTeX and then run:

cd <FULL-PATH>/PrairieLearn
python tools/ --subdir /path/to/course