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Yes—you can turn the Desmos Graphing Calculator into a small interactive sketching tool. Drag a movable point, click to capture its coordinates, and let Desmos render the captured points as a polygon or connected line. It is a point-sampling sketcher, not a continuous brush-based paint program.
The project is a lesson in coordinate geometry, lists, state, and interactive actions. The original project was published by HackerNoon on October 27, 2024, and demonstrated by tracing Bowser from Super Mario Bros. (original tutorial).
How the Desmos drawing tool works
Movable point → sampled coordinates → lists → polygon or connected line
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- 4-year subscription for the TI-84 Plus CE online calculator included with purchase
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A point such as (a,b) acts as the cursor. Dragging it changes its current coordinates. A clickable Capture control copies those coordinates into two lists. Desmos then uses the lists as vertices for a polygon or as points in a connected path.
Dragging alone does not leave a trail. This is a click-to-sample interface, so the number and placement of captured points determine how smooth or angular the result looks.
What you need
- The Desmos Graphing Calculator.
- A signed-in Desmos account if you want to use Actions.
- Basic familiarity with coordinate pairs and lists.
- An optional image that you own or are permitted to trace.
Actions are enabled at the account level. In the current Desmos interface, sign in, open Account Settings, choose Advanced, and enable Actions. The official documentation does not indicate that a paid subscription is needed. See Desmos Actions documentation for availability and interface details.
Build a minimal one-stroke sketcher
1. Organize the graph
Create folders for Controls, Cursor, Current stroke, Completed strokes, and, if needed, Stencil image. Folders make the expression list easier to understand and let you duplicate a clean template. See Desmos’s Add an Item guide.
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Set a sensible graph window before drawing. A fixed canvas range helps keep the cursor and controls in the intended workspace.
2. Create a draggable cursor
Add a point with two variables: P=(a,b). Open the point’s options and enable dragging. Give it a large size, a high-contrast color, and a label such as cursor. Desmos explains movable points in Sliders and Movable Points.
The variables a and b represent only the cursor’s current position. They are not the drawing history.
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- Six different graph styles and 15 colors to select from for differentiating the look of each graph drawn
3. Store captured coordinates
Create two empty lists: currentX=[ ] and currentY=[ ]. When the cursor is at (a,b), append its coordinates with Actions: currentX → join(currentX,[a]) and currentY → join(currentY,[b]).
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4. Add a Capture control
Create a separate point, curve, or other graph object outside the canvas and label it Capture. In its options, add these update rules to the On Click field: currentX → join(currentX,[a]) and currentY → join(currentY,[b]).
Move the cursor, click Capture, and repeat. Each click adds one vertex to the current stroke. Keep the control visually distinct from the cursor.
5. Render the stroke as a polygon
Add polygon(currentX,currentY). Desmos interprets the paired list entries as polygon vertices and closes the shape. Use the style menu to choose fill, outline width, and opacity. A transparent or lightly transparent fill with a thin outline can be easier to read while experimenting. See Desmos’s polygon documentation.
Capture a few points around a simple shape and watch the polygon update. This gives you a working one-stroke coordinate sampler.
Why multiple strokes are harder
If every point is appended to the same currentX and currentY lists, the next stroke becomes part of the same polygon. Desmos connects the entire sequence and closes it, often producing a tangled shape.
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The application therefore needs two kinds of state:
- Current stroke: the x- and y-lists that receive new captures.
- Completed strokes: earlier data that remains visible but no longer changes.
Conceptually, a New Shape action saves currentX and currentY, then sets both working lists to [ ]. The original tutorial describes a completed-strokes collection represented conceptually by shapes → join(shapes,[currentX,currentY]).
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Do not claim unlimited shapes. Expression count, nested state, accumulated points, and graph responsiveness impose practical limits.
Add New Shape and Reset
Make a clickable control labeled New. In a fixed-slot design, its action sequence is:
- Copy currentX and currentY into the next completed-stroke variables.
- Advance the stroke counter.
- Set currentX and currentY to empty lists.
Make a second clickable control labeled Reset. It should clear the current lists, reset the stroke counter, and clear every completed-stroke slot used by the graph. Clearing only currentX and currentY will leave older polygons visible.
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Using an image as a tracing stencil
Choose Add Item → Image, upload an image, lower its opacity, and place it behind the plotted objects. Drag its center to reposition it and use its outer handles to resize it; image options also control layering and opacity. See Desmos’s Add an Item guide.
The image is only a visual reference. Desmos does not automatically convert it into coordinates, vector paths, or expressions. Use images you created, have licensed, or are otherwise permitted to use. Permission to view an image does not automatically grant permission to redistribute a traced result.
Use connected points for open strokes
A polygon is closed by definition. If you want a line-like mark rather than a filled closed contour, use connected points or a table with lines enabled. Desmos documents this approach in Graphing and Connecting Coordinate Points.
| Rendering method | Best for | Limitation |
|---|---|---|
| Polygon | Filled geometric shapes or closed contours | Closes the path between the last and first points |
| Connected points | Open outlines and line-like marks | Still uses sampled points, not continuous brush input |
Common visual problems
Unwanted diagonal edge
Because polygon() closes the path, it adds a segment from the final point back to the first. End close to the starting point, split the mark into smaller shapes, use an outline, or switch to connected points.
Strange or unexpected fills
A self-intersecting polygon can produce a fill that does not resemble a brush stroke. Capture simpler contours, draw shorter shapes, lower fill opacity, or use outline-only styling.
Angular results
The tool records only the positions you explicitly capture. More samples improve fidelity but increase list size and editing complexity. Fast dragging does not create additional points automatically.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.Useful improvements
- Make Capture, New, and Reset controls large and high contrast.
- Place controls outside the drawing area.
- Use a consistent canvas range and a visible grid while learning.
- Keep fill opacity low so overlapping shapes remain legible.
- Duplicate a clean template before making structural changes.
- Reserve separate folders for controls, state, and visible artwork.
- Use separate colors or polygon styles for different stroke types.
- Keep demonstrations modest in size so the graph remains responsive.
Actions can also drive repeated updates with a ticker, which opens possibilities such as animated playback of saved points. Tickers do not turn this design into continuous pointer input. See the Actions reference.
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- Advanced functions accessed through pull-down display menus.
- Horizontal and vertical split screen options. Vibrant backlit color screen
- I/o port for communication with other TI products.Seven different graph styles for differentiating the look of each graph drawn. Fourteen interactive zoom features
Troubleshooting
| Problem | Likely cause | Recovery |
|---|---|---|
| The cursor will not move | Dragging is disabled. | Open the point options and enable dragging. |
| The action arrow or On Click field is missing | You are signed out or Actions are disabled. | Sign in, enable Actions under Account Settings → Advanced, and reload if necessary. |
| join() behaves unexpectedly | A scalar was supplied. | Append [a] and [b], not a and b. |
| New drawings merge with old ones | The working lists were not saved and cleared. | Preserve the current stroke before resetting the working lists. |
| The polygon has a diagonal closing edge | Polygons are closed. | Close the contour, use an outline, or use connected points. |
| The fill looks wrong | The polygon crosses itself. | Use simpler contours, shorter shapes, or outline-only styling. |
| An image hides the drawing | The image is layered in front. | Change its layering in the image options. |
| Reset clears only the latest line | Completed strokes use separate state. | Reset every slot or state variable, not only the current lists. |
| The graph becomes difficult to edit | Too many expressions or samples have accumulated. | Duplicate a clean template and keep the working drawing small. |
What this project is—and is not
This is best understood as a point-sampling polygon sketcher. It is useful for exploring coordinate pairs, geometric representation, lists, mutable state, event-driven updates, interactive math-art projects, and tracing simple shapes in a self-contained graph.
It is a poor replacement for a conventional drawing application if you need continuous brush input, layers, erasers, pressure sensitivity, anti-aliasing, open strokes, color palettes, text tools, selection and transformation, or reliable raster/vector export. A conventional canvas or digital-art application is substantially better for those tasks.
Desmos’s version is valuable because the drawing is exposed as mathematical data. Every captured point is visible in the model, and every action changes an inspectable list.
Frequently asked questions
Can Desmos draw continuously while I drag the cursor?
No. This method records coordinates when you click the Capture control. Dragging the point changes its current position but does not automatically create a trail.
Why does my polygon add a line across the drawing?
Polygons are closed, so Desmos connects the last captured point back to the first. Use connected points for an open outline or break the drawing into smaller shapes.
How do I keep a new stroke from joining the previous one?
Store completed strokes separately from the current x- and y-lists. A fixed number of stroke slots is often easier to manage than unrestricted nested lists.
Do I need a paid Desmos account to use Actions?
The official Actions documentation describes Actions as an account setting and does not indicate that a paid subscription is required. Sign in and enable Actions under Account Settings → Advanced.
Can Desmos turn my tracing image into a drawing automatically?
No. An added image is a visual stencil only; you must capture points yourself to create the plotted shape.
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Further project ideas
- Use different polygon colors for different stroke types.
- Simulate thicker marks with narrow, parallel polygons.
- Add a fixed-slot undo system by preserving previous list states.
- Animate point playback with a ticker.
- Compare polygon closure with connected-point rendering.
- Have students design the data model before building the controls.
- Export a screenshot when the graph reaches a finished state.
Save or share the graph as a Desmos graph, but remember that its drawing exists as variables and lists inside that graph. It is not automatically an independent image file or a conventional drawing-project format.
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