GMT Documentation

The Geometry Mapping Tool (GMT) helps students learn the Monge method of descriptive geometry, as taught in secondary school (in Portugal, Geometria Descritiva A in years 10 and 11). It also supports teachers in preparing, presenting and sharing exercises.

The idea is simple: you draw on a digital drawing sheet (the Monge view) with dedicated tools, and GMT maps every projection you draw into a live 3D space, so you can see in space what you are constructing on paper.

Besides the tool itself, the GMT platform lets you save exercises, organise them in folders, publish them, build them step by step with notes, and share them with a class through teams.

Sandbox

A free scratch space at /sandbox, open to everyone. Guests can use every tool, but nothing is saved. When you are signed in, your sandbox is saved to your account automatically and is waiting for you on any device.

Sheet (exercise)

A named drawing saved in your account, listed in My Exercises. Sheets can be organised in folders, made public, shared to teams, and built step by step. Creating sheets requires a Premium or Classroom plan.

View-only sheet

A sheet you don't own but can open, because it is public, it was shared with one of your teams, or you are an administrator. You can look at it, rotate the 3D view, browse its steps and print it, but not change it.

Whether you are in the sandbox or in a sheet, the editor has the same parts:

• Title bar (top): Settings, the sheet title, Save to Sheet (sandbox only), view mode, Print and Step Mode.
• 3D view (left): the three-dimensional space where everything you draw is reconstructed. See 3D view.
• Drawing sheet (right): the Monge view, with the x axis (ground line) and the horizontal and frontal projections. See Drawing sheet.
• Toolbox (bottom centre): the nine drawing tools, selected with the mouse or the keys 1 to 9. See Tools.
• Auxiliary toolbar: Precise Mode, New Page, Undo, Redo, Reset Camera and the Tutorial Video for the active tool. See Auxiliary toolbar.
• Tool options panel: appears when a tool has options (name, projection type, mode...). Most options have a single-key shortcut, shown in brackets.
• Step-by-step bar: when Step Mode is on in a sheet. See Step by step.

1. 1Open the Sandbox from the home page or the navigation bar.
2. 2Press 2 to select the Point Tool.
3. 3In the options panel, keep Projection Mode on Point, choose the name A and set Projection Type to Horizontal (H). Make sure Free Mode is on.
4. 4Click on the x axis to choose the abscissa, then click a second time to choose the distance (depth). The horizontal projection A₁ is created.
5. 5Press F to switch to Frontal, keep the name A, and click the same abscissa and then the height. The frontal projection A₂ is created.
6. 6Look at the 3D view: as soon as both projections exist, point A appears in space.

Each tool section below has a short clip of the tool in use, and some have a live example: a real, read-only GMT you can rotate and step through. See it for this quick start in Point Tool.

Guest (not signed in)

Can use the sandbox with every tool. Work is not saved and is lost when you leave the page. A banner reminds you to sign in to save your work.

Free

A free account. Your sandbox is saved to your account, you can join one team, open exercises shared with your team, browse public exercises in Discover and keep your editor settings on every device. You cannot create or save sheets.

Premium (for students)

Everything in Free, plus up to 50 saved sheets, folders, step by step, public sheets, the bug-reporting button, and sharing your own exercises with your team.

Classroom (for teachers)

Everything in Premium, with up to 200 saved sheets, plus creating and managing teams (up to 5 teams, up to 50 members each).

Current prices are on the Pricing page. Prices are shown for annual plans and may change as GMT evolves.

Duplicating a sheet counts toward your sheet limit. In My Exercises a counter shows how many sheets you have used, for example "12 of 50 sheets used (38 remaining)".

1. 1Sign in and verify your email address. Subscriptions are only offered to verified accounts; if needed, use Resend Verification on your profile.
2. 2Go to Dashboard → Profile → Subscription & Billing.
3. 3Choose Premium or Classroom in the pricing table and complete the payment.
4. 4Your plan changes as soon as the payment is confirmed. Use Manage Billing to change or cancel your subscription later.

Schools that partner with GMT receive access codes in the format GMT-XXXX-XXXX. A teacher code grants the Classroom plan and a student code grants the Premium plan for the period set by the school.

1. 1Go to Dashboard → Profile.
2. 2In the School code card, enter the code and click Redeem code.
3. 3Your profile then shows "Your plan is provided by your organization. Billing is managed externally."

When the school's access ends, your account returns to the plan you had before. Schools interested in GMT can get in touch through the Schools page.

Sign in and open the Dashboard from the navigation bar. The sidebar has My Exercises, My Teams, Discover, Profile and Logout. Every signed-in user can open the dashboard; on the Free plan, My Exercises shows the sandbox card and an Unlock Sheets Feature panel with an Upgrade Now button.

1. 1In My Exercises, click Create Sheet.
2. 2Fill in the Title (unique among your sheets) and, optionally, a Description.
3. 3Choose the Representation System. Currently the only system is Monge.
4. 4Choose the Scale, from 10 to 50 (default 15). The scale sets how large the units are drawn on the sheet.
5. 5Click create. The sheet appears in your list, ready to open.

Each sheet in the list is shown as a card. Use the search box (Search sheets...) to filter by name.

• Click New folder to create one. Folders have a single level (no subfolders) and names of 1 to 60 characters; you can have up to 50.
• Drag an exercise onto a folder to file it there, or use Move to folder… from the card menu. Moves are instant.
• Exercises without a folder are listed under Unfiled exercises.
• Use Rename and Delete from the folder's menu. A folder can only be deleted when it is empty: move its exercises out first.

Discover (Explore Public Sheets) lists every sheet that its owner has made public. Search with Search public sheets... and open any of them in view-only mode. Discover is available to every signed-in user, including Free accounts.

Only the owner of a sheet can edit it, duplicate it, or make it public. Anyone else who opens a sheet's link is sent to its view-only page.

You can open a sheet in view-only mode when you are signed in and at least one of these is true:

• the sheet is public;
• the sheet was shared with a team you belong to;
• you are an administrator.

In view-only mode you can pan and zoom the drawing, rotate the 3D view, change the camera, switch view mode, print, move between steps and read each step's note (View Note). Drawing tools and the auxiliary toolbar (except Reset Camera) are hidden. If you don't have access, you will see Sheet Not Available.

On Free and Premium, the My Teams page shows Create Teams - Classroom Feature with an Upgrade to Create button.

1. 1Go to Dashboard → My Teams and create a team (Classroom plan).
2. 2Give it a name, for example your class name.
3. 3Open the team to invite members, add folders and share exercises.

Invite link

Click Copy invite link and send it to your students. Opening the link asks them to sign in (or create an account) and then adds them to the team. As the owner you can regenerate the code at any time, which invalidates the old link.

Add by email

Enter a member's email address. They receive an invitation and accept or decline it under Team Invitations in their My Teams page.

• From a sheet card, choose Share and pick the team. Only your own sheets can be shared, and only on Premium or Classroom.
• Team members see shared exercises in the team page and open them in view-only mode. Use Search exercises... and Filter by author to find them; the page shows "Showing X of Y exercises".
• To stop sharing, use Remove from team. A member can remove their own exercises; the owner can remove any.
• The owner can organise shared exercises in team folders (create, rename, delete, move exercises).

• Only the owner sees the member list and can Remove member.
• Members can Leave team at any time. Their shared exercises leave the team with them, and they lose access to the team's exercises unless another of their teams shares the same sheet.
• The owner can Delete Team. This removes the team and its sharing; members' own sheets are not deleted.

Settings customise how coordinates, folding and points are displayed. Signed in, they are saved to your account and follow you on every device; as a guest, they are kept in this browser.

Click Print and choose Both views (3D + Drawing), 3D view only or Drawing view only. Pressing Ctrl+P (Cmd+P on Mac) prints what is currently on screen, following the view mode. To keep a digital copy, choose "Save as PDF" in your browser's print dialog.

On small screens GMT is best used to view exercises: the toolbox, the auxiliary toolbar and step creation are hidden, the view mode becomes a single toggle between 3D and Monge, and the camera type selector is hidden. To draw, use a computer with a mouse.

When an action is not possible, GMT explains why in a GMT Error dialog with a numbered code, for example "Horizontal and Frontal planes are not foldable." Read the message, fix the input, and try again. If you think the message is wrong, report it with Report a Bug and include the code.

The 3D view (left window) reconstructs in space everything you draw on the sheet. As soon as an element has the projections it needs (for example both projections of a point, or two traces of a plane), it appears in 3D.

Reset Camera

Returns the camera to its initial position.

Camera type

Perspective (default), Axonometric, Horizontal (seen from above) or Frontal (seen from the front).

Auto-Rotate (360°)

Press Ctrl+Shift+R to rotate the scene once around itself, a handy way to present a construction.

What the 3D view shows is controlled in Settings: labels, the odd and even bisector planes, the profile reference plane, and whether projections are drawn or only the 3D geometry.

• The horizontal line across the sheet is the x axis (ground line). Positions along it are the abscissa.
• Each point is described by three coordinates, written A(abscissa; distance; height). For example A(3; 4; 5).
• A horizontal projection (index 1, e.g. A₁) shows the distance; a frontal projection (index 2, e.g. A₂) shows the height.
• Points use capital letters (A–Z), lines use lowercase letters (a–z), and planes use Greek letters (α–ω).
• Plane traces are named after the plane and the projection: hα (horizontal trace) and fα (frontal trace).
• By default negative abscissas are on the right; change it in Settings.

• Zoom: scroll the mouse wheel over the sheet.
• Pan: with the View Tool, drag the sheet with the left mouse button.
• Reset Camera (auxiliary toolbar) brings the sheet back to its initial position.

Precise Mode in the auxiliary toolbar sets how positions are rounded when you click. Click it to cycle through:

• Unit Precision: whole units (1, 2, 3...).
• Decimal Precision: one decimal place (2.5).
• Centesimal Precision: two decimal places (2.45).

Snapping: hold Shift while using the Point, Line, Folding or Pencil tools. On the first click the abscissa snaps to existing points; afterwards the cursor snaps to the nearest intersection. The options panel reminds you: "Hold SHIFT for snapping".

In the Name dropdowns, names already used in the sheet are marked Already in sheet, so you can see at a glance which projection is still missing. A name that is already complete (for example a point with both projections) is disabled, so you can't create a duplicate by mistake.

The default tool. Use it to look around and to change how elements look.

• Zoom with the mouse wheel and pan by dragging the sheet.
• Move labels: drag any name (or text) to a clearer position.
• Edit style: click a projection, segment or shape to open its style panel.

Creates point projections, and lines that appear as a single point on the sheet (vertical lines and top/end lines).

1. 1Free Mode on: click on the x axis to choose the abscissa, then click again to choose the distance (horizontal) or height (frontal).
2. 2Free Mode off: click an existing line or segment, then click to choose where on it the projection goes.

Line mode (R) is for lines whose projection on the sheet is a single point: a vertical line (its horizontal projection is a point) or a top (end) line (its frontal projection is a point). Draw the other projection with the Line Tool, perpendicular to the x axis, then place the point projection with the Point Tool.

Associations tie a point to a line or a plane. A profile line can't be defined by its projections alone, because p₁ and p₂ coincide, perpendicular to the x axis. Associate two of its points with it and GMT builds the line in space.

Creates line projections and plane traces.

1. 1Free Mode on: click the first point, then the second point. The line or trace passes through both.
2. 2Free Mode off: click an existing line, segment or trace, then click to place the parallel or perpendicular.

Creates segments, curves and circumferences between existing projections.

Straight segment

Click a point projection, then another. A preview follows the cursor between the two clicks. Use it for edges of figures, e.g. segment AB or triangle ABC.

Curved segment

Click an existing segment to show its two control points. Drag them to bend the segment, then click a third time to confirm. Useful for ellipses, e.g. a profile ellipse joining folded points.

Circumference or arc

Click a point projection (or a folded point) twice to use it as the centre. Then click to set the radius, the start angle and the end angle. Matching start and end draws a full circle; otherwise an arc. Toggle Clockwise with H while drawing the arc. Depending on the plane, the circumference projects as a circle, an ellipse or a segment, and is also built in 3D.

Fills a closed area to show sections and shadows. First choose the Texture:

• Stripe: hatched fill, for sections.
• Projected Shadow: light grey fill.
• Own Shadow: dark grey fill.

Then click a starting point and select, one after another, the segments that close the outline.

Draws construction lines in grey pencil. They exist only on the sheet and are never mapped to 3D, exactly like the light lines you draw by hand.

1. 1Segment, free: two clicks define the guiding line, then two more clicks set where the pencil segment starts and ends.
2. 2Segment, parallel/perpendicular: click the reference element, move the preview line into place and click, then click the start and end of the segment.
3. 3Compass: click the centre, then click two points to draw the arc.

Folds points onto a projection plane (rabattement) and unfolds folded points and lines back into their projections.

1. 1Choose the mode.
2. 2Click the plane trace to use as the folding axis (hinge). The plane must be complete: its other trace must also be on the sheet.
3. 3The first time you fold through a trace, choose the fold direction: Clockwise or Counter-clockwise. The choice is remembered for every later fold through that trace.
4. 4Folding: click either projection of a complete point (it needs both projections). Unfolding Point: click where the folded point goes. Unfolding Line: click two points of the folded line.

• Works with profile, top (end), vertical, ramp, passerby and oblique planes.
• Horizontal and frontal planes can't be folded: "Horizontal and Frontal planes are not foldable."
• If several traces or points overlap where you click, a Select Folding Axis or Select Point dialog lets you choose.
• You can unfold a line onto a matching profile line.

• Click an empty area of the sheet to Add Text, or click existing text to Edit Text.
• The Symbols palette inserts special characters: Greek letters, Operators (≡ ⊥ ∥ ∠ ...) and Marks (′ ″ ₁ ₂ ...).
• Move text with the View Tool and remove it with the Delete Tool.

• Click any element to delete it. Whatever was built from it in 3D is updated too: deleting one projection of a point removes the point from the 3D view.
• Point and line projections, plane traces and folded elements ask for confirmation (Delete Confirmation).
• If several elements overlap where you click, choose which one in "Select which object to delete:".

My point doesn't appear in 3D.

A point appears in 3D only when it has both projections with the same name (e.g. A₁ and A₂). Check the Name dropdown: a name with only one projection is marked Already in sheet but can still be selected to add the missing one.

I can't fold through a plane.

The plane must have both traces on the sheet, and it can't be horizontal or frontal. Also check the point you are folding has both projections.

My sandbox work disappeared.

As a guest, the sandbox isn't saved. Sign in before you start, then use Save to Sheet to keep work as an exercise.

I can't edit a sheet someone shared with me.

Only the owner can edit a sheet. Shared and public sheets open in view-only mode, where you can still rotate the 3D view, follow the steps, read the notes and print.

I can't create a sheet.

Creating sheets requires Premium or Classroom, and you may have reached your plan's sheet limit. Check the counter in My Exercises.

The toolbox is missing.

Drawing tools are hidden on small screens and in view-only sheets. Use a computer, and make sure you are the sheet's owner.

• Tutorial Video in the editor, for the selected tool.
• FAQs for questions about the platform.
• Changelog for what's new.
• Report a Bug from the editor (Premium and Classroom).