# Spirograph Open **Path / graph dropdown → Spirograph**. The green support and blue insert are temporary translucent apparatus above the canvas. Their parts never enter an image export. ## Pegs and media 1. Choose a guide and an insert. The menus beneath their trays open the full illustrated catalogs; their captions identify the current parts. 2. Drag a Fine (1 px), Medium (2 px), or Bold (4 px) peg into an empty socket. 3. Choose **Fill pegs**. Click the peg for Primary ink or right-click for Alt. No Color empties it. Empty sockets cannot hold ink. 4. Choose **Operate**, then click a seated peg. Its gold outline identifies it as the target for **Peg medium** and the ordinary **Materials** gallery. 5. Choose a medium. Each peg keeps its own ink, width, material settings, and miniature stroke preview in its cap. Brush assignment does not draw. 6. Drag the insert's center grip. Every loaded peg draws with its own medium. For precise placement without dragging, open **Choose hole**. Each numbered entry says whether it will **Place fine peg** in an empty hole or **Select peg** already there. Selecting an occupied hole keeps its ink, width and medium. Use **Load Primary** or **Load Alt** to fill the selected peg directly; No Color empties its ink while leaving the peg seated. Activate Fine, Medium or Bold with the keyboard or an accessibility action to change its width. These setup controls do not mark the canvas. Hole numbers run from the outside inward on the circular kit wheels. Their positions are approximate, so instruction-book patterns will be visually similar rather than exact reproductions. All thirteen additive media are available, including Gel pen, Watercolor, Marker, Natural pencil, Crayon, Oil, and Airbrush. These use the same stroke renderers as freehand brushes. Pixel-mixing and cloning tools are not ink media. Gel pen has a solid body, gently varying brightness, and sparse glints. Its material texture remains fixed during a stroke; extra mouse events do not add extra coats. Grain scale changes the variation scale and Paper tooth changes the amount of sheen. Paint load zero deposits nothing. A click selects a peg; moving more than four screen pixels starts a peg drag. Drop it in another socket to move it, or outside the insert to remove it. An invalid drop within the insert restores the original socket. Escape cancels a move. **Deselect peg** returns material choices to the ordinary drawing tool; clicking away from the apparatus also clears peg selection. Drag the green support to reposition the assembly without drawing. **Center guide** returns it to the image center. Removing or replacing an insert clears its pegs, materials, and selection. The raised red close button removes the apparatus while keeping the drawing. Each continuous operation is one Undo step, including all loaded pegs. Drawing respects the active canvas selection, regular guide constraints, and rotated working view. Use the ribbon's **Scale** field or drag the gold square on the support's lower right to enlarge or shrink the apparatus relative to the paper. The scale field accepts values from 0.05 to 64 and remains available to keyboard and accessibility tools. Resizing keeps the center, rolling phase and loaded pegs; pen widths remain in image pixels. It does not resize existing marks or add an Undo step. Canvas zoom remains independent of apparatus scale. Escape during a support move or resize restores the position or size from before that gesture, including the Scale field. Choose **Lift wheel** to pick up the insert without drawing. Drag its center grip or an empty part of its body anywhere on the paper. The wheel keeps its current rotation and loaded pens; the guide stays in place. An amber outline means the wheel is off the track, and **Operate** is disabled. Bring it within 12 screen pixels of a valid contact position to seat it on the current ring or rack. **Escape** during a drag restores the previous placement, including an off-track position. Choose **Operate** after seating to roll and draw again. The next stroke starts at the new location without a connecting line from the old one, and remains a separate Undo step. Moving or resizing the support carries an attached wheel without drawing; only deliberate rolling deposits ink. ## Component catalog The catalog includes 18 guides and 32 inserts. The ribbon starts with the two paired rings and circular wheels 40, 63 and 48; wheel 63 is initially inserted. - Paired rings: 144/96 and 150/105, named with outer/inner tooth counts. These reproduce the Deluxe kit's two circular pitch-track ratios. Both toothed edges are visible; the active edge is darker. Switching **Roll outside** changes the contact track without resizing the physical ring. - Additional rings: 120, 144, 180, 210, and 240 teeth. - Shaped guides: oval, long oval, rounded triangle, square, pentagon, hexagon, egg, and shield. - Rack 150: a closed capsule with straight sides and rounded ends. Wheels roll around its full 150-tooth perimeter. Its proportions are approximate: the rounded-end pitch radius uses 25 tooth-radius units. The original standard and long straight supports remain available with travel limits. - Deluxe circular inserts: 24, 30, 32, 40, 42, 45, 48, 52, 56, 60, 63, 72, 75, 80 and 84 teeth. They have respectively 5, 8, 9, 13, 14, 16, 17, 19, 21, 23, 25, 29, 31, 33 and 35 holes in approximate inward spirals. Every hole can hold an independent pen; the numbered menu uses columns so even the largest wheel remains within the window at the standard ribbon size. - Additional circular inserts: 12, 18, 31, 36, 37 and 64 teeth; the prime counts support longer repeating patterns. - Bar 40: an approximate rounded rectangular wheel with nine holes and a 40-tooth perimeter. It produces 12-fold repetition in the 96-tooth ring and 21-fold repetition in the 105-tooth ring. The outline and hole positions are approximate; they are not measured molded-part dimensions. - Eye 60: a lens-shaped wheel with rounded tips and 13 approximate holes. Its 60-tooth perimeter gives eight repeats in the 96-tooth ring and seven in the 105-tooth ring, matching the kit pattern chart. The outline uses circular side arcs joined to smaller tip arcs; dimensions are approximate. - Triangle 54: an approximate rounded, unequal triangle with 12 holes, following the manufacturer’s illustrated layout. Its 54-tooth perimeter produces 16 repeats in ring 96 and 35 in ring 105. The older experimental Triangle 42 remains available separately. - Shaped inserts: oval, long oval, rounded triangle, square, pentagon, hexagon, egg, and shield. Each has its own socket arrangement. - Quad 60: a four-armed wheel with concave cutouts and ten approximate holes. It rolls along each rounded tip, then pivots between adjacent tip endpoints. It currently supports the inner 96- and 105-tooth kit rings, producing eight and seven repeats. Its fitted size changes by approximately 0.27% between those rings to match the repeating patterns; this is an approximation rather than a measured molded part. Other guides and outside rolling are disabled for this wheel. **Roll outside** places the insert against the outside of a closed guide, producing a different family of curves. Rack 150 always rolls outside; its outside control is selected and disabled. The older straight racks roll along a bounded segment. Inside combinations are conservatively checked for curvature clearance; incompatible parts are disabled. Returning from outside to inside requires a compatible pair. Changing the guide preserves its approximate displayed size by rescaling the entire apparatus, including the insert. ## Contact model Most shaped rings and inserts use a support function `h(n) = 1 + sum(a[k] cos(k*n))`, with positive curvature radius `h + h''`. Its boundary is `h*n + h'*t`; its arc length has an analytic integral. An invertible arc map matches the distances traveled on the guide and insert, then aligns their contact normals. This determines both translation and rotation, including asymmetric shapes. Circles use the exact familiar radius ratio as a fast path. The straight racks match arc length against a line. Rack 150 uses distance around a capsule as its phase: its contact normal stays constant along each straight side and turns continuously around the rounded ends. Matching arc length gives continuous rolling and supports lifting with the wheel's rotation held fixed. The Bar, Eye and Triangle 54 use joined circular arcs for their sides and rounded corners. Their tangents stay continuous at each join, and their positive curvature permits exact arc inversion. The same contact model therefore supports both rolling and lifting. Compatibility and pen subdivision use bounds from the selected profile, including their tighter corners. Quad uses a separate continuous pose parameter through rolling and pivoting. At the middle of a pivot interval both adjacent endpoints touch the ring; the supporting endpoint changes without a jump in wheel position or rotation. Lifting solves for the same rotation at the new placement. Concave cutouts remain empty in both the rendered outline and pointer hit testing. Integer tooth counts fix the perimeter ratio, so closed-guide patterns return to their initial pose after `insert_teeth / gcd(guide_teeth, insert_teeth)` guide circuits. The tooth marks visualize the pitch geometry; there is no rigid-body collision simulation or accumulating integration slip. These are original smooth pitch profiles, not reproductions of commercial molded parts. The paired circular ring counts follow the [Deluxe guide](https://www.worldbrands.es/wp-content/uploads/80977_SpirographDeluxeGuide_V2_esp_ONLINE_O_LOW_compressed.pdf). Circular tooth and hole counts follow the illustrated kit and this [firsthand inventory of a Deluxe set](https://spirographicart.com/2014/05/02/chart-spirograph-wheels-rings/). The spiral socket coordinates are an approximation, not measurements of the molded pieces. The Bar, Eye and Triangle 54 follow visually close approximations with verified contact and repetition. Quad uses the guide-dependent approximation described above; other experimental profiles remain distinct from the kit. The capsule rack's width has not been measured from a physical part; the catalog is not yet a complete Deluxe replica. Pen subdivision is bounded to half an image pixel by a curvature-dependent speed bound. Per-peg stroke state preserves continuous deposition across mouse events. Sparse transparent coats are composited in socket order, with higher numbered sockets above lower ones at crossings. One scratch bitmap is shared among all pegs; the temporary coats and bitmap are released after each drag. The nearest center-path position is projected near the previous phase; this avoids substituting a circular orbit for a noncircular piece. ## Geometry references The physical kits informed the range of mechanisms, not the code or drawings: - [Wild Gears Compact set](https://www.wildgears.com/compact-gear-set.html): circular and noncircular gears, varied socket sizes, and component reuse. - [Wild Gears Oval set](https://www.wildgears.com/oval-gear-set.html): oval inserts and frames with different symmetries. - [Wild Gears Modular Oblong set](https://shop.wildgears.com/products/modular-oblong-gear-set): racks and oblong supports. - [PlayMonster Art Studio instructions](https://playmonster.com/wp-content/uploads/2021/10/artstudio-instructions.pdf): rack use and outside rolling. - [Firsthand Bar wheel demonstration](https://spirographicart.com/2016/06/05/intro-bar-wheel/): 12-point and 21-point repetition in the two kit rings, matching wheel 40. - [Manufacturer pattern guide](https://www.worldbrands.es/wp-content/uploads/80979_Spirograph-Guide_v2_EN_COMPLETE_compressed.pdf): page 7 shows eight and seven repeats for the Eye in the 96- and 105-tooth rings. A 60-tooth perimeter is inferred from these two repetition counts; the guide does not print a tooth count on the Eye. Its Triangle examples show 16 and 35 repeats, consistent with the implemented 54-tooth perimeter. The illustrated Triangle has 12 holes and the instructions use hole 11; this differs from the 10 holes listed in the older firsthand inventory. Nested independently moving inserts, concave tracks, and modular track assembly remain possible extensions requiring additional motion constraints.