Ptolemy's map graticule
Latitude and longitude curved and unevenly spaced on the projection — the original non-uniform grid, shaped to manage distortion.
Basic drawing · user-placed lines · adaptive density
Custom grid — put the detail where the subject needs it
Detail is never spread evenly across a subject, so why should the grid be? The custom grid lets you place every line by hand — packed tight over the eyes, the maker's mark, the tangle of rigging, and left wide open across the empty background. It is the grid-method freed from the rule that every cell be equal, and the same idea that lets a world map space its meridians unevenly to manage distortion. Here is how adaptive density works, where it comes from, and when a bespoke grid beats a uniform one.
- Documented principle
- Ptolemy's graticule (~150 CE)
- Structure
- User-defined divisions
- Origin culture
- Cartography → drawing
- Difficulty
- Intermediate
- Best for
- Uneven detail
- Also known as
- Adaptive grid, freeform grid
See an adaptive grid on five subject categories
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On a portrait the lines crowd around the eyes, nose, and mouth where the likeness lives, and spread wide across the forehead, hair, and background — accuracy concentrated exactly where the subject demands it.
What the overlay shows
The custom grid overlay draws lines wherever you place them. Columns can be different widths and rows different heights, so the field is a mesh of unequal cells — dense where you packed the lines, open where you left them apart. The point is adaptive density: fine cells over the detailed, accuracy-critical parts of a subject, coarse cells over the simple parts that need almost no measuring. This is selective density through manual line placement — a freeform grid overlay rather than the fixed mesh of a uniform generator, with detail where it is needed and nowhere else.
In Grid Maker Pro you add, drag, and remove individual lines, and the tool records each line's exact relative position so the same configuration can be reproduced on the canvas. You can start from a uniform grid and add a few targeted lines, or build a fully bespoke mesh from scratch. The square and rectangular grids are just the even-spaced special cases of this overlay.
The math, briefly
Proportional transfer does not actually require equal cells — it requires matched relative positions. A line at fraction f of the reference width must sit at the same fraction f of the canvas width:
line_canvas = f × W_canvas for each line's fraction f
Three things follow from relaxing the equal-cell rule:
- Density can vary freely. Cluster lines at f = 0.42, 0.46, 0.50 across an eye and the cells there are tiny and forgiving; a single line at f = 0.85 leaves the background as one big easy cell.
- Proportion is per-line, not per-cell. As long as each fraction is reproduced exactly, every feature lands correctly regardless of its neighbours' spacing — which is why an irregular grid is just as accurate as a regular one.
- Uniform grids are the special case. Space the fractions evenly (1/N, 2/N, ...) and you have the square or rectangular grid. The custom grid is the general form they specialise.
The discipline shifts from counting cells to recording positions. Build a grid in the live tool — it stores each line's fraction so the reference and canvas match exactly.
History — what is real and what is myth
Verified history (with primary sources)
c. 150 CE — Ptolemy's graticule. The Geographia laid a coordinate net of latitude and longitude over the known world and gave instructions for projecting it onto a plane.1 On Ptolemy's conic projection — and on nearly every projection since — the graticule is deliberately non-uniform: meridians and parallels space out unevenly to manage the unavoidable distortion of flattening a sphere. The adaptive grid is, at root, a cartographer's idea.
Map projection as managed distortion. John Snyder's Flattening the Earth traces two thousand years of projections, each choosing where to concentrate and where to relax the graticule to preserve area, angle, or distance.2 Matthew Edney's Cartography frames the grid itself as a designed instrument rather than a neutral net.3 The lesson transfers directly to drawing: a grid is a tool you shape to the job.
Selective construction in drawing. Measured drawing never depended on a full uniform mesh. Dürer's measurement treatise builds figures from a few decisive construction lines rather than an even grid,4 and Harold Speed's The Practice and Science of Drawing teaches placing a small number of key lines exactly where structure demands them.5 The custom grid formalises that instinct — lines where they earn their place.
Proportional armatures. Charles Bouleau's The Painter's Secret Geometry reveals the non-uniform "armatures" — diagonals and unequal divisions — underlying Old Master compositions, grids that are anything but evenly spaced.7 Jay Hambidge's dynamic symmetry likewise subdivides the picture by proportion rather than equal intervals.8
Data density. Edward Tufte's principle that reference structure should serve the information, not clutter it, is the same idea in another field: put the grid where the data is and strip it where it is not.6
Claims that need qualifying
"An irregular grid is less accurate." False. Accuracy depends on matching each line's relative position, not on equal spacing. A custom grid is exactly as faithful as a uniform one — it just spends its lines more wisely.
"Custom grids are improvised and unrepeatable." Only without records. Note each line's fraction (or let the tool store it) and the grid is as reproducible as any other — the same configuration redrawn on the canvas every time.
"More lines always means more accuracy." No. Lines over a flat background cost effort and return nothing. Accuracy comes from putting lines where the detail is, not from sheer line count.
When to use it (and when not)
| If you want to... | Use the custom grid | Don't use it for... | Difficulty |
|---|---|---|---|
| Draw a subject with very uneven detail | Dense cells on the face or mark, sparse cells on the empty areas | Subjects with even detail (a uniform grid is simpler) | Intermediate |
| Nail one critical area precisely | Add a cluster of lines through the eyeline, profile, or key edge | Whole-image proportion only (start from a uniform grid) | Beginner |
| Keep a drawing fast outside the focal point | Coarse cells everywhere except where accuracy pays off | Work where every region matters equally | Intermediate |
| Add targeted lines to an even grid | Hybrid: coarse uniform base plus a few bespoke lines | Quick rough transfers (plain grid is enough) | Beginner |
| Subdivide by proportion, not equal intervals | Place lines on φ, thirds, or armature divisions | Mechanical equal-step transfer (use N×N) | Advanced |
Famous examples with the overlay applied
Six places where non-uniform, purpose-placed grid lines are the working idea.
Portrait detail mesh
Lines crowding the eye–nose–mouth triangle and spreading across the forehead — the likeness gets the cells, the simple areas do not.
Botanical & technical illustration
Fine lines through the seed head or mechanism, sparse lines through the stem or housing — density follows the intricacy.
Compositional armature
Diagonals and φ divisions rather than equal intervals — a non-uniform grid that organises a composition by proportion.
Hybrid grid with added lines
A coarse uniform base (solid) plus a few targeted lines (dashed) dropped through the critical area — proportion plus precision.
Data-driven reference lines
Reference lines placed only where they aid reading and stripped everywhere else — the custom grid's logic applied to information design.
Common mistakes
1
Not recording the line positions
A bespoke grid you cannot reproduce on the canvas is useless — without the exact positions, the second grid will not match the first and the transfer drifts.
Fix: note each line's fraction (or let the tool store it) and reproduce those exact positions on the canvas before copying.
2
Adding lines for their own sake
Packing lines across a flat background adds bookkeeping and returns no accuracy — the grid gets cluttered without getting better.
Fix: spend lines only where the detail is. A simple region deserves a single big cell, not a fine mesh.
3
Using a custom grid when a uniform one would do
For evenly detailed subjects, irregular spacing is just extra effort with no payoff — the variable lines slow the work and invite position errors.
Fix: default to a square or rectangular grid, and reach for the custom grid only when the detail is genuinely uneven.
4
Losing the overall proportion in the detail
A grid that is all dense detail-cells and no large-scale lines can nail the eyes while letting the whole head drift too big or off-centre.
Fix: always keep a few coarse lines spanning the whole frame to lock the big proportions before refining the detail zones.
How different disciplines use it
For illustrators
Illustration is full of uneven detail — an intricate face on a plain background, a detailed product against negative space, a busy logo in an empty field. The custom grid puts fine cells exactly where the accuracy matters and leaves the rest fast, which is faster overall than a uniform grid dense enough for the hardest area. It is also ideal for keeping one critical element on-model while drawing everything around it loosely.
For cartographers & technical artists
This is where non-uniform grids originate. Map graticules space their meridians and parallels to manage projection distortion, and technical illustrators apply the same logic to mechanical and scientific subjects — fine reference lines through the working parts, coarse lines through the housing. The grid is treated as a designed instrument, shaped to the information, exactly as a projection is chosen for its purpose.
For painters
Painters use custom lines two ways. First, adaptive density: cluster lines through the head and hands of a figure, leave the drapery and ground sparse. Second, proportional armatures: place lines on the diagonals, thirds, or φ divisions that organise the composition, rather than on equal intervals. Both treat the grid as a thinking tool about where structure and accuracy actually live in the picture.
For students
The custom grid teaches the deepest lesson of the grid-method: that proportion lives in the line positions, not in equal cells. Once a student sees that an irregular grid is just as accurate as a regular one — and that uniform grids are merely the even-spaced special case — the whole family of transfer grids clicks into place. It is also a gentle first encounter with the idea, central to mapmaking, that a grid is something you design.
"Above all else show the data. ... Maximize the data-ink ratio, within reason. Erase non-data-ink, within reason."
Edward Tufte, The Visual Display of Quantitative Information (1983)6
Frequently asked questions
What is a custom grid?
A grid whose lines you place yourself rather than spacing them evenly. Columns and rows can be different widths, and you can pack lines densely over the detailed parts of a subject and leave them sparse over the simple parts. It is the grid-method freed from the requirement that every cell be the same size.
Why would I want unequal cells?
Because detail is rarely spread evenly. A portrait is intricate around the eyes and mouth and simple across the forehead and background. A custom grid puts fine cells exactly where accuracy matters — the face, a maker's mark, a tangle of rigging — without wasting a dense grid on the empty areas, keeping the rest fast and loose.
Does a non-uniform grid still keep proportion?
Yes, as long as you reproduce the same fractional line positions on both surfaces. Proportional transfer depends on each line sitting at the same relative position on the reference and the canvas, not on the cells being equal. A line at 30% of the width transfers a feature accurately whether or not the neighbouring lines are evenly spaced.
How is it different from a square or rectangular grid?
Square and rectangular grids use uniform cells — every column the same width, every row the same height. A custom grid drops that constraint: line spacing varies to match the subject. The square and rectangular grids are special cases of the custom grid where you happen to space the lines evenly.
Where does the idea of a non-uniform grid come from?
From cartography. Ptolemy's Geographia (c. 150 CE) laid latitude and longitude over the known world as a graticule, and on most map projections that graticule is deliberately non-uniform — meridians and parallels space out unevenly to manage the distortion of flattening a sphere. The custom grid applies the same idea to a drawing.
When should I not use a custom grid?
When the subject's detail is fairly even, a uniform square or rectangular grid is simpler and less error-prone — there is no benefit to varying the spacing and the irregular lines just add bookkeeping. Reserve the custom grid for subjects with strongly uneven detail, or for adding a few targeted lines to an otherwise uniform grid.
Can I add custom lines to a uniform grid?
Yes, and it is often the best of both worlds: keep a coarse even grid for the overall proportions, then drop a few extra lines through a critical area — across the eyeline, down a profile, along a key edge — so the hard part gets the accuracy it needs without re-gridding the whole image.
Is a custom grid harder to keep aligned?
It takes a little more care, because you cannot rely on even counting — you have to reproduce the actual line positions. Labelling each line with its position (a tick at 30%, 55%, 70%) and copying those exactly to the canvas keeps it reliable. Grid Maker Pro stores the positions so the reference and canvas grids match.
How do I make a non-uniform grid for drawing?
Start from the subject, not from a fixed number of cells. Add a few coarse lines across the whole frame to hold the big proportions, then drop a tighter grid on the faces and other detailed areas — a denser cluster of lines only where there is detail. Leave plain regions as large cells. In the live tool you place each line by hand, drag it where the detail is, and the tool records its relative position so you can reproduce the same variable-density grid on your canvas.
References
- Ptolemy, C. Geographia. (c. 150 CE). Translation & commentary: Berggren, J.L. & Jones, A., Ptolemy's Geography, Princeton University Press (2000). ISBN 0-691-01042-0.
- Snyder, J.P. Flattening the Earth: Two Thousand Years of Map Projections. University of Chicago Press (1993). ISBN 0-226-76747-7.
- Edney, M.H. Cartography: The Ideal and Its History. University of Chicago Press (2019). ISBN 978-0-226-60568-1.
- Dürer, A. Underweysung der Messung. Nuremberg (1525). Facsimile: Strauss, W.L. (ed.), The Painter's Manual, Abaris (1977). ISBN 0-913870-26-9.
- Speed, H. The Practice and Science of Drawing. Seeley, Service & Co. (1913). Dover reprint (1972). ISBN 0-486-22870-3.
- Tufte, E.R. The Visual Display of Quantitative Information. Graphics Press (1983; 2nd ed. 2001). ISBN 0-9613921-4-2.
- Bouleau, C. The Painter's Secret Geometry: A Study of Composition in Art. Harcourt, Brace & World (1963). Dover reprint (2014). ISBN 978-0-486-78040-7.
- Hambidge, J. The Elements of Dynamic Symmetry. Yale University Press (1920). Dover reprint (1967). ISBN 0-486-21776-0.
Other Basic Drawing Grids
Notes from the studio · Practitioners on the custom grid
Illustrative composites of how the tool gets used in practice — not quotes from named individuals.
Five lines through the eyes, one across the whole head. The face gets the measuring and the background gets none — that's the whole trick.
A technical drawing is mostly empty housing and a few critical parts. I grid the parts and ignore the rest.
I teach it last, because once students see that proportion is in the positions and not the equal squares, every grid finally makes sense.
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