01
Piping & Instrumentation Isometrics (P&ID)
Drafting chemical and process piping spools with precise 30° skew angles, weld locations, and fitting elevations.
工学・技術用方眼紙
等角投影紙 (アイソメ)
立体図面、配管図、3Dゲームマップ
A4 Portrait · 210 × 297 mm
100%
正確な1:1物理スケール。印刷後50mm校正枠をご確認ください。
CSS: 96 DPIセクション 02 — 数学的原理と幾何標準
幾何学的基礎と座標計算式
60° Equilateral Rhombic Geometry
Isometric projection represents 3-dimensional objects on a 2D plane by foreshortening all three principal axes equally at 120° angles to one another. The grid consists of vertical lines (90°) intersected by parallel diagonals inclined at +30° and -30° from the horizontal.
計算式:
h = s · sin(60°) = s · (√3 / 2) ≈ 0.866025 · s; θ ∈ {30°, 90°, 150°}歴史的起源と科学の進展
Isometric projection was formalized in 1822 by Professor William Farish of Cambridge University. Farish recognized that mechanical engineers needed an optical drawing method that preserved measurable linear scale along all three axes without perspective foreshortening.
GraphPages.com では、すべてのベクター描画処理がブラウザ内で直接実行されるため、用紙余白や目盛りの寸法精度が 0.05 mm 以内に保たれます。
セクション 03 — 分野別活用シーン
産業・学術分野における実務応用
02
Exploded Assembly CAD Drawings
Illustrating mechanical disassembly sequences, bolt patterns, and internal sub-assemblies with measurable 1:1 scale.
03
Tabletop RPG Dungeon & Battle Maps
Mapping multi-level isometric dungeons, cliffside terrain, and three-dimensional castle interiors for gaming campaigns.
04
2.5D Pixel Art & Architectural Mockups
Constructing pixel-perfect retro game environments, building cutaways, and modular furniture prototypes.
セクション 04 — 作図・プロットガイド
等角投影紙 (アイソメ) でのステップ別作図手順
ステップ 01
Orient the Isometric Axes
Identify the three primary axis directions: vertical for height (Z), +30° right for length (X), and +30° left for width (Y).
ステップ 02
Construct the Bounding Box
Draw the overall envelope of your object along the primary isometric lines using direct measurement increments.
ステップ 03
Plot Non-Isometric Lines via Offsets
Non-isometric edges (such as roof slopes or bevels) cannot be measured directly. Locate their endpoints along isometric lines, then connect them.
ステップ 04
Draft Isometric Circles (Ellipses)
Construct circles on isometric planes using the four-center rhombus approximation method or isometric ellipse guides.
セクション 05 — プリンター校正ガイド
プリンター設定と実寸検証ガイド
100% 実寸印刷の正確性を保証するために
Physical millimeter spacing applies along all three axis directions. Verify that the distance between vertical lines matches your selected spacing using a ruler.
- 印刷ダイアログで「倍率：100%」または「実際のサイズ」を選択してください。
- 「用紙に合わせる」などの自動縮小設定を必ずオフにしてください。
- 余白に印刷された 50 mm 校正バーを定規で測り、正確性を確認してください。
セクション 06 — よくあるご質問
よくあるご質問 (FAQ)
What is the difference between isometric and trimetric grid?
In an isometric grid, all three coordinate axes are spaced at 120° and scaled equally (1:1:1). In dimetric and trimetric projections, axes use differing angles and scale factors to accentuate specific viewports.
Can I sketch directly on this isometric grid online?
Yes! Click 'Open in Virtual Studio' to draw 3D diagrams directly in your browser with line angle locking and vector SVG export.
What spacing is recommended for isometric paper?
5 mm spacing is the international standard for mechanical engineering notes and student drafting. 10 mm spacing is ideal for larger architectural models.
How are circles drawn on isometric paper?
Circles project as ellipses with an aspect ratio of approximately 1.732 : 1. They are drawn using a 4-center circular arc approximation inside an isometric rhombus.
仮想スタジオで開く — 等角投影紙 (アイソメ)
ブラウザ上でこの方眼紙に直接ダイアグラムを描いたり、座標をマークしたり、図形を描画できます。