01
Piping & Instrumentation Isometrics (P&ID)
Drafting chemical and process piping spools with precise 30° skew angles, weld locations, and fitting elevations.
Kertas Teknikal & Kejuruteraan
Kertas Isometrik
Lukisan 3D, paip & pemetaan permainan
A4 Portrait · 210 × 297 mm
100%
Skala fizikal 1:1 sebenar. Ukur kotak penentukuran 50 mm pada cetakan.
CSS: 96 DPIBahagian 02 — Prinsip Matematik
Asas Geometri dan Formula Koordinat
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.
Formula:
h = s · sin(60°) = s · (√3 / 2) ≈ 0.866025 · s; θ ∈ {30°, 90°, 150°}Asal-usul Sejarah & Evolusi Saintifik
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.
Di GraphPages.com, semua operasi vektor diproses terus dalam pelayar anda tanpa mampatan pelayan, menjamin ketepatan ukuran fizikal dan margin sehingga 0.05 mm.
Bahagian 03 — Kegunaan Praktikal
Aplikasi Sebenar Merentasi Industri
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.
Bahagian 04 — Tutorial Melakar
Panduan Langkah demi Langkah Melakar pada Kertas Isometrik
LANGKAH 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).
LANGKAH 02
Construct the Bounding Box
Draw the overall envelope of your object along the primary isometric lines using direct measurement increments.
LANGKAH 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.
LANGKAH 04
Draft Isometric Circles (Ellipses)
Construct circles on isometric planes using the four-center rhombus approximation method or isometric ellipse guides.
Bahagian 05 — Penentukuran Pencetak
Panduan Persediaan Pencetak & Pengesahan Skala
Menjamin Ketepatan Skala Fizikal 1:1 Sebenar
Physical millimeter spacing applies along all three axis directions. Verify that the distance between vertical lines matches your selected spacing using a ruler.
- Dalam dialog cetakan, pilih Skala: 100% atau Saiz Sebenar.
- Nyahaktifkan 'Fit to Printable Area' bagi mengelakkan herotan cetakan.
- Ukur palang penentukuran 50 mm pada margin bawah dengan pembaris fizikal.
Bahagian 06 — Soalan Lazim
Soalan Lazim (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.
Buka dalam Studio Maya — Kertas Isometrik
Lakarkan rajah, tandakan koordinat atau lukis bentuk geometri di atas grid ini secara terus dalam pelayar anda.