Coordinate Grid Calculator
Generate coordinate grids for square, rectangular, triangular, and hexagonal tilings
Generate Coordinate Grid
Number of points along each side (max 10 for display)
Side length of cell
X coordinate of grid origin
Y coordinate of grid origin
Grid Properties
Spacing: 1 units horizontally and vertically
Characteristics: Regular square cells with 4 cells meeting at each vertex
Origin: (0, 0) - center
Coordinate Points (First 20)
| Index | X | Y | Coordinate |
|---|---|---|---|
| 0 | -0.5 | -0.5 | (-0.5, -0.5) |
| 1 | 0.5 | -0.5 | (0.5, -0.5) |
| 2 | 1.5 | -0.5 | (1.5, -0.5) |
| 3 | 2.5 | -0.5 | (2.5, -0.5) |
| 4 | 3.5 | -0.5 | (3.5, -0.5) |
| 5 | -0.5 | 0.5 | (-0.5, 0.5) |
| 6 | 0.5 | 0.5 | (0.5, 0.5) |
| 7 | 1.5 | 0.5 | (1.5, 0.5) |
| 8 | 2.5 | 0.5 | (2.5, 0.5) |
| 9 | 3.5 | 0.5 | (3.5, 0.5) |
| 10 | -0.5 | 1.5 | (-0.5, 1.5) |
| 11 | 0.5 | 1.5 | (0.5, 1.5) |
| 12 | 1.5 | 1.5 | (1.5, 1.5) |
| 13 | 2.5 | 1.5 | (2.5, 1.5) |
| 14 | 3.5 | 1.5 | (3.5, 1.5) |
| 15 | -0.5 | 2.5 | (-0.5, 2.5) |
| 16 | 0.5 | 2.5 | (0.5, 2.5) |
| 17 | 1.5 | 2.5 | (1.5, 2.5) |
| 18 | 2.5 | 2.5 | (2.5, 2.5) |
| 19 | 3.5 | 2.5 | (3.5, 2.5) |
Showing first 20 of 25 points
Example: Square Grid
Problem Setup
Grid type: Square grid
Cell side: 1.5 units
Points per side: 4 points
Origin: (0, 0) - vertex placement
Step-by-Step Calculation
1. Formula: x = x₀ + i × a, y = y₀ + j × a
2. First row (j=0): (0,0), (1.5,0), (3,0), (4.5,0)
3. Second row (j=1): (0,1.5), (1.5,1.5), (3,1.5), (4.5,1.5)
4. Continue for 4×4 = 16 total points
Result: 16 evenly spaced coordinate points
Grid Types
Square
Regular squares, 4 cells per vertex
Rectangular
Different width and height
Triangular
Equilateral triangles, 6 cells per vertex
Hexagonal
Regular hexagons, 3 cells per vertex
Key Formulas
Square Grid
x = x₀ + i × a
y = y₀ + j × a
Triangular Grid
h = a × √3/2
shift = (row % 2) × a/2
Hexagonal Grid
Area = 3√3a²/2
Complex spacing patterns
Understanding Coordinate Grids and Tilings
What is a Coordinate Grid?
A coordinate grid is a system of evenly spaced points arranged in a regular pattern. These grids are fundamental to geometry, computer graphics, and many engineering applications.
Regular Tilings
- •Only three regular tilings exist: square, triangular, and hexagonal
- •Based on internal angles that sum to 360° at vertices
- •Square: 90° × 4 = 360°
- •Triangle: 60° × 6 = 360°
- •Hexagon: 120° × 3 = 360°
Applications
Computer Graphics
Pixel grids, texture mapping, game development
Engineering
Structural analysis, finite element methods
Architecture
Floor patterns, tiling designs, layout planning
Nature
Crystal structures, honeycomb patterns
Fun Fact: Hexagonal grids are optimal for coverage - they provide the most area with the least perimeter, which is why bees use hexagonal cells!