@ue-too/board / pointConversion

Function: pointConversion()

pointConversion(point): object

Defined in: packages/board/src/utils/coorindate-conversion.ts:50

Converts an isometric 3D point to a flat 2D world point.

Parameters

point

Point

The 3D point in isometric space (with optional z coordinate)

Returns

object

The 2D point in flat world coordinates

x

x: number

y

y: number

Remarks

This function performs an isometric projection transformation, converting 3D coordinates to 2D using standard isometric angles (30 degrees).

The transformation uses:

• cos(30°) ≈ 0.866 for x-axis projection
• cos(60°) = 0.5 for y-axis projection
• Z-coordinate is added directly to the y-axis (height)

Mathematical formulas:

x_2d = (x_3d * cos30) - (y_3d * cos30)
y_2d = (x_3d * cos60) + (y_3d * cos60) + z_3d

This creates the classic isometric diamond grid appearance where:

• Moving along +X goes down-right
• Moving along +Y goes down-left
• Moving along +Z goes straight up

Example

// Convert a 3D cube corner to 2D isometric projection
const point3D = { x: 10, y: 10, z: 5 };
const point2D = pointConversion(point3D);
// Result: { x: 0, y: 15 }
// x: (10 * 0.866) - (10 * 0.866) = 0
// y: (10 * 0.5) + (10 * 0.5) + 5 = 15

// 2D point without z-coordinate
const flatPoint = { x: 20, y: 0 };
const projected = pointConversion(flatPoint);
// Result: { x: 17.32, y: 10 }