# Applying a Horizontal Scale about an Origin Point

This post applies if your grid to ground conversion requires applying a horizontal scale about an origin point and is defined by:

• Horizontal Origin Northing (N0)
• Horizontal Origin Easting (E0)
• Horizontal Scale Factor

Scale based grid to ground transformations are probably the most common. If the origin point is not defined, it is usually implied to be 0,0 and so a simple scale can be applied. The wrinkle with this transform occurs when that scale is based on a known point instead of an undefined (0,0) origin. If the user is performing this process step by step, it requires translating the original point cloud data to the known point, applying the scale, and then translating the data back. Luckily, these three steps can be reduced into a single linear transform to obtain the same results by using these formulas:

E’ = E * scale + (1 – scale) * Eo
N’ = N * scale + (1 – scale) * No
Z’ = Z

Once these values are calculated, they can be applied using LP360, True View EVO, GeoCue or TerraScan.

## Calculating Linear Transformation

Use the following spreadsheet to help you quickly compute the values to enter into the LP360 and True View EVO Affine Transform LAS PCT or TerraScan Linear transformation for applying a horizontal scale about an origin point:

## LP360 – Affine Transform LAS PCT

Input the values from the spreadsheet into the LP360 Affine Transform LAS PCT by enabling only the Scale and Translate options after creating your point cloud task:

## TerraScan – Linear Transformation

In TerraScan, open Scan Settings ->Coordinate Transformations -> Transformations. Enter the calculated scale and translate values into the “Multiply by” and “Add constant” fields. Name the transformation and click OK to save:

This transformation is applied to loaded or project points via a Transform action step in a macro or Transform loaded Points options: