# Grasshopper Points from Curve

## Introduction

**LEVEL: INTRODUCTORY**

Points can be defined in 3D world coordinates by placing them in a viewport or numerically define the 3 coordinates. In this case the points are defined in world space.

The points can however also be defined in parametric space, a location on an object. This will define the location in relation to the geometry, instead of the location in world space. By defining a point parametrically, its location will adapt along with the geometry. If the curve is moved, shortend or its shape is changed, the point will adapt accordingly. Working in world space does not have this advantage.

## One dimensional space of a curve

Locations on a curve are defined by 1 dimensional space coordinates **U**. A position on a curve can be defined by the length or is related to the length of the curve. In this case the position is related to world space. However the location on a curve can also be defined by its relative position on the curve. The start point will have the value 0 and the end point the value 1. A point placed on the line will have a value between 0 and 1. The curve is Parametrised.

### Reparameterisation

In some cases it can be that the parameterisation of the curve is giving an indication of the length of the curve. This can be a maximum value larger than 1. When the curve is reparameterised the U value will be evenly distributed from 0 to 1.

### Extracting a point or points

There are several methods of extracting points from objects. Key in the method is the definition of the dimension. This can be in units of length or it can be in units of a reparameteresized curve. Another method is the division of the curve in segments based on length or relative number of segments. There are two kinds of points which can be extracted.

- The Control Vertices
- Points on the Curve

The choice on which tool to use to extract a point from a curve doesn't only depend on if the curve is reparameterized but also on the additional information the component can output. In most of the cases the component supports the selection of more than 1 point or will generate more than 1 points. In essence any point on the curve can be selected.

### Selecting multiple points on a curve by division

In some cases like the construction of a steel truss or the even distribution of objects along a line it can be useful to divide a curve in evenly spaced parts. Grasshopper has 3 options to do this. The difference in the options are in the way the division is defined. This can be relative, in length or the distance between the points on the curve.

## Examples

The use of curves for point generation forms a part of the main strategy of generating geometry in Grasshopper. The points can be used as location for other objects. They can be used for generating curves or surfaces and they can be used for defining relations.