# From Points to Curves

#### Goals

The aim is to familiarize yourself with the basic features of points and curves and learn to create and modify curves.

#### Content in a nutshell

1. How to draw a curve by control points and draw a curve by interpolation points?
2. How to modify curves (with fillet, extend, trim, offset)?
3. What are points and point clouds?

#### Curve by control point & curve by interpolation point

Curves in many surface modelers (like Rhino) are NUBS curves.

Curve by control points: The connection lines of adjacent control points are tangent to the curve, so the control point is not on the curve.

Curve by interpolation points: The curve connects the points smoothly. The position of the curve is settled, but the curvature is flexible.

#### Modify curves

Fillet: connect straight line or curve by an arc if the circle of the certain radius could be tangent to the two lines (or curves).

###### Fillet two lines with different radius.

Trim: Cut off the end of the curve outside another curve or surface.

Extend: Extend the curve to another curve or surface.

Offset: Copy the curve that all the locations on the copied curve are a specified distance from the original curve.

#### Point and point cloud

A point cloud is a set of points. It could represent 3D shapes and objects (Wikipedia: point cloud). Point cloud produced by 3D scanners projects the object in reality (such as terrain, historical buildings, and manufacturing components) to a 3D model.

#### Examples

What you can create with a point cloud?