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# 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

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

**Curve by control point & ****curve by interpolation point**

**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.

###### Draw curves through the same points by different methods: curve by control points (blue); curves by interpolation points (red).

**Modify curves**

**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.

###### Left: trim; vertical line can be used to trim the horizontal line.

###### Middle: extend; horizontal black line can be extended to the vertical line.

###### Right: offset; the distance between the new pink curve and the original blue curve is constant (distance is measured perpendicular to the 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? **

###### Left: a greyscale heightmap picture of a terrain;

###### Original photo: Julien Lecaché

###### Right: Point cloud model of the terrain (closer look).

###### All pictures in this page: Fanyi Jin (except heightmap)

###### Point cloud model of the terrain (overall look)

###### 3D scan of Lau Pa Sat hawker center in Singapore in a format of a colored point cloud. Done in collaboration between SUTD and Aalto Design of Structures group.

**Chapters**