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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
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
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).
![](https://digitaldesign.aalto.fi/wp-content/uploads/2021/02/fillet2-1024x178.jpg)
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.
![](https://digitaldesign.aalto.fi/wp-content/uploads/2021/02/extend-and-trim-and-offset-1024x311.jpg)
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