Computational Thinking: Lecture 3: Mixing and Sculpting

Computational Thinking

Joel Gethin Lewis

Lecture 3: Mixing and Sculpting

The third dimension is usually described in terms of a new letter: z.
The direction and orientation of the three dimensions varies in a similar way to the way the direction of y varies in two dimensions between high school graphs and digital screen co-ordinates, so always check which way is what.
See how Pythagoras works in three dimensions in this Better Explained article.
Also see this Immersive linear algebra course - what is Linear Algebra?.

You can map any three variables into three dimensions to help you think about them spatially (i.e. in physical space).
An example of this is mixing together Red, Green and Blue (RGB) colours to make any other colour.
Digital colour mixing is additive while analogue paint mixing is subtractive.
How does projected light mix?
There are other ways of mixing variables to make colours - for example Hue, Saturation and Brightness (HSB).
I often use HSB in digital work to make it easy to blend between colours - much easier than RGB. You can visualise colour using a colour wheel or a colour solid. Complementary colours are on opposite sides of the colour wheel.
Colour theory is a huge area of study, for graphic design and even psychology.

One way of storing three dimensional information is using point clouds.
The output of three dimensional scanners is often in point clouds - a grid of positions, each with a depth value - think of Pin Art toys from the 1980's.
Another way of storing three dimensional data is to use Voxels (from the initial letters of volume and element, with the insertion of -x- for ease of pronunciation).
Voxels can be a super efficient way of storing three dimension information - used for everything from MRI scanners to Minecraft.
Creative uses of points in space: Motorstudio Design Room / Hermès × Tokujin Yoshioka / Shining360 by Claire Hentschker.

Another way of storing three dimensional information is using a series of polygons.
Polygons are geometric objects with at least three straight lines and angles.
Polygons are plane figures - i.e. they are flat.
Some examples: squares, triangles and pentagons.
Triangles are often used in three dimensional software and games - for more information about why this is so see this Computerphile video about A Universe of Triangles.
A Polyhedron is a three dimensional shape made of multiple polygons.
The Platonic Solids are a set of three dimensional shapes that have been known about since Ancient Greece and possibly back to Neolithic times.