3D Fundamentals Tutorial 2

In this video we lay the groundwork needed to represent and transform positions and 3D space, we define the relationship between our 3D space and the screen coordinates, and we setup a data structure to hold our test cube geometry.

Video

The tutorial video is on YouTube here.

• Fix an error in Mat2.h (vector * Matrix multiplication) 0:16
• Introducing 3D space 1:57
• Implementing the Vec3 class 3:19

• Inherits from Vec2 (z-component added)
• Overload all operators for 3D
• Advantage of inheritence here: enables passing Vec3s into functions that accept Vecc2& references

• Calculating the length of a 3D vector (i.e., in R3) 4:57
• The Mat3 3D Matrix class 5:57
• Choosing a coordinate system 7:37

• We choose a Left Handed coordinate system
• And start with defining World Space (=object space for now) and Screen Space

• Setting up a World Space (we'll all it Pube Space) 10:08

• We set the Origin (0,0,0) of world space in the middle of the screen

- This makes for better (easier) scaling

• We will use NDC (Normalized Device Coordinates)

- Meaning: we don't use pixel values, but normalized values relative to screen size

- (e.g. x=1.0 means far right end of screen, x=-1.0 for far left end of screen

- Main advantage: become independent from screen size

- Note: Direct 3D and OpenGL use NDC

• We will use the Pre-Clip 3D space definition: z=1.0 indicates half cube depth

• Transforming vertices from Pube Space to Screen Space 14:01

• Introducing the PubespaceTransformer class

• ...

Downloads

The GitHub repository for the tutorial code is here.

See also

• Planet Chili Patreon
• Next in series (Tutorial 3)
• 3D Fundamentals Series