3D Fundamentals Tutorial 2
From Chilipedia
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
(multiplication of vectors with matrices) 0:16  Introducing 3D space 1:57
 Implementing the
Vec3
class 3:19
 Inherits from
Vec2
(zcomponent added)  Overload all operators for 3D
 Advantage of inheritence here: enables passing
Vec3
s into functions that acceptVecc2&
references
 Inherits from
 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 (Chili likes to call 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 PreClip 3D space definition: z=1.0 indicates half cube depth
 Transforming vertices from Pube Space to Screen Space 14:01
 Introducing the
PubeScreenTransformer
class
 Introducing the
 Testing: drawing a cube 17:07

Cube
class created as a data structure to hold the vertices

 Representing lines: vertex container + vector of indices 18:34
 This strategy avoids having to transform vertices multiple times
 Same concept as IndexBuffer used in Direct3D to draw primitives 20:40
 Make the
Cube
class return aIndexedLineList
struct
 Code for drawing: transform the vertices and iterate through the index buffer 21:50
 Limitations observed: not square and not 3D. Why? 23:22
 Screen size is not square, we'll use a quick fix for now
 We still lack 3D visual cues because we don't account for the zcomponent yet (we're still in Orthographic Projection)
Downloads
The GitHub repository for the tutorial code is here.