3D Fundamentals Tutorial 2

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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.


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 (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 (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 Pre-Clip 3D space definition: z=1.0 indicates half cube depth
  • Transforming vertices from Pube Space to Screen Space 14:01
  • Introducing the PubeScreenTransformer class
  • 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 a IndexedLineList 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 z-component yet (we're still in Orthographic Projection)


The GitHub repository for the tutorial code is here.

See also