3D Fundamentals Tutorial 4

In this video we find out why things look smaller the farther away they are. What does that have to do with projection? I'll tell you... all this science is making me so horny, mah dick is gonna project right out of these pants gurl.

Video

The tutorial video is on YouTube here.

• Orthographic vs. Perspective projection 0:15

• The cube we are drawing seems off
• Reason: we are ignoring the z-component of the vertices
• No matter how far or close from our viewpoint, we always draw the same size surfaces

• How does vision and perspective work? 2:55

• The physical/optical picture: why do things farther away appear smaller in our vision?
• Lightsource -> photons -> reflection -> image sensor

• A demonstration setup for vision with a "pinhole camera" in 2D 6:15

• Pinhole acts as a focal point
• Images get mirrored through the pinhole onto the image sensor (/Retina) 12:44
• In computer graphics, we avoid this mirroring by moving the image plane in front of the focal point (mathematically, not physically) 13:44

• The z-divide (/perspective-divide) 15:02

• How do we calculate a point on the image plane given a point in object space? Divide by z!

• Keep in mind: two key conventions we use 19:55

• We will keep the image plane 1 unit in front of the focal point
• As objects come closer to the focal point, they will project onto larger parts of the image space (z->0)
• Objects can't cross the focal plane. We will need clipping to take care of this (in later video)

• Condition for points to fall whithin screen space: |x|<|z| and |y|<|z| 21:08
• The projection matrix: not needed for now, will be covered later (needed for Direct3D) 22:06
• Implementing the z-divide into our code 23:05

Downloads

The GitHub repository for the tutorial code is here.

See also

• Planet Chili Patreon
• Next in series (Tutorial 5)
• 3D Fundamentals Series