Wolfenstein 3D

Rendering feats of yesteryear

Matt Godbolt / @mattgodbolt

Wolfenstein 3D

Hardware

  • 1992
  • 12MHz 16-bit 286
  • 33/66MHz 486DX2 just released $799 ($1400 in today's)
  • No video acceleration
  • No floating point (until 486)

Raycasting

By Kieff - Own work, Public Domain
https://commons.wikimedia.org/w/index.php?curid=20389654

Wolf3D's raycaster

  • Flat plane
  • Square grid only
  • Untextured floor and ceiling

Map

Map

Intersections

p δy δy δx δx

Math #1

x x+1 x+2 y+1 y y-1 dx dy ?? -dy

Geometry

  • sin(θ) = opp / hyp
  • cos(θ) = adj / hyp
  • tan(θ) = opp / adj

Geometry

-dy / tan(θ) -dy

Math #2

x x+1 x+2 y+1 y y-1 -dy / tan(θ) -dy δy = 1/tan(θ) dx -dx tan(θ) δx = -tan(θ)

For each ray: setup

  • θ is ray direction
  • x, y are player tile pos
  • dx, dy are offset within tile
  • Depending on θ:
    • tileStepX, tileStepY = ±1
    • xStep, yStep = tan(θ), 1/tan(θ) [δx, δy]
    • xIntercept = x + dx + -dy / tan(θ)
      yIntercept = y + dy + dx/tan(θ)

For each ray: trace


for (;;) {
  while (yIntercept < y) {  // < or > depending on yStep
    if (map[x][yIntercept>>16]) goto hitVert;
    x += tileStepX;
    yIntercept += yStep;
  }
  while (xIntercept < x) {  // < or > depending on xStep
    if (map[xIntercept>>16][y]) goto hitHoriz;
    y += tileStepY;
    xIntercept += xStep;
  }
}

Distance

p φ p = d cos(φ) d β Δx Δy θ d φ β p
  • p = d cos(φ)
  • φ = θ - β
  • p = d cos(θ - β)

Math #3

p = d cos(φ)
φ = θ - β
p = d cos(θ - β)
cos(A - B) ≡ cos(A) cos(B) + sin(A) sin(B)
p = d [ cos(θ) cos(β) + sin(θ) sin(β) ]
p = d cos(θ) cos(β) + d sin(θ) sin(β)

Distance

θ d Δx Δy
Δx = d cos(θ)
Δy = d sin(θ)

Math #3

p = d cos(φ)
φ = θ - β
p = d cos(θ - β)
cos(A - B) ≡ cos(A) cos(B) + sin(A) sin(B)
p = d [ cos(θ) cos(β) + sin(θ) sin(β) ]
p = d cos(θ) cos(β) + d sin(θ) sin(β)
Δx = d cos(θ)
Δy = d sin(θ)
p = Δx cos(β) + Δy sin(β)

Distance

Δx Δy φ β p
p = Δx cos(β) + Δy sin(β)

Scaling

  • Wall height = constant / p
  • Pre-create scale function per possible height
  • (Ab)use VGA memory planes

Sprites

  • Distance calculated similarly to walls
  • Drawn back-to-front
  • Scaled similarly to walls
  • Each column compared to nearest
  • Sprites "compiled" into runs of opaque pixels

Questions?

matt@godbolt.org @mattgodbolt