3D Shapes

Psh, 3D was so 2010, it's all about sniffing glue to pass the time

Box

Rectangular Prism

Given

  • Vertex -- (left, top, front)
  • Width (x), Height(y), Depth(z)

Defining Points

  • 8 vertices

Sphere

Rotate a circle around x or y (not z though)
Don't connect points. Therefore, plot things twice

Given

  • Center
  • Radius

Defining Points

- Points on circumference

θ: Circle Creation: 0 - 2π
φ: Rotation: 0 - π
x = rcosθ + Cx
y = rsinθcos&φ + Cy
z = rsinθsinφ + Cz 

for rot: 0 - 1
    for circ: 0 - 1
        x = rcos(pi * circ) + Cx
        y = rsin(pi * circ)cos(2pi * rot) + Cy
        z = rsin(pi * circ)sin(2pi * rot) + Cz

Torus (courtesy of Mr. Kats)

Dounut Shape

Given

torus.png - Center
- Distance from center to center of cross section (R)
- Radius of cross section (r)

Defining Points

- Points on the surface

Torus = Circle + Translation + Rotation
y-rotation Circle + Translation
[cosφ 0 sinφ][rcosφ + r] = [ 0 1 0 ][rsinφ] = [-sinφ 0 cosφ][0] =