Algebraic surfaces

Introduction

This page covers another way of writing out the formulas necessary to create graphs than covered on the Parametric equations page. It may seem unnecessarily complicated at times, but as you can see, this method can provide quite complex shapes and designs.

Spindel

Spindel/Hourglass

for x = -100,100, 1 do 
for y = -100,100, 1 do 
for z = -100,100, 1 do 

if (x^2)+(y^2)-(z^2)==1 then 
p = Instance.new("Part") 
p.formFactor = "Symmetric" 
p.CFrame = CFrame.new(Vector3.new(x/10, y/10, z/10)) 
p.Size = Vector3.new(1,1,1) 
p.Anchored = true 
p.BottomSurface = "Smooth" 
p.TopSurface = "Smooth" 
p.Parent = game.Workspace 
p.BrickColor = BrickColor.new(26) 
end 

end 
end 
end 

Kreuz

Kreuz/Cross

for x = -10,10, 1 do 
for y = -10,10, 1 do 
for z = -10,10, 1 do 

if x*y*z==0 then 
p = Instance.new("Part") 
p.formFactor = "Symmetric" 
p.CFrame = CFrame.new(Vector3.new(x, y, z)) 
p.Size = Vector3.new(1,1,1) 
p.Anchored = true 
p.BottomSurface = "Smooth" 
p.TopSurface = "Smooth" 
p.Parent = game.Workspace 
p.BrickColor = BrickColor.new(26) 
end 

end 
end 
end 

Gupf

Gupf

for x = -100,100, 1 do 
for y = -100,100, 1 do 
for z = -100,100, 1 do 

if x^2+y^2+z==0  then 
p = Instance.new("Part") 
p.formFactor = "Symmetric" 
p.CFrame = CFrame.new(Vector3.new(x, z, y)) 
p.Size = Vector3.new(1,1,1) 
p.Anchored = true 
p.BottomSurface = "Smooth" 
p.TopSurface = "Smooth" 
p.Parent = game.Workspace 
p.BrickColor = BrickColor.new(26) 
end 

end 
end 
end 

Diabolo

Diabolo

for x = -100,100, 1 do 
for y = -100,100, 1 do 
for z = -100,100, 1 do 
if x^2==(y^2+z^2)^2  then 
p = Instance.new("Part") 
p.formFactor = "Symmetric" 
p.CFrame = CFrame.new(Vector3.new(x*1, z*1, y*1)) 
p.Size = Vector3.new(1,1,1) 
p.Anchored = true 
p.BottomSurface = "Smooth" 
p.TopSurface = "Smooth" 
p.Parent = game.Workspace 
p.BrickColor = BrickColor.new(26) 
end 

end 
end 
end 

Sattel/Saddle

Sattel/Saddle

for x = -300,300, 1 do 
for y = -300,300, 1 do 
for z = -300,300, 1 do 

if x^2+y^2*z+z^3==0 then

p = Instance.new("Part") 
p.formFactor = "Symmetric" 
p.CFrame = CFrame.new(Vector3.new(x*.1, z*.1, y*.1)) 
p.Size = Vector3.new(1,1,1) 
p.Anchored = true 
p.BottomSurface = "Smooth" 
p.TopSurface = "Smooth" 
p.Parent = game.Workspace 
p.BrickColor = BrickColor.new(26) 
end 

end 
end 
end 

UFO

UFO

for x = -10,10, .25 do 
for y = -10,10, .25 do 
for z = -10,10, .25 do 

if (z^2-x^2-y^2-1)==0  then 
p = Instance.new("Part") 
p.formFactor = "Symmetric" 
p.CFrame = CFrame.new(Vector3.new(x*7, z*7, y*7)) 
p.Size = Vector3.new(1,1,1) 
p.Anchored = true 
p.BottomSurface = "Smooth" 
p.TopSurface = "Smooth" 
p.Parent = game.Workspace 
p.BrickColor = BrickColor.new(26) 
end 

end 
end 
end 

Trichter

Trichter

for x = -10,10, .25 do 
for y = -10,10, .25 do 
for z = -10,10, .25 do 

if x^2+z^3==y^2*z^2  then 
p = Instance.new("Part") 
p.formFactor = "Symmetric" 
p.CFrame = CFrame.new(Vector3.new(x*4, z*4, y*4)) 
p.Size = Vector3.new(1,1,1) 
p.Anchored = true 
p.BottomSurface = "Smooth" 
p.TopSurface = "Smooth" 
p.Parent = game.Workspace 
p.BrickColor = BrickColor.new(26) 
end 

end 
end 
end 

Sphäre/Sphere

Sphäre/Sphere

for x = -14,14, .25 do 
for y = -14,14, .25 do 
for z = -14,14, .25 do 

if x^2+y^2+z^2==25  then 
p = Instance.new("Part") 
p.formFactor = "Symmetric" 
p.CFrame = CFrame.new(Vector3.new(x*1.5, y*1.5, z*1.5)) 
p.Size = Vector3.new(1,1,1) 
p.Anchored = true 
p.BottomSurface = "Smooth" 
p.TopSurface = "Smooth" 
p.Parent = game.Workspace 
p.BrickColor = BrickColor.new(26) 
end 

end 
end 
end

Fanfare/horn

horn

for x = -14,14, .25 do 
for y = -14,14, .25 do 
for z = -14,14, .25 do 

if -x^3+z^2+y^2==0  then 

p = Instance.new("Part") 
p.formFactor = "Symmetric" 
p.CFrame = CFrame.new(Vector3.new(x*7.5, y*1, z*1)) 
p.Size = Vector3.new(1,1,1) 
p.Anchored = true 
p.BottomSurface = "Smooth" 
p.TopSurface = "Smooth" 
p.Parent = game.Workspace 
p.BrickColor = BrickColor.new(26) 
end 

end 
end 
end 

See Also

Algebraic Surfaces