Algebraic surfaces

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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.

Heart

Süss/Heart
for x = -14,14, .25 do 
for y = -14,14, .25 do 
for z = -14,14, .25 do 

if (math.floor(x^2)+math.floor((9/4)* y^2)+math.floor(z^2)-1)^3 - math.floor(x^2*z^3)-math.floor((9/80)*y^2*z^3)==0 then 

p = Instance.new("Part") 
p.formFactor = "Symmetric" 
p.CFrame = CFrame.new(Vector3.new(x*1.5, z*1.5, y*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

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 math.floor(x^2)+math.floor(y^2)+math.floor(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 math.floor(-x^3)+math.floor(z^2)+math.floor(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

No title

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

if math.floor(x^2)+math.floor(y^2)+math.floor(z^2)==math.floor(z^4)  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

Whitney

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

if math.floor(x^2)-math.floor(y^2*z)==0  then 

p = Instance.new("Part") 
p.formFactor = "Symmetric" 
p.CFrame = CFrame.new(Vector3.new(x*5, z*5, y*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

Bell

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

if math.floor(x^2)+math.floor(y^2)+math.floor(z^3)==math.floor(z^2)  then 

p = Instance.new("Part") 
p.formFactor = "Symmetric" 
p.CFrame = CFrame.new(Vector3.new(x*1, z*2, 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

Egg

Dattel/Egg
for x = -14,14, .25 do 
for y = -14,14, .25 do 
for z = -14,14, .25 do 

if math.floor(3*x^2)+math.floor(3*y^2)+math.floor(z^2)==10 then 

p = Instance.new("Part") 
p.formFactor = "Symmetric" 
p.CFrame = CFrame.new(Vector3.new(x*5, z*5, y*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

"Plop"

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

if math.floor(x^2) + math.floor(z+y^2)^3 == 0 then 

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

end 
end 
end

Distel

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

if math.floor(x^2)+math.floor(y^2)+math.floor(z^2)+math.floor(1000*(x^2+y^2)*(x^2+z^2)*(y^2+z^2))==1 then 

p = Instance.new("Part") 
p.formFactor = "Symmetric" 
p.CFrame = CFrame.new(Vector3.new(x*3, y*3, z*3)) 
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

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