3D math conversion- 3D graph surface equation into catersian coordinate equation

[Reptorian]

What you do is integrate the separated group into the larger separated group as it if was algebra in order to convert it into Cartesian coordinate.

Remember f= Height of Y. Yes I mean that symbol of graph.

The Cartesian coordinate rule is f(x,y,x,t...)=0

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Example one-The Ellipsoid

The equation for the ellipsoid follows by
x^2/a^2+y^2/b^2+z^2/c^2=1

To convert it-

Step 1- Add the () into the larger group

(x^2/a^2+y^2/b^2+z^2/c^2)=1

Step 2-Then eliminate the 1 by subtracting both equation by 1 in order to finally convert it into Cartesian coordinate

f(x,y,x,t...)=(x^2/a^2+y^2/b^2+z^2/c^2)-1
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Example two-Elliptic Paraboloid

The equation for the elliptic paraboloid follows by
z/c=x^2+y^2/b^2

To convert it to Cartesian coordinate requires you to subtract z/c. Remember to add f(x,y,x,t...)=(Cartesian form of the original equation)

f(x,y,x,t...)=x^2/a^2+y^2/b^2-z/c
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Convert to Cartesian form the rest yourself
- Hyperbolic Paraboloid equation is z/c=x^2-y^2/b^2 -
- Cone equation is z^2/c^2=x^2+y^2/b^2
- Hyperboloid of One Sheet equation is 1=x^2/a^2+y^2/b^2-z^2/c^2
- Hyperboloid of Two Sweet equation is 1=-x^2/a^2-y^2/b^2+z^2/c^2

Pictures of each geometry when A=2, B=4, C=6
Ellipsoid-



Elliptic Paraboloid-



Hyperbolic Paraboloid-



Cone-



Hyperboloid of One Sheet-



Hyperboloid of Two Sheet-


Answers for the conversion
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-Hyperbolic Paraboloid in Cartesian form is f(x,y,x,t...)=x^2/a^2-y^2/b^2-z/c -

-Cone in Cartesian form is f(x,y,x,t...)= x^2/a^2+y^2/b^2-z^2/c^2 -

-Hyperboloid of One Sheet in Cartesian form is f(x,y,x,t...)= (x^2/a^2+y^2/b^2-z^2/c^2)-1 -

-Hyperboloid of Two Sheet in Cartesian form is f(x,y,x,t...)=(-x^2/a^2-y^2/b^2+z^2/c^2)-1 -
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Extra notice- Removed unnecessary parenthesis in the equation conversion to remove the errors. Although the ones in the pic is still valid.

[Efs]

Oh fuck Math in the ass so hard.
Math is the reason I'm failing school, we don't get along.

[Reptorian]

There's nothing that is absolutely hard about it. I thought the same way as you until I actually start to get motivated and understand it.

[Miller0700]

Where is all this coming from, might I ask?

[Reptorian]

I did look into the quadric equations on a calculus book. Then, I decided to apply the knowledge of algebra for use into the k3dsurf program and ended up creating a tutorial. Next lesson is linear approximation.

[Miller0700]

Cool.

[Faby]

That thing's like holy water to my poor demonic eyes D:

IT BURNS ME SO