Is There an Equation for a Rectangular Prism in Cartesian Coordinates?

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The discussion centers on the mathematical representation of a rectangular prism in Cartesian coordinates. Unlike smooth surfaces such as ellipsoids, a rectangular prism is defined by the intersection of six planes, making it impossible to represent as a single differentiable function. The participants emphasize the need to understand the equations for planes to accurately describe the geometry of a rectangular prism.

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michael pranit
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Hello,
I am trying to understand the concept of solid geometry(spheres, cubes, polyhedra etc) as a function of their co-ordinates.
for example, the general ellipsoid, is a quadratic surface which is given in Cartesian coordinates by:
(x^2/a^2)+(y^2/b^2)+(z^2/c^2)=1
a,b,c being the semi axis.
-Is there an equation to a rectangular prism as a function of the x,y,z coordinates like the ellipsoid?
Could someone clarify/explain.
Any help will be appreciated.
Thank you
 
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The rectangular prism is the the sum of 6 planes. Do you know the equations for planes?
 
Because a "rectangular prism" is not smooth (it has edges and corners) you cannot give it as one differentiable function. You can, as Matterwave suggests, write equations for each of the six planes.
 

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