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In mathematics, an implicit surface is a surface in Euclidean space defined by an equation
An implicit surface is the set of zeros of a function of three variables. Implicit means that the equation is not solved for x or y or z.
The graph of a function is usually described by an equation z = f {\displaystyle z=f} and is called an explicit representation. The third essential description of a surface is the parametric one: , y , z ] {\displaystyle ,y,z]} , where the x-, y- and z-coordinates of surface points are represented by three functions x , y , z {\displaystyle x\,,y\,,z} depending on common parameters s , t {\displaystyle s,t}. Generally the change of representations is simple only when the explicit representation z = f {\displaystyle z=f} is given: z − f = 0 {\displaystyle z-f=0} , ] {\displaystyle ]} .
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