Difference between revisions of "Surface Command"

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: Yields the Cartesian parametric 3D surface for the given ''x''-expression ''a'', ''y''-expression ''b'' and ''z'' -expression ''c'', using two parameter variables within the given intervals [''Start Value'', ''End Value''].
 
: Yields the Cartesian parametric 3D surface for the given ''x''-expression ''a'', ''y''-expression ''b'' and ''z'' -expression ''c'', using two parameter variables within the given intervals [''Start Value'', ''End Value''].
:{{Example|1=<div>
+
:{{Example|1= Let ''r'' and ''R'' be two positive real numbers: <code><nowiki>Surface[(R + r cos( u)) cos(v) , (R + r cos( u)) sin(v) , r sin(u ), u, 0, 2 π , v, 0, 2 π]</nowiki></code> creates the torus generated by a circle of radius ''r'' whose center rotates about zAxis at a distance ''R''.}}
:*<code><nowiki>Surface[2 sin(t) * sin(v), sin(v), cos(v), t, 0, 2π, v, -π, π]</nowiki></code>
 
::creates the related surface in Graphics View 3D.
 
:*Let, ''r'' and ''R'', two positive real,
 
::<code><nowiki>Surface[(R + r cos( u)) cos(v) , (R + r cos( u)) sin(v) , r sin(u ), u, 0, 2 π , v, 0, 2 π]</nowiki></code>
 
::creates the torus generated by a circle of radius ''r'' which center rotates about zAxis at a distance ''R''.</div>}}
 
 
 
  
 
:{{note|1=<div>
 
:{{note|1=<div>
 
:*''End Value'' must be greater than or equal to ''Start Value'' and both must be finite.
 
:*''End Value'' must be greater than or equal to ''Start Value'' and both must be finite.
 
:*''x, y'' and ''z'' are not allowed as  parameter variables.</div>}}
 
:*''x, y'' and ''z'' are not allowed as  parameter variables.</div>}}

Revision as of 22:19, 9 June 2013


Surface[ <Expression a>, <Expression b>, <Expression c>, <Parameter Variable 1>, <Start Value>, <End Value>, <Parameter Variable 2>, <Start Value>, <End Value> ]
Yields the Cartesian parametric 3D surface for the given x-expression a, y-expression b and z -expression c, using two parameter variables within the given intervals [Start Value, End Value].
Example: Let r and R be two positive real numbers: Surface[(R + r cos( u)) cos(v) , (R + r cos( u)) sin(v) , r sin(u ), u, 0, 2 π , v, 0, 2 π] creates the torus generated by a circle of radius r whose center rotates about zAxis at a distance R.


Note:
  • End Value must be greater than or equal to Start Value and both must be finite.
  • x, y and z are not allowed as parameter variables.
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