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# Online 3D Function Visualizer

The following tool can be used to visualize your 3D function online without using any external software:

To use this tool correctly, you have to enter your mathematical expression in terms of \(x\) and \(y\). The lower and upper bounds of each variable are also controllable and can be set with any user-defined values. Once these steps are completed, you have to click on the ''calculate'' button in order to simulate what you have entered. Also, you can use your mouse to rotate and zoom your model as well as indicating the values of \(\{x, y, z\}\) of any point on the graph.

The following table gives some useful hints about how to enter the desired functions correctly:

Expression | Description |
---|---|

\(\sin(x), \cos(x), \tan(x)\) | The sine, cosine, and tangent of \(x\) in radians |

\(\text{asin}(x), \text{acos}(x), \text{atan}(x)\) | The inverse of the preceding trigonometric functions |

\(\sinh(x), \cosh(x), \tanh(x)\) | The sinh, cosh, and tanh of \(x\) in radians |

\(\text{asinh}(x), \text{acosh}(x), \text{atanh}(x)\) | The inverse of the preceding hyperbolic functions |

\(\text{sqrt}(x)\) | The square root of \(x\) (\(x\) must be \(+ve\)) |

\(\log(x)\) | The natural logarithm of \(x\) |

\(\text{lg}(x),\) or \(\log10(x)\) | The common logarithm of \(x\) with base \(10\) |

\(\text{pow}(x, y)\) | The power of \(x\) to the \(y\) |

\(\min(x), \max(x)\) | The min. and max. values of \(x\) |

\(\text{abs}(x)\) | The absolute value of \(x\) |

\(\text{round}(x), \text{ceil}(x), \text{floor}(x), \text{trunc}(x)\) | The round, ceil, floor, and truncate values of \(x\) |

\(\text{random}\) | A random value |

\(\text{PI}\) | Returns the \(\pi\) value |

\(\exp(x)\) | The exponential value of \(x\) |

\(\text{fac}(x)\) | The factorial value of \(x\) |

\(\text{hypot},\) or \(\text{pyt}\) | The hypotenuse of \(x\) and \(y \ \rightarrow\) \(\text{hypot}=\sqrt{x^2+y^2}\) |

\(\text{atan2}()\) | The arctangent of the quotient of its arguments, as a numeric value between \(\pi\) and \(-\pi\) in radians |

\(\text{E}\) | The base of natural logarithms \(\rightarrow\) \(\text{E}=e^1 \approx 2.718\) |

Also, we can use \(if\)-statement to set constraints on the function. For
example: \(if \ (y > x, \sin(x) + \sin(y))\) will plot only the part
of \(\sin(x) + \sin(y)\) when \(y > x\). To fill the rejected part of the
plot (i.e., when \(y\) is *not greater* than \(x\)) with any other
function, then we can use the following option: \(if \ (y > x, \sin(x)
+ \sin(y), \cos(x) + \cos(y))\), which means that the 3D plot is a
combination of two functions \(\rightarrow\) the first one: \(\sin(x) +
\sin(y)\) when \(y > x\), and the other one: \(\cos(x) + \cos(y)\) when \(y
\leqslant x\).

The user should note that the computational time increases as the plot resolution increases. Thus, for some specific functions, the rendering will consume long time to produce and control (rotate, zoom, etc) the corresponding 3D graph at a high resolution.