# Advanced math drafting tools

## Complete freedom to draw any complex graph or shape: enter the parameters and the formula(s) This second main dialog (dialog 2/2), will direct you [by clicking on the propper image or button] to:

• the specific math function dialog (either 2D or 3D curve or 3D surface),
• directly to an action (XLS to entity dialog, load LLP project dialog, back to main dialog 1/2),
• or to the Settings dialog.

## Example dialog:

### 3D Surface – X = f (u,v) | Y = g (u,v) | Z = h (u,v) Enter the proper parameters and create any customized 2D curve, 3D curve or 3D surface, to get complex shapes for further processing or direct use.

Check examples of advanced projects

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## How to draw a sine wave in AutoCAD/GStarCAD/ZwCAD using LitioLAB drawing tools

There several different ways to draw a sine wave in AutoCAD/GStarCAD/ZwCAD with LitioLAB.

• First, with the basic sine tool of LitioLAB. Just enter the sine wave lenght and its amplitude.
• Next, with the function of X - y=f(x), with some changes to the basic sine function.
• also, with the X Y function of U - x=f(u) ; y=g(u)
• With some few parameter changes, you can draw more waves in the same space. Or a longer graph with the same wave lenght.
• Finally, a zigzag graph.

## How to draw the Gaussian function in AutoCAD/GStarCAD/ZwCAD with the advanced drawing tools of LitioLAB

The mathematical definition of the Gaussian function, rewriten in a calculator-like form, is as follows:
f(x) = a * exp((-1.0)*(x-b)^2/(2*c^2))

ZwCAD users need to check LitioLAB user manual to review the math functions available and how to adapt the formulas to ZwCAD.

The EXP() function is not available in ZwCAD. Use E^() instead.

For an easy example we consider a = 1; b = 0; c^2 = 0.1

Thus, the formula would turn as follows:
f(x) = 1 * exp((-1.0)*(x-0)^2/(2*0.1))

If we use the additional parameter boxes for the arbitrary constants a, b, and c, to rewrite the formula, in order to have an easy way to work with this function in the future:
f(x) = C1 * exp((-1.0)*(x-C2)^2/(2*J1))
where:
a = C1
b = C2
c^2 = J1

We canload these values in the parameter boxes, and replace the values by these parameters in the formula: C1 = 1.0 ; C2 = 0.0 ; J1 = 0.1

We can try what happens, if we change parameter values, e.g., as follows:

b = C2 = 0.1 It moves the graph to the right
a = C1 = 1.25 It stretches the graph upwards
c^2 = J1 = 0.2 & 0.05 it softens or sharpens the graph