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Nice 3D graphs

   Don't be afraid, we don't want to teach you complicated mathematics. We just want to show you an interresting software you can use to make nice 3D graphics. We will use mainly simle mathematical equations.

   The name of the software is Grapher - you can download it here . (You can find the link to this program on our download page for members - and we update it there when necessary.) Download the software, install it and you can start create 3D graphs.
   We apologize to all, who are the friends of mathematics. Why? We are going to simplify some things and explain something what they surely know.
At the beginning
   When we want to create graphs in 3D we need 3 axes - X (horizontal), Y (vertical) and Z (horizontal - but it goes from us to the depth of the monitor). In the Grapher software you can rotate with axes - so sometimes can be horizontal the axe Y as well.
   Imagine a graph as many dots in space. Mathematical equation which describes it says how the coordinates x, y and z of these dots depends on each other. If you for example write x = y = z then the graph is a plane in space with dots 1,1,1 and 2,2,2 and 6,6,6 etc. If you want your graph to be not so simple then you have to use a little bit more complicated equation - not the linear one. You can choose for example x^2 or sin x.
Let's go
   Let's create our first graph. Write to the upper window of Grapher this:
   y = z = x
   The first line defines color of our graph (but the 3D picture will be only black and white) - our definition uses RG (red, green) components - the graph will be yellow. You can use RGB values between 0 and 1.
    Grapher in action The second line says we create a graph for x, y and z axes and the standard values for them - from 5 to 5 (for these values is the graph counted). And the 3rd line is the equation of the graph itself - it's the equation of the plane mentioned earlier.
   Now press the F5 key (or use Project/Graph in the menu) and graph is created. If you want to watch it in 3D then choose View/Eyes/Anaglyph in menu. We recommend to change the color for left eye to red and to cyan (red component is 0, green and blue are 255) in Options/Graphing/Anaglyph. In Options/Graphing/Eyes set Depth Perception for Anaglyph to the first position from left.
   When you create the graph you can rotate it by arrows in Rotate View. If you use doubleclick to an arrow then the graph rotates itself in the space. It's often very nice with 3D glasses.
Better pictures
   And now we try a little bit more complicated graphs. If you add one more line to our first code - for example z = 5 - then there is one more plane in the graph (it's z coordinate is 5, the other ones change from -5 to 5). You can add more similar lines: z = 2, z = -2, x = 5 - and you have much more planes.
    And one more graph If you don't like simple planes, try this equation: y = sin(x). You will se a wavy plane. If you add z = cos(x) you have one more wave plane - normal to the first one. You can use z = x ^ 2 instead of the secon equation - with a strong 3D effect.
   And now you can start your own experiments. If you don't have any idea, try z=x*sin(x)^2, z=x^3*sin(x)^2 or z=x^3*sin(x)^3. You can change the range of coordinates by writing this: var x = -5 to 5 step 20 instead of crt(x,y,z) (last value - step - says how many steps is used between -5 and 5). You can change the -5 to 5 values as well.
   If you need help then just try to use quite large helpfile from authors of the Grapher.

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3D software tools for 3D photos and 2D to 3D conversion

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