Plotting a function in 3D (theory)

Question

I made a program which draws/plots a function like it is given in the picture https://scontent-frt3-1.xx.fbcdn.net/hphotos-xpl1/v/t1.0-9/12190859_1244435358915759_7264646259310407538_n.jpg?oh=5560ccfd7ec8b03f915450a8b9fcc008&oe=56BBEF62

In my idea,I take an interval of -10 and 10 or a bigger interval for x and y. In the case of 2D,you take the value x which is between -10 and 10 ( you will have many points) and you take (X,Y) point,where y is the calculated value. Example y=x*x+3; for -10, x is -10 and y is 103.so you take the point (-10,103) and so on you increase x by 0.1,until it gets the value 10, here you can plot your function.I know that z=f(x,y) but I do not know how to increase x and y in the case of 3D,Have I to increase them at the same time or? This is my question

Answer 1

Programmatically, you'd run through a nested loop

for x = -10 to 10 do
    for y = -10 to 10 do
        z[x,y] = f(x,y)

Then comes the harder part: Convert this $z$-array into a perspective display with shading and occlusion and all ...