Thread: 3D to 2D

this is a mathematical problem i have tried to solve for so long but never done it.
I ahve a coordinate system based on 3D with the coordinates x,y,z. But i have only a normal screen to display it, wich is x,y coordinates. And i have 2 axes wich they can move around, so its 2 angles. lets call them A and B. And u can constantly turn around this axes, so A and B can constantly be changed so u can see a object from different angles. So when A and B both = 0° what u would see would be purely the X and Y coordinate of the objects, but as they chance how do i turn X,Y,Z coordinates to X,Y coordinates when u know what value angle A and B is?

Its a simple rotation matrix Zelos

for example to rotate the X-Y axis (ie a Z rotation) by and angle Theta you would use the matrix

X_new = Cos(Theta) X + Sin(Theta) Y + 0 Z
Y_new = -Sin(Theta) X + Cos(Theta) Y + 0 Z
Z_New = 0 X + 0 Y + 1 Z

Just cyclicly permute the X, Y and Z to obtain the other 2 rotations and you just times rotations together to get what you want.

how come Z doesnt have any trigometric function?

Z doesnt have any trig functions as it is the axis that remains "still" during the rotation ie. we are rotating about the Z axis.

You do know how to get the matrix representation of the system i posted, i couldnt work out an easy way of writing the matrix so i just wrote out the system. You need to multiply the corresponding matrices together to get your arbitrary rotation matrix, but remember the order in which you rotate matters.

okey, im for some odd reason not familiar with this, could u plz write it with both axes?

Do you want the rotation matrices for all three rotations?

3 rotations? its only 2 axes u rotate around. In a world with N dimensions u need only N-1 axes to rotate around to see every possible angle around a object.- But if 3 is needed id like them. Btw id also like the other way around if u can fix it, so i get the X,Y coordinates to X,Y,Z

Zelos - there are three co-ord. axis so you have three main rotations. They are


for rotations around the X axis


for rotations around the Y axis


for rotations around the Z axis

Try http://mathworld.wolfram.com/RotationMatrix.html for some more information but you form the required rotations by multiplying these matrices together.

thx, i´ll try it right away