3D Calculations

[malu05]

Introduction:

Hello.

Im working on the World Of Warcraft Advanced Machinima Tool but need some help with some of the 3D Calculations i use.

We have the cameras position (X,Y,Z) and rotation (X,Z)

They are defined as: posx1 posy1 posz1

And the target is defined as posx2 posy2 posz2

What i want to do is to have the camera always facing towards the target.

So i need to calculate the Rotaion X and Z for the camera.

In my head that sounds very simple but it does not work that well.

The problem:

The X and Z rotation is not defined in 360degrees.

Both goes from 0 to 6.2833 where 6.2833 is 360

And not only that, the X rotation is counterclockwise while the Z rotation is clockwise

You can see it here:

The main Coord system is mirrored.

And the camera rotation is also mirrored.

Let take a example, here is a little 3D space.

Now to calculate the X rotation i need the X and Y values of both target and camera.

$radToDeg = -180 / $pi
$result = atan(($posy1 - $posy2) / ($posx2 - $posx1)) * $radToDeg
            if $posx2 < $posx1 Then
                if $result < 0 Then
                    $result = 270 + $result
                Else
                    $result = 270 + $result
                EndIf
            EndIf
            if $posx2 >= $posx1 Then
                if $result < 0 Then
                    $result = 90 + $result
                Else
                    $result = 90 + $result
                EndIf
            EndIf
            $result = $result - 360
            $result = (($result + 360 - ($result * 2)) + 180)
                        

                       $RotCalcX = $result /  57.294733659064504320977830121115 ;Scaled down to the 0 to 6.2833 ratiooÝ÷ ØÚ0¶¬¥ªí±ç¦¶Þ×M¢ºÞrÕ¡zx&«¢éݶ­j¸¶Ø^^º-jب+²±º.Ûh¶­j¸´­¶®Z¶*'ÆÛkÉ2J)Üz)ÞyÛh©q©ºV­ì~Û¢ØXjwYêÞË(ë­ª¡×¢§^Â
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Edited July 7, 2008 by malu05

[weaponx]

The X and Z rotation is not defined in 360degrees.

Both goes from 0 to 6.2833 where 6.2833 is 360

And not only that, the X rotation is counterclockwise while the Z rotation is clockwise

6.2833 = 2 pi

See unit circle:

http://en.wikipedia.org/wiki/Unit_circle

[malu05]

6.2833 = 2 pi

See unit circle:

http://en.wikipedia.org/wiki/Unit_circle

Ahhh... didnt know that part. ^^

But im still not sure how to calculate the Camera rotation around the X axis

And how the 2 seperate calculations should be joined? (or if it even is 2 calculations)

[weaponx]

RotZ:

0° = 0 pi (Horizon)

90° = pi / 2 = ~1.5 (Ground)

180° = pi = 3.14 (Rear Horizon - Upside-down)

270° = 3pi/2 = 4.71 (Sky)

360° = 2pi = 6.28 (Horizon)

[malu05]

RotZ:

0° = 0 pi (Horizon)

90° = pi / 2 = ~1.5 (Ground)

180° = pi = 3.14 (Rear Horizon - Upside-down)

270° = 3pi/2 = 4.71 (Sky)

360° = 2pi = 6.28 (Horizon)

I think you miss understand.

Lets say the camera is located at -300 , 200 , 10 and the target is located at -351 , 240 , 11

How do i calculate the rotaion around the X axis?

[weaponx]

I think you miss understand.

Lets say the camera is located at -300 , 200 , 10 and the target is located at -351 , 240 , 11

How do i calculate the rotaion around the X axis?

No I understand. I am helping you to understand the concept of radians so you can complete your task.

Edited July 7, 2008 by weaponx

[malu05]

No I understand. I am helping you to understand the concept of radians so you can complete your task.

I found this on geocities.

http://www.geocities.com/wronski12/3d_tutor/basics.html

x2-x1                        y2-y1
tg(Yan)= -----  , tg(Zan)= ---------------------------
         z1-z2           sqrt((x2-x1)^2 + (z2-z1)^2)

Where the Yangel matches my calculation but the other calculation also gives a invalid result.

[malu05]

Seems like the first calculation i made can be used with some tweak. Tho i still would love a more clean calculation if someone knows how it should be done.

The first calculation devide's X and Y rotation by 2 and multiply them.

There is currently only 4 angels that are corrupt and that is when the X or Y position are close equal

Correct

Cameraposition =    -134.572677612305 .     -8935.6123046875 .  143.96760559082
Target Position =   -172.489761352539 .     -8899.083984375 .   144.477661132813

zx= 6.26973425214815 -      zy= 6.26922292422834
rotation set            = 6.26947858818825

Cameraposition =    -259.972808837891 .     -8795.4580078125 .  166.467803955078
Target Position =   -172.489761352539 .     -8899.083984375 .   144.477661132813

zx= 0.246262596623854 -     zy= 0.209104898862212
rotation set            = 0.227683747743033

In both of these examples the zx and zy are quite close.

WRONG:

Cameraposition =    -172.497985839844 .     -8950.833984375 .   143.96760559082
Target Position =   -172.489761352539 .     -8899.083984375 .   144.477661132813

zx= 4.72851227272154 -      zy= 6.27332948057586
rotation set            = 5.5009208766487

Cameraposition =    -192.866882324219 .     -8900.1630859375 .  150.919052124023
Target Position =   -172.489761352539 .     -8899.083984375 .   144.477661132813

zx= 0.306169381117432 -     zy= 1.40481149256352
rotation set            = 0.855490436840475

In the first example the camX position is within 1 coord of the targetX position, this results in a drop in the zx contra the zy.

In the sec example the camY position is within 2 coord of the targetY position, this results in a drop in the zy contra the zx.

so i guess i got a idea what the problem is.

So the fix was like this:

if _max($posx1,$posx2) - _min($posx1,$posx2) > _max($posy1,$posy2) - _min($posy1,$posy2) Then
    $RotCalcB = $result2 
Else    
    $RotCalcB = $result3 
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Edited July 7, 2008 by malu05