CODEWITHSUNDEEP
openglmatrix
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Reputation: 579

I try to understand the View Matrix in OpenGL

I try to construct my own View Matrix in OpenGL.

I'm following this link https://www.opengl.org/sdk/docs/man2/xhtml/gluLookAt.xml

From the OpenGL doc, I have following.

eye position = eye(xe, ye, ze) center position = cen(0, 0, 0)

up = up(xu, yu, zu). (e.g. up = (0, 1, 0))

forward vector 

f' = cen - eye = (0, 0, 0) - (xe, ye, ze) = (-xe, -ye, -ze)

side vector 

s' = f' x up

I don't understand why f' x up, why not up x f'

u' = s' x f'

I do't understand why u' = s' x f', why not u' = f' x s'

we normalize s', u', f'

s = norm(s'), u = norm(u'), f=norm(f')

We construct the rotation matrix with row-major(what we learn in algebra class)

R = 
s_x u_x f_x 0
s_y u_y f_y 0
s_z u_z f_z 0
0   0    0  1

translation matrix:

T = 
1 0 0 x
0 1 0 y
0 0 1 z
0 0 0 1

we know

M = T*R
View Matrix V = invert(M)
V = invert(T*R) = invert(R)invert(T)
V = transpose(R)invert(T) 

transpose(R) = 
s_x s_y s_z 0
u_x u_y u_z 0
f_x f_y f_z 0
0   0    0  1


invert(T) = 
1 0 0 -x
0 1 0 -y
0 0 1 -z
0 0 0 1

so

View Matrix V = transpose(R)invert(T)

But from the OpenGL doc., f change to -f

The rotation changes to following 

R = 
s_x u_x -f_x 0
s_y u_y -f_y 0
s_z u_z -f_z 0
0   0    0  1

I Don't understand why we need to change the forward vector to negative.

Upvotes: 1

Views: 287

Answers (1)

Nico Schertler
Nico Schertler

Reputation: 32637

The cross product order just follows from its definition. It is just like it is. You are setting up a right-handed coordinate system. So if you align the thumb of your right hand with the first factor and the index finger with the second factor, then the middle finger will point in the direction of the cross product (perpendicular to both). There is really not much more to tell about this.

And since you are setting up a right-handed coordinate system, the forward direction of the camera must be mapped to the negative z-direction. That's why the third column of the rotation matrix is inverted. If you don't do this, you end up with a left-handed coordinate system, where the camera looks in the direction of the positive z-axis.

Upvotes: 2

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