GLULOOKAT() MachTen Programmer’s Manual GLULOOKAT()

NAME
gluLookAt - define a viewing transformation

C SPECIFICATION
void gluLookAt( GLdouble eyeX,
GLdouble eyeY,
GLdouble eyeZ,
GLdouble centerX,
GLdouble centerY,
GLdouble centerZ,
GLdouble upX,
GLdouble upY,
GLdouble upZ )

delim $$

PARAMETERS
eyeX, eyeY, eyeZ
Specifies the position of the eye point.

centerX, centerY, centerZ
Specifies the position of the reference
point.

upX, upY, upZ Specifies the direction of the up vector.

DESCRIPTION
gluLookAt creates a viewing matrix derived from an eye
point, a reference point indicating the center of the
scene, and an UP vector.

The matrix maps the reference point to the negative z axis
and the eye point to the origin. When a typical projec-
tion matrix is used, the center of the scene therefore
maps to the center of the viewport. Similarly, the direc-
tion described by the UP vector projected onto the viewing
plane is mapped to the positive y axis so that it points
upward in the viewport. The UP vector must not be paral-
lel to the line of sight from the eye point to the refer-
ence point.

Let

F ~=~ left ( down 20 { ~ matrix {
ccol {"centerX" above "centerY" above "centerZ"}
ccol { ~-~ above ~-~ above ~-~}
ccol {"eyeX" above "eyeY" above "eyeZ"} } } ~~ right )

Let UP be the vector $("upX", "upY", "upZ")$.

Then normalize as follows: f ~=~ F over {|| F ||}

UP sup prime ~=~ UP over {|| UP ||}

Finally, let $s ~=~ f ~times~ UP sup prime$, and $u ~=~ s
~times~ f$.

M is then constructed as follows: M ~=~ left ( matrix {
ccol { ~s[0] above ~u[0] above -f[0] above 0 }
ccol { ~s[1] above ~u[1] above -f[1] above 0 }
ccol { ~s[2] above ~u[2] above -f[2] above 0 }
ccol { 0 above 0 above 0 above 1 } } ~~right )

and gluLookAt is equivalent to glMultMatrixf(M); glTrans-
lated (-eyex, -eyey, -eyez);