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GLULOOKAT()							     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 projection matrix is used, the center
     of the scene therefore maps to the center of the viewport.  Similarly,  the
     direction	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 parallel to the line of sight from the eye point
     to the reference 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);  glTranslated  (-eyex,
     -eyey, -eyez);

SEE ALSO
     glFrustum, gluPerspective

								     GLULOOKAT()

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<https://man.freebsd.org/cgi/man.cgi?query=gluLookAt&sektion=3&manpath=FreeBSD+Ports+15.1.quarterly>

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