On Thu, 14 Dec 2006, Miller, Raul D wrote:
+
+ Ok. Hmm...
+
+ First off, glTranslated -eye is equivalent to
+ glMultMatrix (=/~i.4)+_4{.&>4{.-eye
Using the phrase '_4{.&>4{. y' where y is of
length<4 to get a 4x4 result is very clever to me.
+
+ So I think what you really want is: given a projection (technically,
+ or modelview -- but that's probably a bad choice) matrix, find the
+ corresponding gluLookAt parameters. To actually use those
+ gluLookAt parameters you'd typically want the corresponding matrix
+ to be the identity, but that's easy enough.
+
+ Let's say that our parameters for gluLookAt are three 3vectors:
+ eye, center and up. Conceptually, gluLookAt converts these
+ to an x, y and z axis (M) and an origin (eye) and builds the
+ corresponding 4matrix. But you can build other 4matrices which
+ cannot be built by gluLookAt. Also, note that the precise location
+ of center and up do not matter -- all that matters is their direction
+ with respect to eye. And, for that matter, even their precise
+ direction isn't the issue -- the axes generated by gluLookAt have
+ to be orthogonal to each other, so if the vector from eye to
+ center is not orthogonal to the vector from eye to up we will
+ not be able to recover that information.
+
+ Anyways, let's say that the multiplication matrix we want to arrive at
+ through gluLookAt is y:
+
+ assert 0 0 0 1-:3{y
+ eye=: -4 8 12 {,y
I think this should be eye=: -3 7 11{,y
+ scale=:+/&.:*: eye
+ 's up nf'=: 3 3 {.y
What do s and nf stand for here? I think it does
make sense to use the middle vector in 3 3{.y for up.
+ center=: eye-scale*nf
+
+ In other words, given:
+
+ tAkool=:3 :0
+ assert 0 0 0 1-:3{y
+ eye=. -4 8 12 {,y
+ scale=.+/&.:*: eye
+ 's up nf'=. 3 3 {.y
+ center=. eye-scale*nf
+ eye,center,up
+ )
+ normalize=: ] % +/&.:*:
+ X=: (1&|[EMAIL PROTECTED] * _1&|[EMAIL PROTECTED]) - _1&|[EMAIL PROTECTED] *
1&|[EMAIL PROTECTED]
+
+ lookAt=:3 :0
+ y+9#0
+ 'eye center up'=. 3 3$y
+ f=.normalize center-eye
+ s=.normalize f X normalize up
+ u=.normalize s X f
+ M=.s,u,(-f),:_4{.1
+ M+/ .*(=/~i.4)+_4{.&>4{.-eye
+ )
+
+ (] -: [EMAIL PROTECTED]) tAkool lookAt ?9#0
+ 1
I cannot understand why you are checking this match?
Is the double application of tAkool lookAt necessary to
first create the valid input and then to test the input?
Such a strategy seems like forcing a match.
+
+
+
+ --
+ Raul
+
+
Thank you, Raul.
(B=)
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