suzanne.soy/racket
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

Documented new additions to racket/math

Browse Source
This commit is contained in:
Neil Toronto 2012-06-06 11:31:49 -06:00
parent b7ff3eb1fb
commit e644e6afb1
2 changed files with 63 additions and 13 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

30
collects/images/scribblings/flomap.scrbl
View File

@ -1176,18 +1176,19 @@ In the following example, a photo of the State of the Union address was taken us
@interaction[#:eval flomap-eval
(flomap->bitmap state-of-the-union-fm)]
We would like it to have been taken with a perfect ``rectilinear'' (or ``perspective projection'') lens with a 120-degree diagonal angle of view.
Following the steps above, we apply a projection transform using @racket[(equal-area-projection pi)] for @racket[from-proj] and @racket[(perspective-projection (* 2/3 pi))] for @racket[to-proj]:
Following the steps above, we apply a projection transform using @racket[(equal-area-projection (degrees->radians 180))] for @racket[from-proj] and @racket[(perspective-projection (degrees->radians 120))] for @racket[to-proj]:
@interaction[#:eval flomap-eval
(flomap->bitmap
(flomap-transform
state-of-the-union-fm
(flomap-projection-transform (perspective-projection (* 2/3 pi))
(equal-area-projection pi))))]
(flomap-projection-transform
(perspective-projection (degrees->radians 120))
(equal-area-projection (degrees->radians 180)))))]
Notice that the straight geometry in the House chamber (especially the trim around the ceiling) is represented by straight edges in the corrected photo.
When @racket[crop?] is @racket[#t], the output flomap is no larger than the input flomap.
When @racket[crop?] is @racket[#f], the output flomap is large enough to contain the entire transformed flomap.
An uncropped result can be quite large, especially with angles of view at or near @racket[180] degrees (@racket[pi] radians).
An uncropped result can be quite large, especially with angles of view at or near @racket[180] degrees.
@interaction[#:eval flomap-eval
(define rectangle-fm
(draw-flomap (λ (fm-dc)
@ -1198,24 +1199,27 @@ An uncropped result can be quite large, especially with angles of view at or nea
32 32))
(flomap->bitmap rectangle-fm)
(flomap-transform-bounds
(flomap-projection-transform (perspective-projection (* 1/2 pi))
(equal-area-projection pi)
#f)
(flomap-projection-transform
(perspective-projection (degrees->radians 90))
(equal-area-projection (degrees->radians 180))
#f)
32 32)
(flomap->bitmap
(flomap-transform
rectangle-fm
(flomap-projection-transform (perspective-projection (* 1/2 pi))
(orthographic-projection (* 7/8 pi))
#f)))]
(flomap-projection-transform
(perspective-projection (degrees->radians 90))
(orthographic-projection (degrees->radians 160))
#f)))]
To crop manually, apply @racket[flomap-transform] to explicit rectangle arguments:
@interaction[#:eval flomap-eval
(flomap->bitmap
(flomap-transform
rectangle-fm
(flomap-projection-transform (perspective-projection (* 1/2 pi))
(orthographic-projection (* 7/8 pi))
#f)
(flomap-projection-transform
(perspective-projection (degrees->radians 90))
(orthographic-projection (degrees->radians 160))
#f)
-10 -10 42 42))]
}

46
collects/scribblings/reference/numbers.scrbl
View File

@ -1016,6 +1016,24 @@ is little-endian.}
An approximation to the ratio of a circle's circumference to its
diameter: @number->string[pi].}
@defproc[(degrees->radians [x real?]) real?]{
Converts an @racket[x]-degree angle to radians.
@mz-examples[
#:eval math-eval
(degrees->radians 180)
(sin (degrees->radians 45))
]}
@defproc[(radians->degrees [x real?]) real?]{
Converts @racket[x] radians to degrees.
@mz-examples[
#:eval math-eval
(radians->degrees pi)
(radians->degrees (* 1/4 pi))
]}
@defproc[(sqr [z number?]) number?]{
Returns @racket[(* z z)].}
@ -1054,6 +1072,26 @@ Returns the hyperbolic cosine of @racket[z].}
Returns the hyperbolic tangent of @racket[z].}
@defproc[(exact-round [x real?]) real?]{
Equivalent to @racket[(inexact->exact (round x))].
}
@defproc[(exact-floor [x real?]) real?]{
Equivalent to @racket[(inexact->exact (floor x))].
}
@defproc[(exact-ceiling [x real?]) real?]{
Equivalent to @racket[(inexact->exact (ceiling x))].
}
@defproc[(exact-truncate [x real?]) real?]{
Equivalent to @racket[(inexact->exact (truncate x))].
}
@defproc[(order-of-magnitude [r (and/c real? positive?)]) (and/c exact? integer?)]{
Computes the greatest exact integer @racket[m] such that:
@racketblock[(<= (expt 10 m)
@ -1069,6 +1107,14 @@ Hence also:
(order-of-magnitude 1/101)]
}
@defproc[(nan? [x real?]) boolean?]{
Returns @racket[#t] if @racket[x] is @racket[eqv?] to @racket[+nan.0] or @racket[+nan.f], @racket[#f] otherwise.}
@defproc[(infinite? [x real?]) boolean?]{
Returns @racket[#t] if @racket[z] is @racket[+inf.0], @racket[-inf.0], @racket[+inf.f], @racket[-inf.f]; @racket[#f] otherwise.}
@; ----------------------------------------------------------------------
@close-eval[math-eval]
@; ----------------------------------------------------------------------