Merge pull request #288 from borglab/feature/lines
Representation for lines in 3D - Line3release/4.3a0
Akshay Krishnan
GitHub
commit
ec29903eaa
189
doc/math.lyx
189
doc/math.lyx
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@ -1,7 +1,9 @@
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#LyX 2.1 created this file. For more info see http://www.lyx.org/
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\lyxformat 474
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#LyX 2.3 created this file. For more info see http://www.lyx.org/
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\lyxformat 544
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\begin_document
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\begin_header
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\save_transient_properties true
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\origin unavailable
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\textclass article
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\use_default_options false
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\begin_modules
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@ -14,16 +16,18 @@ theorems-ams-bytype
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\language_package default
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\inputencoding auto
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\fontencoding global
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\font_roman times
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\font_sans default
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\font_typewriter default
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\font_math auto
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\font_roman "times" "default"
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\font_sans "default" "default"
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\font_typewriter "default" "default"
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\font_math "auto" "auto"
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\font_default_family rmdefault
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\use_non_tex_fonts false
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\font_sc false
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\font_osf false
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\font_sf_scale 100
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\font_tt_scale 100
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\font_sf_scale 100 100
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\font_tt_scale 100 100
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\use_microtype false
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\use_dash_ligatures true
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\graphics default
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\default_output_format default
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\output_sync 0
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@ -53,6 +57,7 @@ theorems-ams-bytype
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\suppress_date false
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\justification true
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\use_refstyle 0
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\use_minted 0
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\index Index
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\shortcut idx
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\color #008000
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@ -65,7 +70,10 @@ theorems-ams-bytype
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\tocdepth 3
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\paragraph_separation indent
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\paragraph_indentation default
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\quotes_language english
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\is_math_indent 0
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\math_numbering_side default
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\quotes_style english
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\dynamic_quotes 0
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\papercolumns 1
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\papersides 1
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\paperpagestyle default
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@ -98,6 +106,11 @@ width "100col%"
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special "none"
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height "1in"
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height_special "totalheight"
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thickness "0.4pt"
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||||
separation "3pt"
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shadowsize "4pt"
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framecolor "black"
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backgroundcolor "none"
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status collapsed
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\begin_layout Plain Layout
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@ -654,6 +667,7 @@ reference "eq:LocalBehavior"
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\begin_inset CommandInset citation
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LatexCommand cite
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key "Spivak65book"
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literal "true"
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\end_inset
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@ -934,6 +948,7 @@ See
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\begin_inset CommandInset citation
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LatexCommand cite
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key "Spivak65book"
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literal "true"
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\end_inset
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@ -1025,6 +1040,7 @@ See
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\begin_inset CommandInset citation
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LatexCommand cite
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key "Spivak65book"
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literal "true"
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\end_inset
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@ -2209,6 +2225,7 @@ instantaneous velocity
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LatexCommand cite
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after "page 51 for rotations, page 419 for SE(3)"
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key "Murray94book"
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literal "true"
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\end_inset
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@ -2965,7 +2982,7 @@ B^{T} & I_{3}\end{array}\right]
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\begin_layout Subsection
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\begin_inset CommandInset label
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LatexCommand label
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name "sub:Pushforward-of-Between"
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name "subsec:Pushforward-of-Between"
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\end_inset
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@ -3419,6 +3436,7 @@ A retraction
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\begin_inset CommandInset citation
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LatexCommand cite
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key "Absil07book"
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literal "true"
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\end_inset
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@ -3873,7 +3891,7 @@ BetweenFactor
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, derived in Section
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\begin_inset CommandInset ref
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LatexCommand ref
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reference "sub:Pushforward-of-Between"
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reference "subsec:Pushforward-of-Between"
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\end_inset
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@ -4430,7 +4448,7 @@ In the case of
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\begin_inset Formula $\SOthree$
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\end_inset
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the vector space is
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the vector space is
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\begin_inset Formula $\Rthree$
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\end_inset
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@ -4502,7 +4520,7 @@ reference "Th:InverseAction"
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\begin_layout Subsection
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\begin_inset CommandInset label
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LatexCommand label
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name "sub:3DAngularVelocities"
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name "subsec:3DAngularVelocities"
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\end_inset
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@ -4695,6 +4713,7 @@ Absil
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LatexCommand cite
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after "page 58"
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key "Absil07book"
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literal "true"
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\end_inset
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@ -5395,6 +5414,7 @@ While not a Lie group, we can define an exponential map, which is given
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\begin_inset CommandInset citation
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LatexCommand cite
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key "Ma01ijcv"
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literal "true"
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\end_inset
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@ -5402,6 +5422,7 @@ key "Ma01ijcv"
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\begin_inset CommandInset href
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LatexCommand href
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name "http://stat.fsu.edu/~anuj/CVPR_Tutorial/Part2.pdf"
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literal "false"
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\end_inset
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@ -5605,6 +5626,7 @@ The exponential map uses
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\begin_inset CommandInset citation
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LatexCommand cite
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key "Absil07book"
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literal "true"
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\end_inset
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@ -6293,7 +6315,7 @@ d^{c}=R_{w}^{c}\left(d^{w}+(t^{w}v^{w})v^{w}-t^{w}\right)
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\end_layout
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\begin_layout Section
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Line3 (Ocaml)
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Line3
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\end_layout
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\begin_layout Standard
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@ -6345,6 +6367,14 @@ R'=R(I+\Omega)
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\end_inset
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\end_layout
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\begin_layout Subsection
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Projecting Line3
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\end_layout
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\begin_layout Standard
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Projecting a line to 2D can be done easily, as both
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\begin_inset Formula $v$
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\end_inset
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@ -6430,13 +6460,21 @@ or the
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\end_layout
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\begin_layout Subsection
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Action of
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\begin_inset Formula $\SEthree$
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\end_inset
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on the line
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\end_layout
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\begin_layout Standard
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Transforming a 3D line
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\begin_inset Formula $(R,(a,b))$
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\end_inset
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from a world coordinate frame to a camera frame
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\begin_inset Formula $(R_{w}^{c},t^{w})$
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\begin_inset Formula $T_{c}^{w}=(R_{c}^{w},t^{w})$
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\end_inset
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is done by
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@ -6466,17 +6504,115 @@ b'=b-R_{2}^{T}t^{w}
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\end_inset
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Again, we need to redo the derivatives, as R is incremented from the right.
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The first argument is incremented from the left, but the result is incremented
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on the right:
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where
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\begin_inset Formula $R_{1}$
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\end_inset
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and
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\begin_inset Formula $R_{2}$
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\end_inset
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are the columns of
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\begin_inset Formula $R$
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\end_inset
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, as before.
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\end_layout
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\begin_layout Standard
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To find the derivatives, the transformation of a line
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\begin_inset Formula $l^{w}=(R,a,b)$
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\end_inset
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from world coordinates to a camera coordinate frame
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\begin_inset Formula $T_{c}^{w}$
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\end_inset
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, specified in world coordinates, can be written as a function
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\begin_inset Formula $f:\SEthree\times L\rightarrow L$
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\end_inset
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, as given above, i.e.,
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\begin_inset Formula
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\begin{eqnarray*}
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R'(I+\Omega')=(AB)(I+\Omega') & = & (I+\Skew{S\omega})AB\\
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I+\Omega' & = & (AB)^{T}(I+\Skew{S\omega})(AB)\\
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\Omega' & = & R'^{T}\Skew{S\omega}R'\\
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\Omega' & = & \Skew{R'^{T}S\omega}\\
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\omega' & = & R'^{T}S\omega
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\end{eqnarray*}
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\[
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f(T_{c}^{w},l^{w})=\left(\left(R_{c}^{w}\right)^{T}R,a-R_{1}^{T}t^{w},b-R_{2}^{T}t^{w}\right).
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\]
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\end_inset
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Let us find the Jacobian
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\begin_inset Formula $J_{1}$
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\end_inset
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of
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\begin_inset Formula $f$
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\end_inset
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with respect to the first argument
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\begin_inset Formula $T_{c}^{w}$
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\end_inset
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, which should obey
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\begin_inset Formula
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\begin{align*}
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f(T_{c}^{w}e^{\xihat},l^{w}) & \approx f(T_{c}^{w},l^{w})+J_{1}\xi
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\end{align*}
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\end_inset
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Note that
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\begin_inset Formula
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\[
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T_{c}^{w}e^{\xihat}\approx\left[\begin{array}{cc}
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R_{c}^{w}\left(I_{3}+\Skew{\omega}\right) & t^{w}+R_{c}^{w}v\\
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0 & 1
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\end{array}\right]
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\]
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\end_inset
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Let's write this out separately for each of
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\begin_inset Formula $R,a,b$
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\end_inset
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:
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\begin_inset Formula
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\begin{align*}
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\left(R_{c}^{w}\left(I_{3}+\Skew{\omega}\right)\right)^{T}R & \approx\left(R_{c}^{w}\right)^{T}R(I+\left[J_{R\omega}\omega\right]_{\times})\\
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a-R_{1}^{T}\left(t^{w}+R_{c}^{w}v\right) & \approx a-R_{1}^{T}t^{w}+J_{av}v\\
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b-R_{2}^{T}\left(t^{w}+R_{c}^{w}v\right) & \approx b-R_{2}^{T}t^{w}+J_{bv}v
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\end{align*}
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\end_inset
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Simplifying, we get:
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\begin_inset Formula
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\begin{align*}
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-\Skew{\omega}R' & \approx R'\left[J_{R\omega}\omega\right]_{\times}\\
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-R_{1}^{T}R_{c}^{w} & \approx J_{av}\\
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-R_{2}^{T}R_{c}^{w} & \approx J_{bv}
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\end{align*}
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\end_inset
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which gives the expressions for
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\begin_inset Formula $J_{av}$
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\end_inset
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and
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\begin_inset Formula $J_{bv}$
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\end_inset
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.
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The top line can be further simplified:
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\begin_inset Formula
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\begin{align*}
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-\Skew{\omega}R' & \approx R'\left[J_{R\omega}\omega\right]_{\times}\\
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-R'^{T}\Skew{\omega}R' & \approx\left[J_{R\omega}\omega\right]_{\times}\\
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-\Skew{R'^{T}\omega} & \approx\left[J_{R\omega}\omega\right]_{\times}\\
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-R'^{T} & \approx J_{R\omega}
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\end{align*}
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\end_inset
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@ -6687,6 +6823,7 @@ Spivak
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\begin_inset CommandInset citation
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LatexCommand cite
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key "Spivak65book"
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literal "true"
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||||
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\end_inset
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||||
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@ -6795,6 +6932,7 @@ The following is adapted from Appendix A in
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\begin_inset CommandInset citation
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LatexCommand cite
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key "Murray94book"
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literal "true"
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\end_inset
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@ -6924,6 +7062,7 @@ might be
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LatexCommand cite
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after "page 45"
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key "Hall00book"
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literal "true"
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||||
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||||
\end_inset
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||||
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||||
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BIN
doc/math.pdf
BIN
doc/math.pdf
Binary file not shown.
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@ -0,0 +1,120 @@
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#include <gtsam/geometry/Line3.h>
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namespace gtsam {
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Line3 Line3::retract(const Vector4 &v, OptionalJacobian<4, 4> Dp, OptionalJacobian<4, 4> Dv) const {
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Vector3 w;
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w << v[0], v[1], 0;
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Rot3 incR;
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if (Dp) {
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Dp->setIdentity();
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incR = Rot3::Expmap(w);
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Dp->block<2, 2>(0, 0) = ((incR.matrix()).transpose()).block<2, 2>(0, 0);
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}
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if (Dv) {
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Matrix3 Dw;
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incR = Rot3::Expmap(w, Dw);
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Dv->setIdentity();
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Dv->block<2, 2>(0, 0) = Dw.block<2, 2>(0, 0);
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} else {
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incR = Rot3::Expmap(w);
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}
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Rot3 Rt = R_ * incR;
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return Line3(Rt, a_ + v[2], b_ + v[3]);
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}
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Vector4 Line3::localCoordinates(const Line3 &q, OptionalJacobian<4, 4> Dp,
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OptionalJacobian<4, 4> Dq) const {
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Vector3 omega;
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Matrix3 D_log;
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omega = Rot3::Logmap(R_.inverse() * q.R_, D_log);
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if (Dp) {
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Matrix3 D_log_wp = -((q.R_).matrix()).transpose() * R_.matrix();
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Matrix3 Dwp = D_log * D_log_wp;
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Dp->setIdentity();
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Dp->block<2, 2>(0, 0) = Dwp.block<2, 2>(0, 0);
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(*Dp)(2, 2) = -1;
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(*Dp)(3, 3) = -1;
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}
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if (Dq) {
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Dq->setIdentity();
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Dq->block<2, 2>(0, 0) = D_log.block<2, 2>(0, 0);
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}
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Vector4 local;
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local << omega[0], omega[1], q.a_ - a_, q.b_ - b_;
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return local;
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}
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void Line3::print(const std::string &s) const {
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std::cout << s << std::endl;
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R_.print("R:\n");
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std::cout << "a: " << a_ << ", b: " << b_ << std::endl;
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}
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bool Line3::equals(const Line3 &l2, double tol) const {
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Vector4 diff = localCoordinates(l2);
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return fabs(diff[0]) < tol && fabs(diff[1]) < tol
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&& fabs(diff[2]) < tol && fabs(diff[3]) < tol;
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}
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Unit3 Line3::project(OptionalJacobian<2, 4> Dline) const {
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Vector3 V_0;
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V_0 << -b_, a_, 0.0;
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||||
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||||
Unit3 l;
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if (Dline) {
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// Jacobian of the normalized Unit3 projected line with respect to
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// un-normalized Vector3 projected line in homogeneous coordinates.
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Matrix23 D_unit_line;
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l = Unit3::FromPoint3(Point3(R_ * V_0), D_unit_line);
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// Jacobian of the un-normalized Vector3 line with respect to
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// input 3D line
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Matrix34 D_vec_line = Matrix34::Zero();
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D_vec_line.col(0) = a_ * R_.r3();
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D_vec_line.col(1) = b_ * R_.r3();
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D_vec_line.col(2) = R_.r2();
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D_vec_line.col(3) = -R_.r1();
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// Jacobian of output wrt input is the product of the two.
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*Dline = D_unit_line * D_vec_line;
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} else {
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l = Unit3::FromPoint3(Point3(R_ * V_0));
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}
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return l;
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}
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Point3 Line3::point(double distance) const {
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// defining "center" of the line to be the point where it
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// intersects rotated XY axis
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Point3 center(a_, b_, 0);
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Point3 rotated_center = R_ * center;
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return rotated_center + distance * R_.r3();
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||||
}
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||||
Line3 transformTo(const Pose3 &wTc, const Line3 &wL,
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||||
OptionalJacobian<4, 6> Dpose, OptionalJacobian<4, 4> Dline) {
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Rot3 wRc = wTc.rotation();
|
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Rot3 cRw = wRc.inverse();
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||||
Rot3 cRl = cRw * wL.R_;
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Vector2 w_ab;
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||||
Vector3 t = ((wL.R_).transpose() * wTc.translation());
|
||||
Vector2 c_ab(wL.a_ - t[0], wL.b_ - t[1]);
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||||
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||||
if (Dpose) {
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||||
Matrix3 lRc = (cRl.matrix()).transpose();
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||||
Dpose->setZero();
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||||
// rotation
|
||||
Dpose->block<2, 3>(0, 0) = -lRc.block<2, 3>(0, 0);
|
||||
// translation
|
||||
Dpose->block<2, 3>(2, 3) = -lRc.block<2, 3>(0, 0);
|
||||
}
|
||||
if (Dline) {
|
||||
Dline->setIdentity();
|
||||
(*Dline)(0, 3) = -t[2];
|
||||
(*Dline)(1, 2) = t[2];
|
||||
}
|
||||
return Line3(cRl, c_ab[0], c_ab[1]);
|
||||
}
|
||||
|
||||
}
|
||||
|
|
@ -0,0 +1,135 @@
|
|||
/* ----------------------------------------------------------------------------
|
||||
* GTSAM Copyright 2010, Georgia Tech Research Corporation,
|
||||
* Atlanta, Georgia 30332-0415
|
||||
* All Rights Reserved
|
||||
* Authors: Frank Dellaert, et al. (see THANKS for the full author list)
|
||||
* See LICENSE for the license information
|
||||
* -------------------------------------------------------------------------- */
|
||||
|
||||
/**
|
||||
* @file Line3.h
|
||||
* @brief 4 dimensional manifold of 3D lines
|
||||
* @author Akshay Krishnan
|
||||
* @author Frank Dellaert
|
||||
*/
|
||||
// \callgraph
|
||||
|
||||
#pragma once
|
||||
|
||||
#include <gtsam/geometry/Rot3.h>
|
||||
#include <gtsam/geometry/Pose3.h>
|
||||
|
||||
namespace gtsam {
|
||||
|
||||
/**
|
||||
* A 3D line (R,a,b) : (Rot3,Scalar,Scalar)
|
||||
* @addtogroup geometry
|
||||
* \nosubgrouping
|
||||
*/
|
||||
class Line3 {
|
||||
private:
|
||||
Rot3 R_; // Rotation of line about x and y in world frame
|
||||
double a_, b_; // Intersection of line with the world x-y plane rotated by R_
|
||||
// Also the closest point on line to origin
|
||||
public:
|
||||
enum { dimension = 4 };
|
||||
|
||||
/** Default constructor is the Z axis **/
|
||||
Line3() :
|
||||
a_(0), b_(0) {}
|
||||
|
||||
/** Constructor for general line from (R, a, b) **/
|
||||
Line3(const Rot3 &R, const double a, const double b) :
|
||||
R_(R), a_(a), b_(b) {}
|
||||
|
||||
/**
|
||||
* The retract method maps from the tangent space back to the manifold.
|
||||
* The method q = p + v, where p is this line, v is an increment along
|
||||
* the tangent space and q is the resulting line.
|
||||
* The tangent space for the rotation of a line is only two dimensional -
|
||||
* rotation about x and y
|
||||
* @param v: increment in tangent space
|
||||
* @param Dp: increment of retraction with respect to this line
|
||||
* @param Dv: Jacobian of retraction with respect to the increment
|
||||
* @return q: resulting line after adding the increment and mapping to the manifold
|
||||
*/
|
||||
Line3 retract(const Vector4 &v,
|
||||
OptionalJacobian<4, 4> Dp = boost::none,
|
||||
OptionalJacobian<4, 4> Dv = boost::none) const;
|
||||
|
||||
/**
|
||||
* The localCoordinates method is the inverse of retract and finds the difference
|
||||
* between two lines in the tangent space. It computes v = q - p where q is an input
|
||||
* line, p is this line and v is their difference in the tangent space.
|
||||
* @param q: Line3 on manifold
|
||||
* @param Dp: OptionalJacobian of localCoordinates with respect to this line
|
||||
* @param Dq: OptionalJacobian of localCoordinates with respect to this line
|
||||
* @return v: difference in the tangent space
|
||||
*/
|
||||
Vector4 localCoordinates(const Line3 &q,
|
||||
OptionalJacobian<4, 4> Dp = boost::none,
|
||||
OptionalJacobian<4, 4> Dq = boost::none) const;
|
||||
|
||||
/**
|
||||
* Print R, a, b
|
||||
* @param s: optional starting string
|
||||
*/
|
||||
void print(const std::string &s = "") const;
|
||||
|
||||
/**
|
||||
* Check if two lines are equal
|
||||
* @param l2 - line to be compared
|
||||
* @param tol : optional tolerance
|
||||
* @return boolean - true if lines are equal
|
||||
*/
|
||||
bool equals(const Line3 &l2, double tol = 10e-9) const;
|
||||
|
||||
/**
|
||||
* Projecting a line to the image plane. Assumes this line is in camera frame.
|
||||
* @param Dline: OptionalJacobian of projected line with respect to this line
|
||||
* @return Unit3 - projected line in image plane, in homogenous coordinates.
|
||||
* We use Unit3 since it is a manifold with the right dimension.
|
||||
*/
|
||||
Unit3 project(OptionalJacobian<2, 4> Dline = boost::none) const;
|
||||
|
||||
/**
|
||||
* Returns point on the line that is at a certain distance starting from the
|
||||
* point where the rotated XY axis intersects the line.
|
||||
* @param distance (can be positive or negative) - positive is the positive
|
||||
* direction of the rotated z axis that forms the line. The default value of zero
|
||||
* returns the point where the rotated XY axis intersects the line.
|
||||
* @return Point on the line
|
||||
*/
|
||||
Point3 point(double distance = 0) const;
|
||||
|
||||
/**
|
||||
* Transform a line from world to camera frame
|
||||
* @param wTc - Pose3 of camera in world frame
|
||||
* @param wL - Line3 in world frame
|
||||
* @param Dpose - OptionalJacobian of transformed line with respect to p
|
||||
* @param Dline - OptionalJacobian of transformed line with respect to l
|
||||
* @return Transformed line in camera frame
|
||||
*/
|
||||
friend Line3 transformTo(const Pose3 &wTc, const Line3 &wL,
|
||||
OptionalJacobian<4, 6> Dpose,
|
||||
OptionalJacobian<4, 4> Dline);
|
||||
};
|
||||
|
||||
/**
|
||||
* Transform a line from world to camera frame
|
||||
* @param wTc - Pose3 of camera in world frame
|
||||
* @param wL - Line3 in world frame
|
||||
* @param Dpose - OptionalJacobian of transformed line with respect to p
|
||||
* @param Dline - OptionalJacobian of transformed line with respect to l
|
||||
* @return Transformed line in camera frame
|
||||
*/
|
||||
Line3 transformTo(const Pose3 &wTc, const Line3 &wL,
|
||||
OptionalJacobian<4, 6> Dpose = boost::none,
|
||||
OptionalJacobian<4, 4> Dline = boost::none);
|
||||
|
||||
template<>
|
||||
struct traits<Line3> : public internal::Manifold<Line3> {};
|
||||
|
||||
template<>
|
||||
struct traits<const Line3> : public internal::Manifold<Line3> {};
|
||||
}
|
||||
|
|
@ -0,0 +1,155 @@
|
|||
#include <CppUnitLite/TestHarness.h>
|
||||
#include <gtsam/base/Testable.h>
|
||||
#include <gtsam/base/numericalDerivative.h>
|
||||
#include <gtsam/geometry/Line3.h>
|
||||
#include <gtsam/slam/expressions.h>
|
||||
#include <gtsam/slam/PriorFactor.h>
|
||||
#include <gtsam/nonlinear/ExpressionFactor.h>
|
||||
#include <gtsam/nonlinear/expressionTesting.h>
|
||||
|
||||
using namespace gtsam;
|
||||
|
||||
GTSAM_CONCEPT_TESTABLE_INST(Line3)
|
||||
GTSAM_CONCEPT_MANIFOLD_INST(Line3)
|
||||
|
||||
static const Line3 l(Rot3(), 1, 1);
|
||||
|
||||
// Testing equals function of Line3
|
||||
TEST(Line3, equals) {
|
||||
Line3 l_same = l;
|
||||
EXPECT(l.equals(l_same));
|
||||
Line3 l2(Rot3(), 1, 2);
|
||||
EXPECT(!l.equals(l2));
|
||||
}
|
||||
|
||||
// testing localCoordinates along 4 dimensions
|
||||
TEST(Line3, localCoordinates) {
|
||||
// l1 and l differ only in a_
|
||||
Line3 l1(Rot3(), 2, 1);
|
||||
Vector4 v1(0, 0, -1, 0);
|
||||
CHECK(assert_equal(l1.localCoordinates(l), v1));
|
||||
|
||||
// l2 and l differ only in b_
|
||||
Line3 l2(Rot3(), 1, 2);
|
||||
Vector4 v2(0, 0, 0, -1);
|
||||
CHECK(assert_equal(l2.localCoordinates(l), v2));
|
||||
|
||||
// l3 and l differ in R_x
|
||||
Rot3 r3 = Rot3::Expmap(Vector3(M_PI / 4, 0, 0));
|
||||
Line3 l3(r3, 1, 1);
|
||||
Vector4 v3(-M_PI / 4, 0, 0, 0);
|
||||
CHECK(assert_equal(l3.localCoordinates(l), v3));
|
||||
|
||||
// l4 and l differ in R_y
|
||||
Rot3 r4 = Rot3::Expmap(Vector3(0, M_PI / 4, 0));
|
||||
Line3 l4(r4, 1, 1);
|
||||
Vector4 v4(0, -M_PI / 4, 0, 0);
|
||||
CHECK(assert_equal(l4.localCoordinates(l), v4));
|
||||
|
||||
// Jacobians
|
||||
Line3 l5(Rot3::Expmap(Vector3(M_PI / 3, -M_PI / 4, 0)), -0.8, 2);
|
||||
Values val;
|
||||
val.insert(1, l);
|
||||
val.insert(2, l5);
|
||||
Line3_ l_(1);
|
||||
Line3_ l5_(2);
|
||||
SharedNoiseModel model = noiseModel::Isotropic::Sigma(4, 0.1);
|
||||
Vector4_ local_(l5_, &Line3::localCoordinates, l_);
|
||||
ExpressionFactor<Vector4> f(model, l5.localCoordinates(l), local_);
|
||||
EXPECT_CORRECT_FACTOR_JACOBIANS(f, val, 1e-5, 1e-7);
|
||||
}
|
||||
|
||||
// testing retract along 4 dimensions
|
||||
TEST(Line3, retract) {
|
||||
// l1 and l differ only in a_
|
||||
Vector4 v1(0, 0, 0, 1);
|
||||
Line3 l1(Rot3(), 1, 2);
|
||||
EXPECT(l1.equals(l.retract(v1)));
|
||||
|
||||
// l2 and l differ only in b_
|
||||
Vector4 v2(0, 0, 1, 0);
|
||||
Line3 l2(Rot3(), 2, 1);
|
||||
EXPECT(l2.equals(l.retract(v2)));
|
||||
|
||||
// l3 and l differ in R_x
|
||||
Vector4 v3(M_PI / 4, 0, 0, 0);
|
||||
Rot3 r3;
|
||||
r3 = r3.Expmap(Vector3(M_PI / 4, 0, 0));
|
||||
Line3 l3(r3, 1, 1);
|
||||
EXPECT(l3.equals(l.retract(v3)));
|
||||
|
||||
// l4 and l differ in R_y
|
||||
Vector4 v4(0, M_PI / 4, 0, 0);
|
||||
Rot3 r4 = Rot3::Expmap(Vector3(0, M_PI / 4, 0));
|
||||
Line3 l4(r4, 1, 1);
|
||||
EXPECT(l4.equals(l.retract(v4)));
|
||||
|
||||
// Jacobians
|
||||
Vector4 v5(M_PI / 3, -M_PI / 4, -0.4, 1.2); // arbitrary vector
|
||||
Values val;
|
||||
val.insert(1, l);
|
||||
val.insert(2, v5);
|
||||
Line3_ l_(1);
|
||||
Vector4_ v5_(2);
|
||||
SharedNoiseModel model = noiseModel::Isotropic::Sigma(4, 0.1);
|
||||
Line3_ retract_(l_, &Line3::retract, v5_);
|
||||
ExpressionFactor<Line3> f(model, l.retract(v5), retract_);
|
||||
EXPECT_CORRECT_FACTOR_JACOBIANS(f, val, 1e-5, 1e-7);
|
||||
}
|
||||
|
||||
// testing manifold property - Retract(p, Local(p,q)) == q
|
||||
TEST(Line3, retractOfLocalCoordinates) {
|
||||
Rot3 r2 = Rot3::Expmap(Vector3(M_PI / 4, M_PI / 3, 0));
|
||||
Line3 l2(r2, 5, 9);
|
||||
EXPECT(assert_equal(l.retract(l.localCoordinates(l2)), l2));
|
||||
}
|
||||
|
||||
// testing manifold property - Local(p, Retract(p, v)) == v
|
||||
TEST(Line3, localCoordinatesOfRetract) {
|
||||
Vector4 r2(2.3, 0.987, -3, 4);
|
||||
EXPECT(assert_equal(l.localCoordinates(l.retract(r2)), r2));
|
||||
}
|
||||
|
||||
// transform from world to camera test
|
||||
TEST(Line3, transformToExpressionJacobians) {
|
||||
Rot3 r = Rot3::Expmap(Vector3(0, M_PI / 3, 0));
|
||||
Vector3 t(0, 0, 0);
|
||||
Pose3 p(r, t);
|
||||
|
||||
Line3 l_c(r.inverse(), 1, 1);
|
||||
Line3 l_w(Rot3(), 1, 1);
|
||||
EXPECT(l_c.equals(transformTo(p, l_w)));
|
||||
|
||||
Line3_ l_(1);
|
||||
Pose3_ p_(2);
|
||||
Values val;
|
||||
val.insert(1, l_w);
|
||||
val.insert(2, p);
|
||||
|
||||
SharedNoiseModel model = noiseModel::Isotropic::Sigma(4, 0.1);
|
||||
ExpressionFactor<Line3> f(model, transformTo(p, l_w), transformTo(p_, l_));
|
||||
EXPECT_CORRECT_FACTOR_JACOBIANS(f, val, 1e-5, 1e-7);
|
||||
}
|
||||
|
||||
// projection in camera frame test
|
||||
TEST(Line3, projection) {
|
||||
Rot3 r = Rot3::Expmap(Vector3(0, 0, 0));
|
||||
Line3 wL(r, 1, 1);
|
||||
|
||||
Unit3 expected = Unit3::FromPoint3(Point3(-1, 1, 0));
|
||||
EXPECT(expected.equals(wL.project()));
|
||||
|
||||
Values val;
|
||||
val.insert(1, wL);
|
||||
Line3_ wL_(1);
|
||||
|
||||
SharedNoiseModel model = noiseModel::Isotropic::Sigma(2, 0.1);
|
||||
Unit3_ projected_(wL_, &Line3::project);
|
||||
ExpressionFactor<Unit3> f(model, expected, projected_);
|
||||
EXPECT_CORRECT_FACTOR_JACOBIANS(f, val, 1e-5, 1e-7);
|
||||
}
|
||||
|
||||
int main() {
|
||||
TestResult tr;
|
||||
return TestRegistry::runAllTests(tr);
|
||||
}
|
||||
|
|
@ -11,6 +11,7 @@
|
|||
#include <gtsam/geometry/Pose2.h>
|
||||
#include <gtsam/geometry/Cal3_S2.h>
|
||||
#include <gtsam/geometry/Cal3Bundler.h>
|
||||
#include <gtsam/geometry/Line3.h>
|
||||
#include <gtsam/geometry/PinholeCamera.h>
|
||||
|
||||
namespace gtsam {
|
||||
|
|
@ -31,6 +32,7 @@ typedef Expression<Point3> Point3_;
|
|||
typedef Expression<Unit3> Unit3_;
|
||||
typedef Expression<Rot3> Rot3_;
|
||||
typedef Expression<Pose3> Pose3_;
|
||||
typedef Expression<Line3> Line3_;
|
||||
|
||||
inline Point3_ transformTo(const Pose3_& x, const Point3_& p) {
|
||||
return Point3_(x, &Pose3::transformTo, p);
|
||||
|
|
@ -40,6 +42,12 @@ inline Point3_ transformFrom(const Pose3_& x, const Point3_& p) {
|
|||
return Point3_(x, &Pose3::transformFrom, p);
|
||||
}
|
||||
|
||||
inline Line3_ transformTo(const Pose3_ &wTc, const Line3_ &wL) {
|
||||
Line3 (*f)(const Pose3 &, const Line3 &,
|
||||
OptionalJacobian<4, 6>, OptionalJacobian<4, 4>) = &transformTo;
|
||||
return Line3_(f, wTc, wL);
|
||||
}
|
||||
|
||||
namespace internal {
|
||||
// define getter that returns value rather than reference
|
||||
inline Rot3 rotation(const Pose3& pose, OptionalJacobian<3, 6> H) {
|
||||
|
|
|
|||
Loading…
Reference in New Issue