From f602d28a715286db59ba9589035d06fc9aa42696 Mon Sep 17 00:00:00 2001 From: pyposebot Date: Wed, 18 Sep 2024 17:45:25 +0000 Subject: [PATCH] Add docs from pypose/pypose --- .../_modules/pypose/lietensor/convert/index.html | 13 +++++-------- docs/preview/pr/353/convert/index.html | 2 +- .../pr/353/generated/pypose.quat2unit/index.html | 4 ++-- docs/preview/pr/353/searchindex.js | 2 +- 4 files changed, 9 insertions(+), 12 deletions(-) diff --git a/docs/preview/pr/353/_modules/pypose/lietensor/convert/index.html b/docs/preview/pr/353/_modules/pypose/lietensor/convert/index.html index c473f5d3e..6056776a0 100644 --- a/docs/preview/pr/353/_modules/pypose/lietensor/convert/index.html +++ b/docs/preview/pr/353/_modules/pypose/lietensor/convert/index.html @@ -1072,8 +1072,8 @@

Source code for pypose.lietensor.convert

 
 
[docs]def quat2unit(input: LieTensor, eps=1e-12) -> LieTensor:
     r'''
-    Normalize the quaternion part of a ``LieTensor``, which has to be a Lie Group.
-    If input is a Lie algebra, then do nothing and return the input tensor.
+    Normalize the quaternion part of a ``LieTensor``, which has to be a Lie group.
+    If input is a not a Lie group, then do nothing and return the input.
     If the quaternion parts are zeros, then initilize identity quaternions.
 
     The quaternion parts :math:`v` are normalized as
@@ -1090,11 +1090,7 @@ 
Source code for pypose.lietensor.convert
     Return:
         :obj:`LieTensor`: the output LieTensor.
     '''
-    assert isinstance(input, LieTensor), "Input should be a LieTensor"
-
-    if input.ltype in liealgebra:
-        return input
-    elif input.ltype in liegroup:
+    if isinstance(input, LieTensor) and (input.ltype in liegroup):
         data = input.tensor()
         if input.ltype in [SO3_type, RxSO3_type]:
             data[..., :4] = normalize(data[..., :4], p=2, dim=-1, eps=eps)
@@ -1105,7 +1101,8 @@ 
Source code for pypose.lietensor.convert
             output.rotation().identity_()
         return output
     else:
-        raise "LieType of Input LieTensor not recognized."

+        warnings.warn("Input is not Lie group, doing thing and returning input..")
+        return input
diff --git a/docs/preview/pr/353/convert/index.html b/docs/preview/pr/353/convert/index.html index 2c2b7475f..52abd425a 100644 --- a/docs/preview/pr/353/convert/index.html +++ b/docs/preview/pr/353/convert/index.html @@ -288,7 +288,7 @@

ConvertLieTensor into matrix form.

quat2unit

-

Normalize the quaternion part of a LieTensor, which has to be a Lie Group.

+

Normalize the quaternion part of a LieTensor, which has to be a Lie group.

cart2homo

Converts batched Cartesian coordinates to Homogeneous coordinates by adding ones to last dimension.

diff --git a/docs/preview/pr/353/generated/pypose.quat2unit/index.html b/docs/preview/pr/353/generated/pypose.quat2unit/index.html index cd6b606f7..5371b84a0 100644 --- a/docs/preview/pr/353/generated/pypose.quat2unit/index.html +++ b/docs/preview/pr/353/generated/pypose.quat2unit/index.html @@ -251,8 +251,8 @@

pypose.quat2unit
pypose.quat2unit(input, eps=1e-12)[source]ΒΆ
-

Normalize the quaternion part of a LieTensor, which has to be a Lie Group. -If input is a Lie algebra, then do nothing and return the input tensor. +

Normalize the quaternion part of a LieTensor, which has to be a Lie group. +If input is a not a Lie group, then do nothing and return the input. If the quaternion parts are zeros, then initilize identity quaternions.

The quaternion parts \(v\) are normalized as

diff --git a/docs/preview/pr/353/searchindex.js b/docs/preview/pr/353/searchindex.js index 6725964bb..3ce4c53da 100644 --- a/docs/preview/pr/353/searchindex.js +++ b/docs/preview/pr/353/searchindex.js @@ -1 +1 @@ -Search.setIndex({"docnames": ["convert", "func", "functions", "generated/pypose.Act", "generated/pypose.Adj", "generated/pypose.AdjT", "generated/pypose.Exp", "generated/pypose.Inv", "generated/pypose.Jinvp", "generated/pypose.Jr", "generated/pypose.LieTensor", "generated/pypose.Log", "generated/pypose.Parameter", "generated/pypose.Retr", "generated/pypose.RxSO3", "generated/pypose.SE3", "generated/pypose.SO3", "generated/pypose.Sim3", "generated/pypose.add", "generated/pypose.add_", "generated/pypose.bmv", "generated/pypose.bspline", "generated/pypose.bvmv", "generated/pypose.bvv", "generated/pypose.cart2homo", "generated/pypose.chspline", "generated/pypose.cummul", "generated/pypose.cummul_", "generated/pypose.cumops", "generated/pypose.cumops_", "generated/pypose.cumprod", 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"so3": [3, 4, 6, 7, 8, 9, 10, 11, 13, 14, 15, 26, 30, 32, 40, 46, 52, 58, 67, 98, 104, 105, 106, 107, 113, 116], "mapsto": [3, 4, 6, 7, 8, 9, 11, 13, 67], "torch": [3, 4, 6, 10, 11, 12, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 105, 107, 108, 109, 110, 111, 112, 114, 115], "randn": [3, 10, 14, 15, 16, 17, 18, 20, 22, 23, 24, 33, 35, 55, 59, 60, 61, 62, 64, 66, 67, 74, 85, 86, 98, 103, 105, 107, 108, 109, 115], "3": [3, 4, 6, 8, 9, 10, 11, 15, 17, 20, 21, 23, 24, 25, 33, 34, 35, 36, 37, 42, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 66, 67, 69, 71, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 89, 90, 92, 94, 96, 99, 100, 101, 102, 103, 109, 110, 112, 114, 115], "size": [3, 10, 14, 15, 16, 17, 20, 22, 23, 26, 28, 30, 35, 37, 38, 42, 43, 58, 74, 83, 98, 105, 107, 108, 109], "1": [3, 4, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 30, 32, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 69, 71, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 89, 90, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 105, 106, 107, 108, 109, 110, 112, 113, 114, 115], "pp": [3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 25, 26, 28, 30, 32, 33, 34, 35, 38, 39, 40, 41, 42, 43, 44, 45, 46, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 69, 71, 74, 82, 87, 88, 89, 90, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 115], "identity_so3": [3, 16, 58, 109, 116], "2": [3, 4, 6, 7, 8, 10, 11, 12, 14, 15, 16, 17, 20, 21, 22, 23, 24, 25, 26, 28, 30, 32, 33, 34, 37, 38, 39, 40, 41, 43, 44, 45, 46, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 69, 71, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 94, 95, 96, 97, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 113, 114, 115], "equival": [3, 4, 6, 7, 8, 10, 11, 13, 18, 28, 32, 35, 62, 67, 69, 71, 98], "7576": 3, "1503": 3, "0": [3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 21, 24, 25, 26, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 62, 63, 64, 66, 67, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 113, 114, 115], "9920": 3, "se3": [3, 4, 6, 7, 8, 10, 11, 13, 18, 21, 26, 30, 32, 39, 44, 47, 51, 56, 67, 92, 106, 116], "randn_se3": [3, 4, 6, 7, 8, 10, 11, 13, 15, 18, 26, 28, 30, 35, 67, 69, 71, 82, 87, 88, 89, 98, 103, 104, 106, 107, 112, 113, 116], "same": [3, 4, 8, 10, 18, 32, 35, 42, 50, 53, 67, 69, 71, 72, 74, 75, 76, 77, 78, 79, 80, 81, 83, 94, 95, 97, 98, 99, 100, 101, 110, 112], "5676": 3, "0452": 3, "0929": 3, "0000": [3, 12, 24, 34, 35, 49, 50, 51, 52, 53, 57, 63, 74, 75, 76, 77, 78, 79, 80, 81, 90, 115], "sim3": [3, 4, 6, 7, 8, 10, 11, 13, 32, 41, 45, 53, 67, 116], "randn_sim3": [3, 4, 6, 7, 8, 11, 13, 17, 32, 67, 98, 106, 108, 116], "respect": [3, 6, 7, 8, 11, 17, 22, 26, 28, 30, 33, 35, 55, 56, 58, 63, 66, 67, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 90, 102, 103], "1551": 3, "2930": 3, "4531": 3, "6140": 3, "1263": 3, "7607": 3, "rxso3": [3, 4, 6, 7, 8, 10, 11, 13, 17, 32, 38, 43, 50, 67, 108, 113, 116], "randn_rxso3": [3, 4, 6, 7, 8, 11, 13, 14, 32, 67, 98, 105, 116], "The": [4, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 25, 26, 28, 30, 32, 33, 49, 50, 51, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 89, 90, 91, 92, 93, 94, 95, 97, 98, 99, 100, 101, 102, 103, 105, 106, 107, 108, 109, 110, 112, 113, 115], "dot": [4, 8], "product": [4, 8, 20, 22, 23, 30, 67, 69, 71, 107, 108], "between": [4, 8, 10, 21, 25, 49, 51, 53, 57, 58, 59, 62, 79, 107, 108, 110], "adjoint": [4, 8], "matrix": [4, 6, 8, 10, 11, 20, 21, 22, 34, 50, 51, 52, 53, 56, 58, 59, 60, 61, 62, 63, 69, 71, 82, 83, 84, 85, 108, 110, 116], "given": [4, 6, 8, 11, 13, 21, 33, 38, 39, 40, 41, 42, 43, 44, 45, 46, 57, 58, 63, 66, 69, 71, 74, 82, 84, 85, 86, 103], "an": [4, 6, 7, 8, 11, 17, 34, 47, 48, 50, 51, 52, 53, 56, 59, 62, 63, 67, 71, 74, 82, 84, 89, 91, 102], "second": [4, 8, 35, 63, 82], "algebra": [4, 6, 7, 8, 9, 11, 13, 18, 67, 93], "mathcal": [4, 6, 7, 8, 9, 11, 18, 26, 28, 30, 55, 56, 64, 66, 94, 95, 96, 97, 99, 100, 101, 102], "g": [4, 6, 7, 8, 10, 11, 12, 28, 55, 58, 59, 62, 63, 64, 66, 71, 72], "output": [4, 6, 7, 8, 10, 11, 18, 20, 22, 23, 26, 28, 30, 33, 34, 35, 38, 39, 40, 41, 42, 43, 44, 45, 46, 49, 50, 51, 52, 53, 58, 59, 60, 61, 63, 65, 67, 69, 71, 74, 75, 76, 77, 78, 79, 80, 81, 82, 91, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 115], "ltype": [4, 6, 7, 8, 11, 14, 15, 16, 17, 34, 42, 67, 105, 107, 108, 109], "so3_typ": [4, 6, 7, 8, 10, 11, 34, 40, 46, 67, 96, 98, 102], "se3_typ": [4, 6, 7, 8, 10, 11, 34, 39, 44, 67, 95, 98, 100, 107], "times7": [4, 6, 7, 8, 11], "times6": [4, 6, 7, 8, 11], "sim3_typ": [4, 6, 7, 8, 10, 11, 34, 41, 45, 67, 97, 98, 101, 108], "times8": [4, 6, 7, 8, 11], "rxso3_typ": [4, 6, 7, 8, 10, 11, 34, 38, 43, 67, 94, 98, 99], "times5": [4, 6, 7, 8, 11], "let": [4, 6, 7, 8, 11, 50, 51, 52, 53, 56], "mathbf": [4, 6, 7, 8, 11, 22, 33, 34, 50, 51, 52, 53, 55, 56, 58, 59, 60, 61, 62, 63, 64, 66, 67, 69, 71, 72, 73, 74, 83, 84, 85, 86, 87, 89, 107, 108, 112, 115], "y": [4, 6, 7, 8, 11, 18, 32, 33, 50, 51, 52, 53, 55, 56, 59, 60, 61, 62, 63, 64, 66, 67, 69, 71, 72, 75, 76, 77, 78, 79, 80, 81, 102, 106, 113, 115], "_i": [4, 6, 7, 8, 11, 18, 22, 33, 50, 51, 52, 53, 56, 67, 69, 71, 72, 73, 75, 76, 77, 78, 79, 80, 81, 83, 84, 85, 86, 115], "If": [4, 6, 7, 8, 10, 11, 14, 15, 16, 17, 26, 30, 33, 35, 38, 39, 40, 41, 42, 43, 44, 45, 46, 49, 50, 51, 52, 53, 57, 58, 61, 62, 63, 64, 65, 66, 69, 71, 72, 74, 82, 85, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 105, 107, 108, 109, 112, 114], "s": [4, 6, 7, 8, 11, 14, 17, 18, 21, 35, 50, 53, 57, 59, 62, 63, 67, 71, 72, 74, 86, 87, 89, 94, 96, 97, 99, 101, 102, 103, 105, 106, 107, 108, 113], "ar": [4, 8, 10, 12, 14, 15, 16, 17, 18, 21, 22, 25, 26, 28, 30, 33, 55, 56, 57, 58, 59, 60, 61, 62, 63, 66, 67, 69, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 105, 107, 108, 109, 112], "instanc": [4, 6, 7, 8, 11, 47, 48, 59, 62, 67], "textrm": 4, "so": [4, 60, 61, 63], "In": [4, 8, 10, 21, 25, 50, 51, 52, 53, 60, 61, 65, 83], "case": [4, 10, 18, 60, 61, 65, 74, 77, 94, 95, 97, 98, 99, 100, 101], "element": [4, 6, 11, 14, 15, 16, 17, 18, 34, 35, 50, 51, 52, 53, 58, 67, 69, 71, 91, 94, 95, 97, 98, 99, 100, 101, 105, 107, 108, 109], "rotat": [4, 6, 7, 10, 11, 14, 15, 32, 33, 34, 50, 51, 52, 53, 56, 58, 94, 96, 97, 99, 100, 101, 102, 105, 107, 108, 109, 116], "us": [4, 6, 8, 10, 12, 14, 15, 16, 17, 35, 38, 39, 40, 41, 42, 43, 44, 45, 46, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 62, 63, 64, 65, 69, 71, 72, 74, 77, 78, 82, 83, 84, 85, 86, 87, 88, 89, 94, 95, 96, 97, 99, 100, 101, 102, 105, 107, 108, 109, 110, 114], "repres": [4, 6, 10, 11, 14, 15, 50, 51, 52, 53, 56, 63, 102, 108], "tangent": [4, 8, 18, 25], "vector": [4, 7, 11, 15, 17, 18, 20, 21, 22, 23, 51, 53, 56, 59, 60, 61, 62, 69, 71, 74, 105, 107, 108, 113, 115], "move": [4, 62], "from": [4, 6, 7, 8, 10, 11, 14, 15, 16, 17, 20, 34, 49, 57, 58, 59, 62, 63, 69, 71, 74, 91, 94, 95, 96, 97, 99, 100, 101, 102, 104, 105, 106, 107, 108, 109, 113, 114], "space": [4, 8, 18, 24, 25, 37, 60, 61], "right": [4, 6, 7, 8, 9, 11, 16, 18, 22, 23, 26, 30, 50, 51, 52, 53, 58, 59, 62, 63, 66, 69, 71, 72, 73, 75, 76, 78, 80, 83, 84, 85, 86, 87, 89], "side": [4, 83, 84, 85, 86], "left": [4, 6, 7, 8, 10, 11, 18, 22, 23, 26, 27, 28, 30, 31, 50, 51, 52, 53, 59, 62, 63, 66, 69, 71, 72, 73, 75, 76, 78, 80, 87, 89, 107], "t": [4, 7, 8, 11, 14, 17, 21, 22, 25, 28, 34, 50, 51, 52, 53, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 69, 71, 72, 73, 87, 89, 95, 97, 100, 101, 105, 107, 108], "translat": [4, 6, 7, 8, 10, 11, 15, 17, 50, 51, 53, 56, 67, 95, 97, 100, 101, 107, 108, 116], "part": [4, 6, 7, 8, 10, 11, 67, 93, 94, 97, 99, 101, 104, 106, 113], "_": [4, 6, 18, 21, 50, 51, 53, 55, 59, 60, 61, 62, 63, 64, 66, 69, 71, 74, 96, 102], "i": [4, 6, 8, 11, 21, 22, 26, 28, 30, 33, 34, 50, 51, 52, 53, 55, 56, 57, 58, 64, 66, 67, 72, 73, 74, 83, 84, 85, 86, 94, 95, 97, 99, 100, 101, 102, 115], "time": [4, 9, 18, 20, 21, 22, 26, 28, 30, 34, 35, 50, 51, 52, 53, 55, 58, 59, 60, 61, 62, 63, 64, 65, 66, 82, 83, 84, 85, 86], "skew": [4, 6, 8, 11, 58, 115], "vec2skew": [4, 8, 58, 116], "begin": [4, 6, 8, 11, 14, 15, 17, 18, 21, 25, 33, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 69, 71, 72, 73, 74, 77, 84, 87, 89, 96, 102, 105, 107, 108, 109, 115], "arrai": [4, 6, 8, 11], "cc": [4, 8, 63], "end": [4, 6, 8, 11, 14, 15, 17, 18, 21, 25, 33, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 69, 71, 72, 73, 74, 77, 84, 87, 89, 96, 102, 105, 107, 108, 109, 115], "6": [4, 6, 8, 10, 11, 18, 21, 36, 37, 49, 62, 69, 71, 74, 82, 87, 88, 89, 90, 92, 96, 103, 107, 114], "se": [4, 110], "s_i": [4, 6, 7, 11, 50, 53, 56, 67], "scale": [4, 6, 7, 10, 11, 14, 17, 18, 50, 53, 56, 67, 77, 87, 89, 94, 97, 98, 99, 101, 105, 108, 116], "7": [4, 6, 8, 10, 11, 15, 36, 51, 57, 59, 82, 89, 90, 92, 103, 108], "sim": [4, 8, 55, 64, 66, 102], "4": [4, 6, 8, 10, 16, 21, 22, 25, 26, 32, 33, 36, 37, 49, 50, 51, 52, 53, 56, 59, 60, 61, 62, 67, 71, 82, 83, 90, 92, 94, 105, 106, 114], "rxso": 4, "e": [4, 6, 8, 10, 11, 12, 21, 28, 63, 71, 81, 94, 95, 97, 99, 100, 101, 102], "oper": [4, 10, 11, 14, 15, 16, 17, 18, 28, 30, 38, 39, 40, 41, 42, 43, 44, 45, 46, 67, 82, 83, 94, 95, 96, 97, 98, 99, 100, 101, 102, 105, 107, 108, 109], "linear": [4, 50, 53, 55, 56, 58, 59, 60, 61, 62, 63, 64, 65, 66, 69, 71, 74, 83, 84, 85, 86], "which": [4, 6, 10, 11, 14, 15, 16, 17, 18, 20, 21, 23, 34, 35, 50, 51, 52, 53, 56, 58, 59, 60, 61, 62, 63, 66, 67, 69, 71, 72, 74, 77, 82, 85, 86, 91, 93, 94, 95, 97, 98, 99, 100, 101, 102, 105, 107, 108, 109], "exp": [4, 8, 10, 13, 18, 21, 58, 69, 71, 74, 94, 95, 96, 97, 105, 107, 108, 109, 112, 116], "It": [4, 14, 15, 16, 17, 21, 55, 57, 58, 69, 71, 72, 73, 78, 83, 85, 86, 87, 105, 107, 108, 109], "can": [4, 6, 7, 8, 10, 11, 21, 24, 25, 32, 36, 38, 39, 40, 41, 43, 44, 45, 46, 50, 51, 52, 53, 55, 56, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 71, 72, 74, 78, 94, 95, 96, 97, 98, 99, 100, 101, 102, 114], "easili": 4, "verifi": [4, 7], "randn_so3": [4, 6, 7, 8, 9, 10, 11, 12, 13, 16, 26, 30, 32, 42, 54, 67, 74, 94, 95, 97, 98, 99, 100, 101, 109, 111, 113, 116], "allclos": 4, "true": [4, 6, 9, 10, 12, 26, 27, 28, 30, 31, 33, 34, 35, 36, 42, 47, 48, 49, 50, 51, 52, 53, 56, 57, 58, 62, 69, 71, 74, 82, 96, 102, 112, 114], "One": [4, 7, 8, 59, 61, 63, 65], "refer": [4, 8, 11, 49, 53, 61, 62, 63, 65, 83], "eq": [4, 6, 8, 11, 18, 21, 58, 59, 62, 69, 73], "8": [4, 6, 10, 17, 26, 36, 37, 53, 56, 58, 60, 63, 66, 74, 82, 92, 96, 114], "follow": [4, 10, 18, 21, 28, 53, 55, 57, 58, 64, 66, 67, 69, 71, 73, 98, 102], "paper": [4, 6, 8, 11, 21, 53, 56, 59, 62, 69, 71, 73], "zachari": 4, "teed": [4, 8], "et": [4, 8, 11, 21, 53, 58, 62], "al": [4, 8, 11, 21, 53, 58, 62], "backpropag": [4, 8], "3d": [4, 8, 21, 25, 53, 56, 90, 92, 103], "ieee": [4, 8], "cvf": [4, 8], "confer": [4, 8, 21, 69, 71], "comput": [4, 6, 8, 11, 16, 18, 34, 35, 50, 51, 52, 53, 56, 57, 62, 63, 64, 65, 66, 69, 71, 72, 74, 83, 85, 110], "vision": [4, 8, 21, 56, 62, 69, 71, 73], "pattern": [4, 8], "recognit": [4, 8], "cvpr": [4, 8], "2021": [4, 8], "gener": [4, 11, 21, 38, 39, 40, 41, 42, 43, 44, 45, 46, 58, 59, 60, 61, 63, 64, 85, 94, 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98], "homogen": [3, 24, 37, 56], "coordin": [3, 21, 24, 37, 49, 56, 57, 90, 92, 103, 110], "y_i": [3, 7, 13, 26, 28, 30, 50, 51, 52, 53], "x_i": [3, 7, 13, 26, 28, 30, 50, 51, 52, 53], "p_i": [3, 58], "where": [3, 4, 6, 8, 11, 13, 14, 15, 16, 17, 18, 21, 22, 26, 28, 30, 33, 34, 35, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 83, 84, 85, 86, 87, 89, 93, 94, 95, 96, 97, 99, 100, 101, 102, 105, 107, 108, 109, 112], "mathbb": [3, 4, 6, 7, 8, 11, 14, 15, 17, 50, 51, 53, 67, 83, 84, 85, 86, 105], "r": [3, 4, 6, 7, 8, 9, 11, 14, 15, 17, 22, 34, 50, 51, 52, 53, 55, 56, 58, 59, 64, 66, 67, 69, 71, 72, 73, 94, 95, 97, 99, 100, 101, 105], "times3": [3, 4, 6, 7, 8, 11, 50, 51, 53, 67], "times4": [3, 4, 6, 7, 8, 11, 67], "denot": [3, 21, 25, 30, 55, 59, 66, 67], "paramet": [3, 4, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 28, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116], "lietensor": [3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 21, 26, 28, 30, 32, 33, 34, 35, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 56, 57, 58, 67, 69, 71, 74, 82, 92, 93, 94, 95, 96, 97, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 116], "input": [3, 4, 6, 7, 8, 9, 11, 13, 18, 19, 21, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 71, 72, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 91, 93, 104, 106, 107, 108, 110, 111, 112, 113, 115], "lie": [3, 4, 6, 7, 8, 9, 11, 13, 18, 53, 67, 93], "group": [3, 4, 6, 7, 8, 9, 11, 13, 18, 30, 53, 67, 93, 98], "tensor": [3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 28, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 112, 113, 114, 115, 116], "return": [3, 4, 6, 7, 8, 9, 10, 11, 13, 18, 20, 21, 22, 23, 24, 25, 26, 28, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 71, 72, 73, 74, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 106, 110, 111, 113, 115], "type": [3, 4, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 28, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 62, 64, 65, 66, 67, 69, 71, 72, 73, 74, 83, 84, 85, 86, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 104, 105, 106, 107, 108, 109, 110, 111, 113, 115], "exampl": [3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 28, 30, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 71, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115], "mathrm": [3, 9, 13, 14, 15, 16, 17, 18, 28, 50, 51, 52, 53, 57, 58, 59, 62, 69, 71, 84, 85, 86, 87, 89, 94, 95, 96, 97, 99, 100, 101, 102, 105, 107, 108, 109], "so3": [3, 4, 6, 7, 8, 9, 10, 11, 13, 14, 15, 26, 30, 32, 40, 46, 52, 58, 67, 98, 104, 105, 106, 107, 113, 116], "mapsto": [3, 4, 6, 7, 8, 9, 11, 13, 67], "torch": [3, 4, 6, 10, 11, 12, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 105, 107, 108, 109, 110, 111, 112, 114, 115], "randn": [3, 10, 14, 15, 16, 17, 18, 20, 22, 23, 24, 33, 35, 55, 59, 60, 61, 62, 64, 66, 67, 74, 85, 86, 98, 103, 105, 107, 108, 109, 115], "3": [3, 4, 6, 8, 9, 10, 11, 15, 17, 20, 21, 23, 24, 25, 33, 34, 35, 36, 37, 42, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 66, 67, 69, 71, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 89, 90, 92, 94, 96, 99, 100, 101, 102, 103, 109, 110, 112, 114, 115], "size": [3, 10, 14, 15, 16, 17, 20, 22, 23, 26, 28, 30, 35, 37, 38, 42, 43, 58, 74, 83, 98, 105, 107, 108, 109], "1": [3, 4, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 30, 32, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 69, 71, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 89, 90, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 105, 106, 107, 108, 109, 110, 112, 113, 114, 115], "pp": [3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 25, 26, 28, 30, 32, 33, 34, 35, 38, 39, 40, 41, 42, 43, 44, 45, 46, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 69, 71, 74, 82, 87, 88, 89, 90, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 115], "identity_so3": [3, 16, 58, 109, 116], "2": [3, 4, 6, 7, 8, 10, 11, 12, 14, 15, 16, 17, 20, 21, 22, 23, 24, 25, 26, 28, 30, 32, 33, 34, 37, 38, 39, 40, 41, 43, 44, 45, 46, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 69, 71, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 94, 95, 96, 97, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 113, 114, 115], "equival": [3, 4, 6, 7, 8, 10, 11, 13, 18, 28, 32, 35, 62, 67, 69, 71, 98], "7576": 3, "1503": 3, "0": [3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 21, 24, 25, 26, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 62, 63, 64, 66, 67, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 113, 114, 115], "9920": 3, "se3": [3, 4, 6, 7, 8, 10, 11, 13, 18, 21, 26, 30, 32, 39, 44, 47, 51, 56, 67, 92, 106, 116], "randn_se3": [3, 4, 6, 7, 8, 10, 11, 13, 15, 18, 26, 28, 30, 35, 67, 69, 71, 82, 87, 88, 89, 98, 103, 104, 106, 107, 112, 113, 116], "same": [3, 4, 8, 10, 18, 32, 35, 42, 50, 53, 67, 69, 71, 72, 74, 75, 76, 77, 78, 79, 80, 81, 83, 94, 95, 97, 98, 99, 100, 101, 110, 112], "5676": 3, "0452": 3, "0929": 3, "0000": [3, 12, 24, 34, 35, 49, 50, 51, 52, 53, 57, 63, 74, 75, 76, 77, 78, 79, 80, 81, 90, 115], "sim3": [3, 4, 6, 7, 8, 10, 11, 13, 32, 41, 45, 53, 67, 116], "randn_sim3": [3, 4, 6, 7, 8, 11, 13, 17, 32, 67, 98, 106, 108, 116], "respect": [3, 6, 7, 8, 11, 17, 22, 26, 28, 30, 33, 35, 55, 56, 58, 63, 66, 67, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 90, 102, 103], "1551": 3, "2930": 3, "4531": 3, "6140": 3, "1263": 3, "7607": 3, "rxso3": [3, 4, 6, 7, 8, 10, 11, 13, 17, 32, 38, 43, 50, 67, 108, 113, 116], "randn_rxso3": [3, 4, 6, 7, 8, 11, 13, 14, 32, 67, 98, 105, 116], "The": [4, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 25, 26, 28, 30, 32, 33, 49, 50, 51, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 89, 90, 91, 92, 93, 94, 95, 97, 98, 99, 100, 101, 102, 103, 105, 106, 107, 108, 109, 110, 112, 113, 115], "dot": [4, 8], "product": [4, 8, 20, 22, 23, 30, 67, 69, 71, 107, 108], "between": [4, 8, 10, 21, 25, 49, 51, 53, 57, 58, 59, 62, 79, 107, 108, 110], "adjoint": [4, 8], "matrix": [4, 6, 8, 10, 11, 20, 21, 22, 34, 50, 51, 52, 53, 56, 58, 59, 60, 61, 62, 63, 69, 71, 82, 83, 84, 85, 108, 110, 116], "given": [4, 6, 8, 11, 13, 21, 33, 38, 39, 40, 41, 42, 43, 44, 45, 46, 57, 58, 63, 66, 69, 71, 74, 82, 84, 85, 86, 103], "an": [4, 6, 7, 8, 11, 17, 34, 47, 48, 50, 51, 52, 53, 56, 59, 62, 63, 67, 71, 74, 82, 84, 89, 91, 102], "second": [4, 8, 35, 63, 82], "algebra": [4, 6, 7, 8, 9, 11, 13, 18, 67], "mathcal": [4, 6, 7, 8, 9, 11, 18, 26, 28, 30, 55, 56, 64, 66, 94, 95, 96, 97, 99, 100, 101, 102], "g": [4, 6, 7, 8, 10, 11, 12, 28, 55, 58, 59, 62, 63, 64, 66, 71, 72], "output": [4, 6, 7, 8, 10, 11, 18, 20, 22, 23, 26, 28, 30, 33, 34, 35, 38, 39, 40, 41, 42, 43, 44, 45, 46, 49, 50, 51, 52, 53, 58, 59, 60, 61, 63, 65, 67, 69, 71, 74, 75, 76, 77, 78, 79, 80, 81, 82, 91, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 115], "ltype": [4, 6, 7, 8, 11, 14, 15, 16, 17, 34, 42, 67, 105, 107, 108, 109], "so3_typ": [4, 6, 7, 8, 10, 11, 34, 40, 46, 67, 96, 98, 102], "se3_typ": [4, 6, 7, 8, 10, 11, 34, 39, 44, 67, 95, 98, 100, 107], "times7": [4, 6, 7, 8, 11], "times6": [4, 6, 7, 8, 11], "sim3_typ": [4, 6, 7, 8, 10, 11, 34, 41, 45, 67, 97, 98, 101, 108], "times8": [4, 6, 7, 8, 11], "rxso3_typ": [4, 6, 7, 8, 10, 11, 34, 38, 43, 67, 94, 98, 99], "times5": [4, 6, 7, 8, 11], "let": [4, 6, 7, 8, 11, 50, 51, 52, 53, 56], "mathbf": [4, 6, 7, 8, 11, 22, 33, 34, 50, 51, 52, 53, 55, 56, 58, 59, 60, 61, 62, 63, 64, 66, 67, 69, 71, 72, 73, 74, 83, 84, 85, 86, 87, 89, 107, 108, 112, 115], "y": [4, 6, 7, 8, 11, 18, 32, 33, 50, 51, 52, 53, 55, 56, 59, 60, 61, 62, 63, 64, 66, 67, 69, 71, 72, 75, 76, 77, 78, 79, 80, 81, 102, 106, 113, 115], "_i": [4, 6, 7, 8, 11, 18, 22, 33, 50, 51, 52, 53, 56, 67, 69, 71, 72, 73, 75, 76, 77, 78, 79, 80, 81, 83, 84, 85, 86, 115], "If": [4, 6, 7, 8, 10, 11, 14, 15, 16, 17, 26, 30, 33, 35, 38, 39, 40, 41, 42, 43, 44, 45, 46, 49, 50, 51, 52, 53, 57, 58, 61, 62, 63, 64, 65, 66, 69, 71, 72, 74, 82, 85, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 105, 107, 108, 109, 112, 114], "s": [4, 6, 7, 8, 11, 14, 17, 18, 21, 35, 50, 53, 57, 59, 62, 63, 67, 71, 72, 74, 86, 87, 89, 94, 96, 97, 99, 101, 102, 103, 105, 106, 107, 108, 113], "ar": [4, 8, 10, 12, 14, 15, 16, 17, 18, 21, 22, 25, 26, 28, 30, 33, 55, 56, 57, 58, 59, 60, 61, 62, 63, 66, 67, 69, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 105, 107, 108, 109, 112], "instanc": [4, 6, 7, 8, 11, 47, 48, 59, 62, 67], "textrm": 4, "so": [4, 60, 61, 63], "In": [4, 8, 10, 21, 25, 50, 51, 52, 53, 60, 61, 65, 83], "case": [4, 10, 18, 60, 61, 65, 74, 77, 94, 95, 97, 98, 99, 100, 101], "element": [4, 6, 11, 14, 15, 16, 17, 18, 34, 35, 50, 51, 52, 53, 58, 67, 69, 71, 91, 94, 95, 97, 98, 99, 100, 101, 105, 107, 108, 109], "rotat": [4, 6, 7, 10, 11, 14, 15, 32, 33, 34, 50, 51, 52, 53, 56, 58, 94, 96, 97, 99, 100, 101, 102, 105, 107, 108, 109, 116], "us": [4, 6, 8, 10, 12, 14, 15, 16, 17, 35, 38, 39, 40, 41, 42, 43, 44, 45, 46, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 62, 63, 64, 65, 69, 71, 72, 74, 77, 78, 82, 83, 84, 85, 86, 87, 88, 89, 94, 95, 96, 97, 99, 100, 101, 102, 105, 107, 108, 109, 110, 114], "repres": [4, 6, 10, 11, 14, 15, 50, 51, 52, 53, 56, 63, 102, 108], "tangent": [4, 8, 18, 25], "vector": [4, 7, 11, 15, 17, 18, 20, 21, 22, 23, 51, 53, 56, 59, 60, 61, 62, 69, 71, 74, 105, 107, 108, 113, 115], "move": [4, 62], "from": [4, 6, 7, 8, 10, 11, 14, 15, 16, 17, 20, 34, 49, 57, 58, 59, 62, 63, 69, 71, 74, 91, 94, 95, 96, 97, 99, 100, 101, 102, 104, 105, 106, 107, 108, 109, 113, 114], "space": [4, 8, 18, 24, 25, 37, 60, 61], "right": [4, 6, 7, 8, 9, 11, 16, 18, 22, 23, 26, 30, 50, 51, 52, 53, 58, 59, 62, 63, 66, 69, 71, 72, 73, 75, 76, 78, 80, 83, 84, 85, 86, 87, 89], "side": [4, 83, 84, 85, 86], "left": [4, 6, 7, 8, 10, 11, 18, 22, 23, 26, 27, 28, 30, 31, 50, 51, 52, 53, 59, 62, 63, 66, 69, 71, 72, 73, 75, 76, 78, 80, 87, 89, 107], "t": [4, 7, 8, 11, 14, 17, 21, 22, 25, 28, 34, 50, 51, 52, 53, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 69, 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