doc: Use citations for a bunch of papers instead of plaintext

This is far from exhaustive, but covers the frequently-repeated ones.

Author: eric-wieser

clifford/_layout.py

@@ -60,8 +60,7 @@ def canonical_reordering_sign(bitmap_a, bitmap_b, metric):
 def gmt_element(bitmap_a, bitmap_b, sig_array):
     """
     Element of the geometric multiplication table given blades a, b.
-    The implementation used here is described in chapter 19 of
-    Leo Dorst's book, Geometric Algebra For Computer Science
+    The implementation used here is described in :cite:`ga4cs` chapter 19.
     """
     output_sign = canonical_reordering_sign(bitmap_a, bitmap_b, sig_array)
     output_bitmap = bitmap_a^bitmap_b

clifford/_multivector.py

@@ -636,7 +636,7 @@ def isBlade(self) -> bool:
 
     def isVersor(self) -> bool:
         """Returns true if multivector is a versor.
-        From Leo Dorsts GA for computer science section 21.5, definition from 7.6.4
+        From :cite:`ga4cs` section 21.5, definition from 7.6.4
         """
         Vhat = self.gradeInvol()
         Vrev = ~self
@@ -837,7 +837,7 @@ def factorise(self) -> Tuple[List['MultiVector'], numbers.Number]:
         """
         Factorises a blade into basis vectors and an overall scale.
 
-        Uses Leo Dorsts algorithm from 21.6 of GA for Computer Science
+        Uses the algorithm from :cite:`ga4cs`, section 21.6.
         """
         if not self.isBlade():
             raise ValueError("self is not a blade")

clifford/tools/g3c/cost_functions.py

@@ -95,7 +95,8 @@ def midpoint_and_error_of_line_cluster(line_cluster):
     """
     Gets an approximate center point of a line cluster
     as well as an estimate of the error
-    Hadfield and Lasenby AGACSE2018
+
+    From :cite:`rotor-between`.
     """
     line_cluster_array = np.array([l.value for l in line_cluster])
     cp_val = val_midpoint_of_line_cluster(line_cluster_array)
@@ -106,7 +107,8 @@ def midpoint_and_error_of_line_cluster_grad(line_cluster):
     """
     Gets an approximate center point of a line cluster
     as well as an estimate of the error
-    Hadfield and Lasenby AGACSE2018
+
+    From :cite:`rotor-between`.
     """
     line_cluster_array = np.array([l.value for l in line_cluster])
     cp_val = val_midpoint_of_line_cluster_grad(line_cluster_array)

clifford/tools/g3c/rotor_parameterisation.py

@@ -36,8 +36,7 @@ def dorst_sinh(A):
 
 def dorst_atanh2(s, c):
     """
-    Atanh2 of a bivector as given in square root and logarithm of rotors
-    by Dorst and Valkenburg
+    Atanh2 of a bivector as given in :cite:`log-of-rotors`
     """
     s2 = (s * s)[0]
     if s2 > 0:
@@ -72,8 +71,8 @@ def decompose_bivector(F):
 def general_logarithm(R):
     """
     Takes a general conformal rotor and returns the log
-    From square root and loagrithm of rotors by Leo Dorst
-    and Robert Valkenburg
+
+    From :cite:`log-of-rotors`.
     """
     F = 2 * (R(4) - R[0]) * R(2)
     S1, S2 = decompose_bivector(F)
@@ -197,8 +196,8 @@ def ga_exp(B):
 def interpolate_TR_rotors(R_n_plus_1, R_n, interpolation_fraction):
     """
     Interpolates TR type rotors
-    Mesh Vertex Pose and Position Interpolation using Geometric Algebra.
-    Rich Wareham and Joan Lasenby
+
+    From :cite:`wareham-interpolation`.
     """
     if interpolation_fraction < np.finfo(float).eps:
         return R_n
@@ -211,11 +210,7 @@ def interpolate_TR_rotors(R_n_plus_1, R_n, interpolation_fraction):
 def interpolate_rotors(R_n_plus_1, R_n, interpolation_fraction):
     """
     Interpolates all conformal type rotors
-    Mesh Vertex Pose and Position Interpolation using Geometric Algebra
-    Rich Wareham and Joan Lasenby
-    and
-    Square Root and Logarithm of Rotors
-    Leo Dorst and Robert Valkenburg
+    From :cite:`wareham-interpolation` and :cite:`log-of-rotors`.
     """
     if interpolation_fraction < np.finfo(float).eps:
         return R_n
@@ -228,8 +223,8 @@ def interpolate_rotors(R_n_plus_1, R_n, interpolation_fraction):
 def extractRotorComponents(R):
     """
     Extracts the translation and rotation information from a TR rotor
-    Mesh Vertex Pose and Position Interpolation using Geometric Algebra.
-    Rich Wareham and Joan Lasenby
+
+    From :cite:`wareham-interpolation`.
     """
     phi = np.arccos(float(R[0]))             # scalar
     phi2 = phi * phi                  # scalar
@@ -245,10 +240,10 @@ def ga_log(R):
     """
     R must be a TR rotor. grades in [0, 2, 4]
 
-    Presented by R. Wareham (Applications of CGA)
-
+    Presented in :cite:`wareham-applications`.
 
-    WARNING: DOES NOT COMMUTE log(A * B) != log(A) + log(B)
+    .. warning::
+        Does not commute, ``log(A * B) != log(A) + log(B)``
     """
     phiP, t_normal_n, t_perpendicular_n = extractRotorComponents(R)
     return phiP + t_normal_n + t_perpendicular_n

clifford/transformations.py

@@ -124,7 +124,7 @@ def adjoint(self) -> "LinearMatrix":
 
         This is such that :math:`f(a) * b = a * \bar f(b)`, where :math:`*` is the scalar product.
 
-        See GA4CS section 4.3.2.
+        See :cite:`ga4cs` section 4.3.2.
         """
         raise NotImplementedError
 
@@ -319,7 +319,7 @@ class OutermorphismMatrix(LinearMatrix):
 
     Such a transformation is grade preserving.
 
-    See GA4CS Chapter 4 for more information
+    See :cite:`ga4cs` Chapter 4 for more information
 
     Arguments
     ---------

docs/refs.bib

@@ -0,0 +1,62 @@
+@book{ga4cs,
+    author = {Dorst, Leo and Fontijne, Daniel and Mann, Stephen},
+    title = {Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry},
+    shorttitle = {Geometric algebra for computer science},
+    year = {2009},
+    isbn = {9780080553108},
+    publisher = {Morgan Kaufmann Publishers Inc.}
+}
+
+@inbook{log-of-rotors,
+    author = {Dorst, Leo and Valkenburg, Robert},
+    year = {2011},
+    month = {01},
+    pages = {81--104},
+    title = {Square Root and Logarithm of Rotors in 3D Conformal Geometric Algebra Using Polar Decomposition},
+    doi = {10.1007/978-0-85729-811-9_5},
+}
+
+@inproceedings{wareham-interpolation,
+    author = {Wareham, Rich and Lasenby, Joan},
+    title = {Mesh Vertex Pose and Position Interpolation Using Geometric Algebra},
+    booktitle = {Articulated Motion and Deformable Objects},
+    year = {2008},
+    publisher = {Springer Berlin Heidelberg},
+    address = {Berlin, Heidelberg},
+    pages = {122--131},
+    isbn = {978-3-540-70517-8}
+}
+
+@inproceedings{wareham-applications,
+    author = {Wareham, Rich and Cameron, Jonathan and Lasenby, Joan},
+    editor = {Li, Hongbo and Olver, Peter J. and Sommer, Gerald},
+    title = {Applications of Conformal Geometric Algebra in Computer Vision and Graphics},
+    booktitle = {Computer Algebra and Geometric Algebra with Applications},
+    year = {2005},
+    publisher = {Springer Berlin Heidelberg},
+    address = {Berlin, Heidelberg},
+    pages = {329--349},
+    isbn = {978-3-540-32119-4}
+}
+
+@article{rotor-between,
+    author = {Lasenby, Joan and Hadfield, Hugo and Lasenby, Anthony},
+    year = {2019},
+    month = {10},
+    pages = {102},
+    title = {Calculating the Rotor Between Conformal Objects},
+    volume = {29},
+    journal = {Advances in Applied Clifford Algebras},
+    doi = {10.1007/s00006-019-1014-8}
+}
+
+@article{direct-linear-interpolation,
+    author = {Hadfield, Hugo and Lasenby, Joan},
+    year = {2019},
+    month = {09},
+    pages = {},
+    title = {Direct Linear Interpolation of Geometric Objects in Conformal Geometric Algebra},
+    volume = {29},
+    journal = {Advances in Applied Clifford Algebras},
+    doi = {10.1007/s00006-019-1003-y}
+}