"""
This code provides access to 10000 points
of a uniform incremental grid on SO3.

The main purpose for this grid is to provide
a systematic method of sampling orientations
in an incremental fashion. The sample sequence
picks new points in such a fashion that it 'avoids'
previous picks. On average, the volume around all points
will be equal.

The sequence was based upon the code described here:

A. Yershova, S. Jain, S. M. LaValle, and J. C. Mitchell.

Generating Uniform Incremental Grids on SO(3) Using
the Hopf Fibration

International Journal of Robotics Research, November 2009.


Instead of recoding this method, I opted for storing a sample sequence
of 10000. At a later junction, a reimplementation of the provide method
could be worthwhile.

The code return a quaternion.

"""
from __future__ import absolute_import, division, print_function
from libtbx.forward_compatibility import object
from scitbx.array_family import flex
from six.moves import range
SO3_sequence = [(0.683013, 0.183013, -0.683013, -0.183013), (-0.183013, 0.683013, 0.183013, -0.683013), (0.5, 0.5, -0.5, -0.5), (-0.5, 0.5, 0.5, -0.5), (0.183013, 0.683013, -0.183013, -0.683013), (-0.683013, 0.183013, 0.683013, -0.183013), (0.683013, 0.183013, 0.683013, 0.183013), (-0.183013, 0.683013, -0.183013, 0.683013), (0.5, 0.5, 0.5, 0.5), (-0.5, 0.5, -0.5, 0.5), (0.183013, 0.683013, 0.183013, 0.683013), (-0.683013, 0.183013, -0.683013, 0.183013), (0.881766, 0.236268, -0.353553, 0.204124), (-0.236268, 0.881766, -0.204124, -0.353553), (0.645497, 0.645497, -0.408248, 4.9996e-17), (-0.645497, 0.645497, -7.4994e-17, -0.408248), (0.236268, 0.881766, -0.353553, -0.204124), (-0.881766, 0.236268, 0.204124, -0.353553), (0.394338, 0.105662, 0.790569, -0.456435), (-0.105662, 0.394338, 0.456435, 0.790569), (0.288675, 0.288675, 0.912871, -2.23589e-16), (-0.288675, 0.288675, 2.79486e-16, 0.912871), (0.105662, 0.394338, 0.790569, 0.456435), (-0.394338, 0.105662, -0.456435, 0.790569), (0.394338, 0.105662, -0.790569, 0.456435), (-0.105662, 0.394338, -0.456435, -0.790569), (0.288675, 0.288675, -0.912871, 1.11794e-16), (-0.288675, 0.288675, -1.67692e-16, -0.912871), (0.105662, 0.394338, -0.790569, -0.456435), (-0.394338, 0.105662, 0.456435, -0.790569), (0.881766, 0.236268, 0.353553, -0.204124), (-0.236268, 0.881766, 0.204124, 0.353553), (0.645497, 0.645497, 0.408248, -9.9992e-17), (-0.645497, 0.645497, 1.2499e-16, 0.408248), (0.236268, 0.881766, 0.353553, 0.204124), (-0.881766, 0.236268, -0.204124, 0.353553), (0.683013, 0.183013, -0.183013, 0.683013), (-0.183013, 0.683013, -0.683013, -0.183013), (0.5, 0.5, -0.5, 0.5), (-0.5, 0.5, -0.5, -0.5), (0.183013, 0.683013, -0.683013, 0.183013), (-0.683013, 0.183013, -0.183013, -0.683013), (0.683013, 0.183013, 0.183013, -0.683013), (-0.183013, 0.683013, 0.683013, 0.183013), (0.5, 0.5, 0.5, -0.5), (-0.5, 0.5, 0.5, 0.5), (0.183013, 0.683013, 0.683013, -0.183013), (-0.683013, 0.183013, 0.183013, 0.683013), (0.394338, 0.105662, -0.456435, -0.790569), (-0.105662, 0.394338, 0.790569, -0.456435), (0.288675, 0.288675, -1.67692e-16, -0.912871), (-0.288675, 0.288675, 0.912871, -2.23589e-16), (0.105662, 0.394338, 0.456435, -0.790569), (-0.394338, 0.105662, 0.790569, 0.456435), (0.881766, 0.236268, 0.204124, 0.353553), (-0.236268, 0.881766, -0.353553, 0.204124), (0.645497, 0.645497, 2.4998e-17, 0.408248), (-0.645497, 0.645497, -0.408248, 4.9996e-17), (0.236268, 0.881766, -0.204124, 0.353553), (-0.881766, 0.236268, -0.353553, -0.204124), (0.881766, 0.236268, -0.204124, -0.353553), (-0.236268, 0.881766, 0.353553, -0.204124), (0.645497, 0.645497, -7.4994e-17, -0.408248), (-0.645497, 0.645497, 0.408248, -9.9992e-17), (0.236268, 0.881766, 0.204124, -0.353553), (-0.881766, 0.236268, 0.353553, 0.204124), (0.394338, 0.105662, 0.456435, 0.790569), (-0.105662, 0.394338, -0.790569, 0.456435), (0.288675, 0.288675, 5.58972e-17, 0.912871), (-0.288675, 0.288675, -0.912871, 1.11794e-16), (0.105662, 0.394338, -0.456435, 0.790569), (-0.394338, 0.105662, -0.790569, -0.456435), (0.809511, 0.106574, -0.572411, -0.0753593), (-0.106574, 0.809511, 0.0753593, -0.572411), (0.64777, 0.497052, -0.458043, -0.351469), (-0.497052, 0.64777, 0.351469, -0.458043), (0.31246, 0.754344, -0.220942, -0.533402), (-0.754344, 0.31246, 0.533402, -0.220942), (0.572411, 0.0753593, 0.809511, 0.106574), (-0.0753593, 0.572411, -0.106574, 0.809511), (0.458043, 0.351469, 0.64777, 0.497052), (-0.351469, 0.458043, -0.497052, 0.64777), (0.220942, 0.533402, 0.31246, 0.754344), (-0.533402, 0.220942, -0.754344, 0.31246), (0.97057, 0.127778, -0.161943, 0.124263), (-0.127778, 0.97057, -0.124263, -0.161943), (0.776649, 0.595944, -0.202378, 0.0266435), (-0.595944, 0.776649, -0.0266435, -0.202378), (0.374626, 0.904427, -0.188586, -0.0781149), (-0.904427, 0.374626, 0.0781149, -0.188586), (0.572411, 0.0753593, 0.64777, -0.497052), (-0.0753593, 0.572411, 0.497052, 0.64777), (0.458043, 0.351469, 0.809511, -0.106574), (-0.351469, 0.458043, 0.106574, 0.809511), (0.220942, 0.533402, 0.754344, 0.31246), (-0.533402, 0.220942, -0.31246, 0.754344), (0.572411, 0.0753593, -0.64777, 0.497052), (-0.0753593, 0.572411, -0.497052, -0.64777), (0.458043, 0.351469, -0.809511, 0.106574), (-0.351469, 0.458043, -0.106574, -0.809511), (0.220942, 0.533402, -0.754344, -0.31246), (-0.533402, 0.220942, 0.31246, -0.754344), (0.97057, 0.127778, 0.161943, -0.124263), (-0.127778, 0.97057, 0.124263, 0.161943), (0.776649, 0.595944, 0.202378, -0.0266435), (-0.595944, 0.776649, 0.0266435, 0.202378), (0.374626, 0.904427, 0.188586, 0.0781149), (-0.904427, 0.374626, -0.0781149, 0.188586), (0.572411, 0.0753593, -0.106574, 0.809511), (-0.0753593, 0.572411, -0.809511, -0.106574), (0.458043, 0.351469, -0.497052, 0.64777), (-0.351469, 0.458043, -0.64777, -0.497052), (0.220942, 0.533402, -0.754344, 0.31246), (-0.533402, 0.220942, -0.31246, -0.754344), (0.809511, 0.106574, 0.0753593, -0.572411), (-0.106574, 0.809511, 0.572411, 0.0753593), (0.64777, 0.497052, 0.351469, -0.458043), (-0.497052, 0.64777, 0.458043, 0.351469), (0.31246, 0.754344, 0.533402, -0.220942), (-0.754344, 0.31246, 0.220942, 0.533402), (0.202378, 0.0266435, -0.595944, -0.776649), (-0.0266435, 0.202378, 0.776649, -0.595944), (0.161943, 0.124263, -0.127778, -0.97057), (-0.124263, 0.161943, 0.97057, -0.127778), (0.0781149, 0.188586, 0.374626, -0.904427), (-0.188586, 0.0781149, 0.904427, 0.374626), (0.809511, 0.106574, 0.351469, 0.458043), (-0.106574, 0.809511, -0.458043, 0.351469), (0.64777, 0.497052, 0.0753593, 0.572411), (-0.497052, 0.64777, -0.572411, 0.0753593), (0.31246, 0.754344, -0.220942, 0.533402), (-0.754344, 0.31246, -0.533402, -0.220942), (0.809511, 0.106574, -0.351469, -0.458043), (-0.106574, 0.809511, 0.458043, -0.351469), (0.64777, 0.497052, -0.0753593, -0.572411), (-0.497052, 0.64777, 0.572411, -0.0753593), (0.31246, 0.754344, 0.220942, -0.533402), (-0.754344, 0.31246, 0.533402, 0.220942), (0.202378, 0.0266435, 0.595944, 0.776649), (-0.0266435, 0.202378, -0.776649, 0.595944), (0.161943, 0.124263, 0.127778, 0.97057), (-0.124263, 0.161943, -0.97057, 0.127778), (0.0781149, 0.188586, -0.374626, 0.904427), (-0.188586, 0.0781149, -0.904427, -0.374626), (0.533402, 0.220942, -0.754344, -0.31246), (-0.220942, 0.533402, 0.31246, -0.754344), (0.351469, 0.458043, -0.497052, -0.64777), (-0.458043, 0.351469, 0.64777, -0.497052), (0.0753593, 0.572411, -0.106574, -0.809511), (-0.572411, 0.0753593, 0.809511, -0.106574), (0.754344, 0.31246, 0.533402, 0.220942), (-0.31246, 0.754344, -0.220942, 0.533402), (0.497052, 0.64777, 0.351469, 0.458043), (-0.64777, 0.497052, -0.458043, 0.351469), (0.106574, 0.809511, 0.0753593, 0.572411), (-0.809511, 0.106574, -0.572411, 0.0753593), (0.754344, 0.31246, -0.533402, 0.220942), (-0.31246, 0.754344, -0.220942, -0.533402), (0.497052, 0.64777, -0.572411, -0.0753593), (-0.64777, 0.497052, 0.0753593, -0.572411), (0.106574, 0.809511, -0.458043, -0.351469), (-0.809511, 0.106574, 0.351469, -0.458043), (0.188586, 0.0781149, 0.904427, -0.374626), (-0.0781149, 0.188586, 0.374626, 0.904427), (0.124263, 0.161943, 0.97057, 0.127778), (-0.161943, 0.124263, -0.127778, 0.97057), (0.0266435, 0.202378, 0.776649, 0.595944), (-0.202378, 0.0266435, -0.595944, 0.776649), (0.188586, 0.0781149, -0.904427, 0.374626), (-0.0781149, 0.188586, -0.374626, -0.904427), (0.124263, 0.161943, -0.97057, -0.127778), (-0.161943, 0.124263, 0.127778, -0.97057), (0.0266435, 0.202378, -0.776649, -0.595944), (-0.202378, 0.0266435, 0.595944, -0.776649), (0.754344, 0.31246, 0.533402, -0.220942), (-0.31246, 0.754344, 0.220942, 0.533402), (0.497052, 0.64777, 0.572411, 0.0753593), (-0.64777, 0.497052, -0.0753593, 0.572411), (0.106574, 0.809511, 0.458043, 0.351469), (-0.809511, 0.106574, -0.351469, 0.458043), (0.754344, 0.31246, -0.220942, 0.533402), (-0.31246, 0.754344, -0.533402, -0.220942), (0.497052, 0.64777, -0.458043, 0.351469), (-0.64777, 0.497052, -0.351469, -0.458043), (0.106574, 0.809511, -0.572411, 0.0753593), (-0.809511, 0.106574, -0.0753593, -0.572411), (0.533402, 0.220942, 0.31246, -0.754344), (-0.220942, 0.533402, 0.754344, 0.31246), (0.351469, 0.458043, 0.64777, -0.497052), (-0.458043, 0.351469, 0.497052, 0.64777), (0.0753593, 0.572411, 0.809511, -0.106574), (-0.572411, 0.0753593, 0.106574, 0.809511), (0.533402, 0.220942, -0.31246, -0.754344), (-0.220942, 0.533402, 0.754344, -0.31246), (0.351469, 0.458043, 0.106574, -0.809511), (-0.458043, 0.351469, 0.809511, 0.106574), (0.0753593, 0.572411, 0.497052, -0.64777), (-0.572411, 0.0753593, 0.64777, 0.497052), (0.904427, 0.374626, 0.0781149, 0.188586), (-0.374626, 0.904427, -0.188586, 0.0781149), (0.595944, 0.776649, -0.0266435, 0.202378), (-0.776649, 0.595944, -0.202378, -0.0266435), (0.127778, 0.97057, -0.124263, 0.161943), (-0.97057, 0.127778, -0.161943, -0.124263), (0.904427, 0.374626, -0.0781149, -0.188586), (-0.374626, 0.904427, 0.188586, -0.0781149), (0.595944, 0.776649, 0.0266435, -0.202378), (-0.776649, 0.595944, 0.202378, 0.0266435), (0.127778, 0.97057, 0.124263, -0.161943), (-0.97057, 0.127778, 0.161943, 0.124263), (0.533402, 0.220942, 0.31246, 0.754344), (-0.220942, 0.533402, -0.754344, 0.31246), (0.351469, 0.458043, -0.106574, 0.809511), (-0.458043, 0.351469, -0.809511, -0.106574), (0.0753593, 0.572411, -0.497052, 0.64777), (-0.572411, 0.0753593, -0.64777, -0.497052), (0.754344, 0.31246, -0.533402, -0.220942), (-0.31246, 0.754344, 0.220942, -0.533402), (0.497052, 0.64777, -0.351469, -0.458043), (-0.64777, 0.497052, 0.458043, -0.351469), (0.106574, 0.809511, -0.0753593, -0.572411), (-0.809511, 0.106574, 0.572411, -0.0753593), (0.533402, 0.220942, 0.754344, 0.31246), (-0.220942, 0.533402, -0.31246, 0.754344), (0.351469, 0.458043, 0.497052, 0.64777), (-0.458043, 0.351469, -0.64777, 0.497052), (0.0753593, 0.572411, 0.106574, 0.809511), (-0.572411, 0.0753593, -0.809511, 0.106574), (0.904427, 0.374626, -0.188586, 0.0781149), (-0.374626, 0.904427, -0.0781149, -0.188586), (0.595944, 0.776649, -0.202378, -0.0266435), (-0.776649, 0.595944, 0.0266435, -0.202378), (0.127778, 0.97057, -0.161943, -0.124263), (-0.97057, 0.127778, 0.124263, -0.161943), (0.533402, 0.220942, 0.754344, -0.31246), (-0.220942, 0.533402, 0.31246, 0.754344), (0.351469, 0.458043, 0.809511, 0.106574), (-0.458043, 0.351469, -0.106574, 0.809511), (0.0753593, 0.572411, 0.64777, 0.497052), (-0.572411, 0.0753593, -0.497052, 0.64777), (0.533402, 0.220942, -0.754344, 0.31246), (-0.220942, 0.533402, -0.31246, -0.754344), (0.351469, 0.458043, -0.809511, -0.106574), (-0.458043, 0.351469, 0.106574, -0.809511), (0.0753593, 0.572411, -0.64777, -0.497052), (-0.572411, 0.0753593, 0.497052, -0.64777), (0.904427, 0.374626, 0.188586, -0.0781149), (-0.374626, 0.904427, 0.0781149, 0.188586), (0.595944, 0.776649, 0.202378, 0.0266435), (-0.776649, 0.595944, -0.0266435, 0.202378), (0.127778, 0.97057, 0.161943, 0.124263), (-0.97057, 0.127778, -0.124263, 0.161943), (0.533402, 0.220942, -0.31246, 0.754344), (-0.220942, 0.533402, -0.754344, -0.31246), (0.351469, 0.458043, -0.64777, 0.497052), (-0.458043, 0.351469, -0.497052, -0.64777), (0.0753593, 0.572411, -0.809511, 0.106574), (-0.572411, 0.0753593, -0.106574, -0.809511), (0.754344, 0.31246, 0.220942, -0.533402), (-0.31246, 0.754344, 0.533402, 0.220942), (0.497052, 0.64777, 0.458043, -0.351469), (-0.64777, 0.497052, 0.351469, 0.458043), (0.106574, 0.809511, 0.572411, -0.0753593), (-0.809511, 0.106574, 0.0753593, 0.572411), (0.188586, 0.0781149, -0.374626, -0.904427), (-0.0781149, 0.188586, 0.904427, -0.374626), (0.124263, 0.161943, 0.127778, -0.97057), (-0.161943, 0.124263, 0.97057, 0.127778), (0.0266435, 0.202378, 0.595944, -0.776649), (-0.202378, 0.0266435, 0.776649, 0.595944), (0.754344, 0.31246, 0.220942, 0.533402), (-0.31246, 0.754344, -0.533402, 0.220942), (0.497052, 0.64777, -0.0753593, 0.572411), (-0.64777, 0.497052, -0.572411, -0.0753593), (0.106574, 0.809511, -0.351469, 0.458043), (-0.809511, 0.106574, -0.458043, -0.351469), (0.754344, 0.31246, -0.220942, -0.533402), (-0.31246, 0.754344, 0.533402, -0.220942), (0.497052, 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(-0.723617, 0.318399, -0.570736, -0.221947), (0.785871, 0.0860668, -0.383298, -0.47758), (-0.0860668, 0.785871, 0.47758, -0.383298), (0.63755, 0.467471, -0.0931562, -0.605245), (-0.467471, 0.63755, 0.605245, -0.0931562), (0.318399, 0.723617, 0.221947, -0.570736), (-0.723617, 0.318399, 0.570736, 0.221947), (0.152183, 0.0166668, 0.618545, 0.770691), (-0.0166668, 0.152183, -0.770691, 0.618545), (0.123461, 0.0905254, 0.15033, 0.97671), (-0.0905254, 0.123461, -0.97671, 0.15033), (0.0616577, 0.140128, -0.358166, 0.921021), (-0.140128, 0.0616577, -0.921021, -0.358166), (0.570736, 0.221947, -0.736817, -0.286532), (-0.221947, 0.570736, 0.286532, -0.736817), (0.383298, 0.47758, -0.494836, -0.616553), (-0.47758, 0.383298, 0.616553, -0.494836), (0.0931562, 0.605245, -0.120264, -0.781368), (-0.605245, 0.0931562, 0.781368, -0.120264), (0.736817, 0.286532, 0.570736, 0.221947), (-0.286532, 0.736817, -0.221947, 0.570736), (0.494836, 0.616553, 0.383298, 0.47758), (-0.616553, 0.494836, -0.47758, 0.383298), (0.120264, 0.781368, 0.0931562, 0.605245), (-0.781368, 0.120264, -0.605245, 0.0931562), (0.784402, 0.305037, -0.494325, 0.217508), (-0.305037, 0.784402, -0.217508, -0.494325), (0.526793, 0.656371, -0.536852, -0.0587948), (-0.656371, 0.526793, 0.0587948, -0.536852), (0.128031, 0.83183, -0.43553, -0.319344), (-0.83183, 0.128031, 0.319344, -0.43553), (0.237807, 0.0924779, 0.885015, -0.389416), (-0.0924779, 0.237807, 0.389416, 0.885015), (0.159708, 0.198992, 0.961153, 0.105263), (-0.198992, 0.159708, -0.105263, 0.961153), (0.0388151, 0.252186, 0.779751, 0.571737), (-0.252186, 0.0388151, -0.571737, 0.779751), (0.237807, 0.0924779, -0.885015, 0.389416), (-0.0924779, 0.237807, -0.389416, -0.885015), (0.159708, 0.198992, -0.961153, -0.105263), (-0.198992, 0.159708, 0.105263, -0.961153), (0.0388151, 0.252186, -0.779751, -0.571737), (-0.252186, 0.0388151, 0.571737, -0.779751), (0.784402, 0.305037, 0.494325, -0.217508), (-0.305037, 0.784402, 0.217508, 0.494325), (0.526793, 0.656371, 0.536852, 0.0587948), (-0.656371, 0.526793, -0.0587948, 0.536852), (0.128031, 0.83183, 0.43553, 0.319344), (-0.83183, 0.128031, -0.319344, 0.43553), (0.736817, 0.286532, -0.221947, 0.570736), (-0.286532, 0.736817, -0.570736, -0.221947), (0.494836, 0.616553, -0.47758, 0.383298), (-0.616553, 0.494836, -0.383298, -0.47758), (0.120264, 0.781368, -0.605245, 0.0931562), (-0.781368, 0.120264, -0.0931562, -0.605245), (0.570736, 0.221947, 0.286532, -0.736817), (-0.221947, 0.570736, 0.736817, 0.286532), (0.383298, 0.47758, 0.616553, -0.494836), (-0.47758, 0.383298, 0.494836, 0.616553), (0.0931562, 0.605245, 0.781368, -0.120264), (-0.605245, 0.0931562, 0.120264, 0.781368), (0.503342, 0.195739, -0.338962, -0.770349), (-0.195739, 0.503342, 0.770349, -0.338962), (0.338037, 0.421186, 0.0916251, -0.836623), (-0.421186, 0.338037, 0.836623, 0.0916251), (0.082156, 0.533776, 0.497661, -0.678724), (-0.533776, 0.082156, 0.678724, 0.497661), (0.901159, 0.350441, 0.102763, 0.233546), (-0.350441, 0.901159, -0.233546, 0.102763), (0.605205, 0.75407, -0.0277779, 0.253639), (-0.75407, 0.605205, -0.253639, -0.0277779), (0.147088, 0.955647, -0.150876, 0.205769), (-0.955647, 0.147088, -0.205769, -0.150876), (0.901159, 0.350441, -0.102763, -0.233546), (-0.350441, 0.901159, 0.233546, -0.102763), (0.605205, 0.75407, 0.0277779, -0.253639), (-0.75407, 0.605205, 0.253639, 0.0277779)]

class sample_orientations(object):
  def __init__(self):
    self.sequence = SO3_sequence
    self.max_n    = len(SO3_sequence)
    self.counter  = 0

  def __next__(self):
    assert self.counter < self.max_n
    tmp = self.sequence[self.counter]
    self.counter+=1
    return tmp

  def restart(self,start_point=0):
    self.counter = start_point


def tst():
  so3 = sample_orientations()
  for ii in range(10000):
    q = flex.double(next(so3))
    q = q*q
    assert abs(1-q)<1e-5

if __name__ == "__main__":
  tst()
  print("OK")