#!/usr/bin/python
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# Copyright (c) 2020, Nifty Chips Laboratory, Hanyang University
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"""
Utility functions for coordinate tranformations.
"""
__author__ = "Jaeduk Han"
__maintainer__ = "Jaeduk Han"
__status__ = "Prototype"
import numpy as np
[docs]
def combine(transform1, transform2):
"""
Returns the resulting transform parameter of
two consecutive transforms
"""
if transform1 == 'R0':
if transform2 == 'R0': return 'R0'
elif transform2 == 'MX': return 'MX'
elif transform2 == 'MY': return 'MY'
elif transform2 == 'MXY': return 'MXY'
elif transform1 == 'MX':
if transform2 == 'R0': return 'MX'
elif transform2 == 'MX': return 'R0'
elif transform2 == 'MY': return 'MXY'
elif transform2 == 'MXY': return 'MY'
elif transform1 == 'MY':
if transform2 == 'R0': return 'MY'
elif transform2 == 'MX': return 'R180'
elif transform2 == 'MY': return 'R0'
elif transform2 == 'MXY': return 'MX'
raise ValueError("Transformation mapping is not matched.")
[docs]
def Mt(transform):
"""
Returns the transform matrix.
Parameters
----------
transform : str
The transform parameter. Possible values are 'R0', 'MX', 'MY', 'MXY', and 'R180'.
Returns
-------
numpy.ndarray(dtype=int)
The transform matrix corresponding to the transform parameter.
"""
transform_map = {
'R0': np.array([[1, 0], [0, 1]]),
'R90': np.array([[0, -1], [1, 0]]),
'R180': np.array([[-1, 0], [0, -1]]),
'R270': np.array([[0, 1], [-1, 0]]),
'MX': np.array([[1, 0], [0, -1]]),
'MY': np.array([[-1, 0], [0, 1]]),
'MXY': np.array([[0, 1], [1, 0]]), # mirror to the y=x line.
}
return transform_map[transform]
[docs]
def Mtinv(transform):
"""
Returns the inverse of the transform matrix.
Parameters
----------
transform : str
The transform parameter. possible values are 'R0', 'MX', 'MY', 'MXY', and 'R180'.
Returns
-------
numpy.ndarray(dtype=int)
The inverse of the transform matrix.
"""
transform_map = {
'R0': np.array([[1, 0], [0, 1]]), 'MX': np.array([[1, 0], [0, -1]]),
'MY': np.array([[-1, 0], [0, 1]]),
'MXY': np.array([[0, 1], [1, 0]]), # mirror to the y=x line.
'R180': np.array([[-1, 0], [0, -1]]),
}
return transform_map[transform]
[docs]
def Md(direction):
"""
Returns the direction(projection) matrix. The direction matrix is used when placing an object based on relative
information to other instance(s). For example, if an instance's center is located at xyc0=[xc0, yc0],
the xy-coordinate of the center of the new instance xyc1 can be computed from the following equation:
(1) xyc1 = xyc0 + 0.5 * Md * (xys0 + xys1)
where xys0, xys1 are the size of the reference and the new instance, respectively, and Md is the direction matrix
corresponding to the direction of the placement.
Parameters
----------
direction : str
The direction parameter. Possible values are 'left', 'right', 'top', 'bottom', 'omni', 'x', 'y'.
Returns
-------
np.array([[int, int], [int, int]])
The direction matrix.
Notes
-----
The following equation will be used instead of (1) in the future versions, to avoid the 0.5 scaling that increases
the precision requirement.
(2) xy1 = xy0 + 0.5 * [(Md + Mt0) * xys0 + (Md - Mt1) * xys1]
"""
direction_map = {
'left': np.array([[-1, 0], [0, 0]]),
'right': np.array([[1, 0], [0, 0]]),
'top': np.array([[0, 0], [0, 1]]),
'bottom': np.array([[0, 0], [0, -1]]),
'omni': np.array([[1, 0], [0, 1]]), # omnidirectional
'x': np.array([[1, 0], [0, 0]]),
'y': np.array([[0, 0], [0, 1]]),
}
return direction_map[direction]
