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3 changes: 3 additions & 0 deletions pyproject.toml
Original file line number Diff line number Diff line change
@@ -0,0 +1,3 @@
[build-system]
requires = ["setuptools>=61", "wheel", "Cython>=3.0"]
build-backend = "setuptools.build_meta"
22 changes: 16 additions & 6 deletions setup.py
Original file line number Diff line number Diff line change
@@ -1,6 +1,8 @@
from setuptools import setup
from setuptools.extension import Extension

from Cython.Build import cythonize

setup(
name = "tps",
version = "0.2",
Expand All @@ -15,13 +17,21 @@
"Operating System :: OS Independent",
"Programming Language :: C",
"Programming Language :: C++",
"Programming Language :: Python :: 2.5",
"Programming Language :: Python :: 2.6",
"Programming Language :: Python :: 2.7",
"Programming Language :: Python :: 3",
"Programming Language :: Python :: 3.12",
"Topic :: Scientific/Engineering",
],
test_suite = 'tps.test.test_suite',
ext_modules=[
Extension("tps._tps", ["tps/_tps.cpp", "tps/thinplatespline.cpp"], libraries=["stdc++"]),
],
python_requires=">=3.8",
ext_modules=cythonize(
[
Extension(
"tps._tps",
["tps/_tps.pyx", "tps/thinplatespline.cpp"],
libraries=["stdc++"],
language="c++",
),
],
language_level=3,
),
)
9 changes: 7 additions & 2 deletions tps/__init__.py
Original file line number Diff line number Diff line change
Expand Up @@ -18,6 +18,11 @@
# FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
# DEALINGS IN THE SOFTWARE.

from _tps import TPS, TPSError, from_control_points
from importlib.util import find_spec

__all__ = ['TPS', 'TPSError', 'from_control_points']
if find_spec("tps._tps") is not None:
from ._tps import TPS, TPSError, from_control_points
else:
from ._tps_py import TPS, TPSError, from_control_points

__all__ = ['TPS', 'TPSError', 'from_control_points']
169 changes: 169 additions & 0 deletions tps/_tps_py.py
Original file line number Diff line number Diff line change
@@ -0,0 +1,169 @@
# Copyright (c) 2011, Omniscale GmbH & Co. KG
#
# Permission is hereby granted, free of charge, to any person obtaining a
# copy of this software and associated documentation files (the "Software"),
# to deal in the Software without restriction, including without limitation
# the rights to use, copy, modify, merge, publish, distribute, sublicense,
# and/or sell copies of the Software, and to permit persons to whom the
# Software is furnished to do so, subject to the following conditions:
#
# The above copyright notice and this permission notice shall be included
# in all copies or substantial portions of the Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
# FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
# DEALINGS IN THE SOFTWARE.

from __future__ import annotations

import math
from typing import Iterable, List, Sequence, Tuple

Point = Tuple[float, float, float, float]


class TPSError(Exception):
pass


def _kernel(r: float) -> float:
if r == 0.0:
return 0.0
r2 = r * r
return r2 * math.log(r2)


def _solve_linear_system(matrix: List[List[float]], vector: List[float]) -> List[float]:
size = len(matrix)
augmented = [row[:] + [vector[index]] for index, row in enumerate(matrix)]

for col in range(size):
pivot_row = max(range(col, size), key=lambda r: abs(augmented[r][col]))
pivot_value = augmented[pivot_row][col]
if abs(pivot_value) < 1e-12:
raise TPSError("could not solve thin plate spline")
if pivot_row != col:
augmented[col], augmented[pivot_row] = augmented[pivot_row], augmented[col]

pivot_value = augmented[col][col]
for j in range(col, size + 1):
augmented[col][j] /= pivot_value

for row in range(size):
if row == col:
continue
factor = augmented[row][col]
if factor == 0.0:
continue
for j in range(col, size + 1):
augmented[row][j] -= factor * augmented[col][j]

return [augmented[row][size] for row in range(size)]


class TPS:
"""
Thin Plate Spline computation class.
"""

def __init__(self, points: Iterable[Point] | None = None) -> None:
self._points: List[Point] = []
self._solved = False
self._weights_x: List[float] = []
self._weights_y: List[float] = []
self._affine_x: List[float] = []
self._affine_y: List[float] = []
if points:
for point in points:
self.add(*point)

def add(self, src_x: float, src_y: float, dst_x: float, dst_y: float) -> None:
self._points.append((src_x, src_y, dst_x, dst_y))
self._solved = False

def solve(self) -> None:
if not self._points:
raise TPSError("could not solve thin plate spline")

count = len(self._points)
size = count + 3
matrix = [[0.0 for _ in range(size)] for _ in range(size)]
vector_x = [0.0 for _ in range(size)]
vector_y = [0.0 for _ in range(size)]

for i, (src_x_i, src_y_i, dst_x_i, dst_y_i) in enumerate(self._points):
vector_x[i] = dst_x_i
vector_y[i] = dst_y_i
matrix[i][count] = 1.0
matrix[i][count + 1] = src_x_i
matrix[i][count + 2] = src_y_i
matrix[count][i] = 1.0
matrix[count + 1][i] = src_x_i
matrix[count + 2][i] = src_y_i
for j, (src_x_j, src_y_j, _, _) in enumerate(self._points):
dx = src_x_i - src_x_j
dy = src_y_i - src_y_j
matrix[i][j] = _kernel(math.hypot(dx, dy))
matrix[i][i] += 1e-12

params_x = _solve_linear_system(matrix, vector_x)
params_y = _solve_linear_system(matrix, vector_y)

self._weights_x = params_x[:count]
self._weights_y = params_y[:count]
self._affine_x = params_x[count:]
self._affine_y = params_y[count:]
self._solved = True

def transform(self, src_x: float, src_y: float) -> Tuple[float, float]:
if not self._points:
raise TPSError("could not solve thin plate spline")

if len(self._points) == 1:
_, _, dst_x, dst_y = self._points[0]
return float(dst_x), float(dst_y)

if len(self._points) == 2:
(src_x_1, src_y_1, dst_x_1, dst_y_1), (src_x_2, src_y_2, dst_x_2, dst_y_2) = (
self._points
)
dx = src_x_2 - src_x_1
dy = src_y_2 - src_y_1
denom = dx * dx + dy * dy
if denom == 0.0:
return float(dst_x_1), float(dst_y_1)
t = ((src_x - src_x_1) * dx + (src_y - src_y_1) * dy) / denom
value_x = dst_x_1 + t * (dst_x_2 - dst_x_1)
value_y = dst_y_1 + t * (dst_y_2 - dst_y_1)
return round(value_x, 12), round(value_y, 12)

if not self._solved:
self.solve()

value_x = self._affine_x[0] + self._affine_x[1] * src_x + self._affine_x[2] * src_y
value_y = self._affine_y[0] + self._affine_y[1] * src_x + self._affine_y[2] * src_y

for (point_x, point_y, _, _), weight_x, weight_y in zip(
self._points,
self._weights_x,
self._weights_y,
):
value = _kernel(math.hypot(src_x - point_x, src_y - point_y))
value_x += weight_x * value
value_y += weight_y * value

return round(value_x, 12), round(value_y, 12)


def from_control_points(points: Sequence[Point], backwards: bool = False) -> TPS:
tps = TPS()
for point in points:
if backwards:
tps.add(point[2], point[3], point[0], point[1])
else:
tps.add(*point)
return tps
3 changes: 1 addition & 2 deletions tps/test/__init__.py
Original file line number Diff line number Diff line change
@@ -1,9 +1,8 @@
from unittest import TestSuite

import test_tps
from . import test_tps

def test_suite():
suite = TestSuite()
suite.addTest(test_tps.test_suite())
return suite

16 changes: 8 additions & 8 deletions tps/test/test_tps.py
Original file line number Diff line number Diff line change
Expand Up @@ -25,17 +25,17 @@
class TestTPS(unittest.TestCase):
def test_init_from_list(self):
t = TPS([(0, 0, 50, 50), (10, 10, 100, 100)])
self.assertEquals(t.transform(4, 5), (72.5, 72.5))
self.assertEqual(t.transform(4, 5), (72.5, 72.5))
t.add(0, 10, 70, 100)
self.assertEquals(t.transform(4, 5), (72.0, 75.0))
self.assertEqual(t.transform(4, 5), (72.0, 75.0))

def test_simple(self):
t = TPS()
t.add(0, 0, 50, 50)
t.add(10, 10, 100, 100)
self.assertEquals(t.transform(4, 5), (72.5, 72.5))
self.assertEqual(t.transform(4, 5), (72.5, 72.5))
t.add(0, 10, 70, 100)
self.assertEquals(t.transform(4, 5), (72.0, 75.0))
self.assertEqual(t.transform(4, 5), (72.0, 75.0))

def test_no_points(self):
try:
Expand All @@ -52,7 +52,7 @@ def test_from_control_points_list(self):
(10, 10, 100, 100),
(0, 10, 70, 100)])

self.assertEquals(t.transform(4, 5), (72.0, 75.0))
self.assertEqual(t.transform(4, 5), (72.0, 75.0))

def test_from_control_points_list_backwards(self):
t = from_control_points([
Expand All @@ -62,11 +62,11 @@ def test_from_control_points_list_backwards(self):
backwards=True)

results = t.transform(72, 75)
self.assertAlmostEquals(results[0], 4.0)
self.assertAlmostEquals(results[1], 5.0)
self.assertAlmostEqual(results[0], 4.0)
self.assertAlmostEqual(results[1], 5.0)

def test_suite():
return unittest.TestLoader().loadTestsFromTestCase(TestTPS)

if __name__ == '__main__':
unittest.main()
unittest.main()