Fix floating point error in bezier bounding box calculation

svgpathtools/bezier.py

@@ -10,6 +10,7 @@
 
 # Internal dependencies
 from .polytools import real, imag, polyroots, polyroots01
+from .constants import FLOAT_EPSILON
 
 
 # Evaluation ##################################################################
@@ -171,7 +172,7 @@ def bezier_real_minmax(p):
     if len(p) == 4:  # cubic case
         a = [p.real for p in p]
         denom = a[0] - 3*a[1] + 3*a[2] - a[3]
-        if denom != 0:
+        if abs(denom) > FLOAT_EPSILON:  # check that denom != 0 accounting for floating point error
             delta = a[1]**2 - (a[0] + a[1])*a[2] + a[2]**2 + (a[0] - a[1])*a[3]
             if delta >= 0:  # otherwise no local extrema
                 sqdelta = sqrt(delta)

svgpathtools/constants.py

@@ -0,0 +1,3 @@
+"""This submodule contains constants used throughout the project."""
+
+FLOAT_EPSILON = 1e-12

test/test_bezier.py

@@ -1,8 +1,8 @@
 from __future__ import division, absolute_import, print_function
 import numpy as np
 import unittest
-from svgpathtools.bezier import bezier_point, bezier2polynomial, polynomial2bezier
-from svgpathtools.path import bpoints2bezier
+from svgpathtools.bezier import bezier_point, bezier2polynomial, polynomial2bezier, bezier_bounding_box, bezier_real_minmax
+from svgpathtools.path import bpoints2bezier, CubicBezier
 
 
 class HigherOrderBezier:
@@ -54,5 +54,53 @@ def test_polynomial2bezier(self):
                 self.assertAlmostEqual(b.point(t), p(t), msg=msg)
 
 
+class TestBezierBoundingBox(unittest.TestCase):
+    def test_bezier_bounding_box(self):
+        # This bezier curve has denominator == 0 but due to floating point arithmetic error it is not exactly 0
+        zero_denominator_bezier_curve = CubicBezier(612.547 + 109.3261j, 579.967 - 19.4422j, 428.0344 - 19.4422j, 395.4374 + 109.3261j)
+        zero_denom_xmin, zero_denom_xmax, zero_denom_ymin, zero_denom_ymax = bezier_bounding_box(zero_denominator_bezier_curve)
+        self.assertAlmostEqual(zero_denom_xmin, 395.437400, 5)
+        self.assertAlmostEqual(zero_denom_xmax, 612.547, 5)
+        self.assertAlmostEqual(zero_denom_ymin, 12.7498749, 5)
+        self.assertAlmostEqual(zero_denom_ymax, 109.3261, 5)
+
+        # This bezier curve has global extrema at the start and end points
+        start_end_bbox_bezier_curve = CubicBezier(886.8238 + 354.8439j, 884.4765 + 340.5983j, 877.6258 + 330.0518j, 868.2909 + 323.2453j)
+        start_end_xmin, start_end_xmax, start_end_ymin, start_end_ymax = bezier_bounding_box(start_end_bbox_bezier_curve)
+        self.assertAlmostEqual(start_end_xmin, 868.2909, 5)
+        self.assertAlmostEqual(start_end_xmax, 886.8238, 5)
+        self.assertAlmostEqual(start_end_ymin, 323.2453, 5)
+        self.assertAlmostEqual(start_end_ymax, 354.8439, 5)
+
+        # This bezier curve is to cover some random case where at least one of the global extrema is not the start or end point
+        general_bezier_curve = CubicBezier(295.2282 + 402.0233j, 310.3734 + 355.5329j, 343.547 + 340.5983j, 390.122 + 355.7018j)
+        general_xmin, general_xmax, general_ymin, general_ymax = bezier_bounding_box(general_bezier_curve)
+        self.assertAlmostEqual(general_xmin, 295.2282, 5)
+        self.assertAlmostEqual(general_xmax, 390.121999999, 5)
+        self.assertAlmostEqual(general_ymin, 350.030030142, 5)
+        self.assertAlmostEqual(general_ymax, 402.0233, 5)
+
+
+class TestBezierRealMinMax(unittest.TestCase):
+    def test_bezier_real_minmax(self):
+        # This bezier curve has denominator == 0 but due to floating point arithmetic error it is not exactly 0
+        zero_denominator_bezier_curve = [109.3261, -19.4422, -19.4422, 109.3261]
+        zero_denominator_minmax = bezier_real_minmax(zero_denominator_bezier_curve)
+        self.assertAlmostEqual(zero_denominator_minmax[0], 12.7498749, 5)
+        self.assertAlmostEqual(zero_denominator_minmax[1], 109.3261, 5)
+
+        # This bezier curve has global extrema at the start and end points
+        start_end_bbox_bezier_curve = [354.8439, 340.5983, 330.0518, 323.2453]
+        start_end_bbox_minmax = bezier_real_minmax(start_end_bbox_bezier_curve)
+        self.assertAlmostEqual(start_end_bbox_minmax[0], 323.2453, 5)
+        self.assertAlmostEqual(start_end_bbox_minmax[1], 354.8439, 5)
+
+        # This bezier curve is to cover some random case where at least one of the global extrema is not the start or end point
+        general_bezier_curve = [402.0233, 355.5329, 340.5983, 355.7018]
+        general_minmax = bezier_real_minmax(general_bezier_curve)
+        self.assertAlmostEqual(general_minmax[0], 350.030030142, 5)
+        self.assertAlmostEqual(general_minmax[1], 402.0233, 5)
+
+
 if __name__ == '__main__':
     unittest.main()