Newer
Older
####################################################################################################
#
# Patro - A Python library to make patterns for fashion design
# Copyright (C) 2017 Fabrice Salvaire
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#
####################################################################################################
"""Module to implement triangle.
"""
####################################################################################################
__all__ = ['Triangle2D']
####################################################################################################
from .Primitive import Primitive3P, ClosedPrimitiveMixin, PathMixin, PolygonMixin, Primitive2DMixin
from .Line import Line2D
####################################################################################################
def triangle_orientation(p0, p1, p2):
"""Return the triangle orientation defined by the three points."""
dx1 = p1.x - p0.x
dy1 = p1.y - p0.y
dx2 = p2.x - p0.x
dy2 = p2.y - p0.y
# second slope is greater than the first one --> counter-clockwise
if dx1 * dy2 > dx2 * dy1:
return 1
# first slope is greater than the second one --> clockwise
elif dx1 * dy2 < dx2 * dy1:
return -1
# both slopes are equal --> collinear line segments
else:
# p0 is between p1 and p2
if dx1 * dx2 < 0 or dy1 * dy2 < 0:
return -1
# p2 is between p0 and p1, as the length is compared
# square roots are avoided to increase performance
elif dx1 * dx1 + dy1 * dy1 >= dx2 * dx2 + dy2 * dy2:
return 0
# p1 is between p0 and p2
else:
return 1
####################################################################################################
def same_side(p1, p2, a, b):
"""Return True if the points p1 and p2 lie on the same side of the edge [a, b]."""
v = b - a
cross1 = v.cross(p1 - a)
cross2 = v.cross(p2 - a)
# return cross1.dot(cross2) >= 0
return cross1*cross2 >= 0
####################################################################################################
class Triangle2D(Primitive2DMixin, ClosedPrimitiveMixin, PathMixin, PolygonMixin, Primitive3P):
##############################################
def __init__(self, p0, p1, p2):
if (p1 - p0).is_parallel((p2 - p0)):
raise ValueError('Flat triangle')
Primitive3P.__init__(self, p0, p1, p2)
# self._p10 = None
# self._p21 = None
# self._p02 = None
##############################################
@property
def is_closed(self):
return True
##############################################
# Fixme: circular import, Segment import triangle_orientation
from .Segment import Segment2D
p0 = self._p0
p1 = self._p1
p2 = self._p2
return (
Segment2D(p0, p1),
Segment2D(p1, p2),
Segment2D(p2, p0),
)
##############################################
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
@property
def bisector_vector0(self):
return (self._p1 - self._p0) + (self._p2 - self._p0)
@property
def bisector_vector1(self):
return (self._p0 - self._p1) + (self._p2 - self._p1)
@property
def bisector_vector2(self):
return (self._p1 - self._p2) + (self._p0 - self._p2)
##############################################
@property
def bisector_line0(self):
return Line2D(self._p0, self.bisector_vector0)
@property
def bisector_line1(self):
return Line2D(self._p1, self.bisector_vector1)
@property
def bisector_line2(self):
return Line2D(self._p2, self.bisector_vector2)
##############################################
def _cache_length(self):
if not hasattr(self._p10):
self._p10 = (self._p1 - self._p0).magnitude
self._p21 = (self._p2 - self._p1).magnitude
self._p02 = (self._p0 - self._p2).magnitude
##############################################
def _cache_angle(self):
if not hasattr(self._a10):
self._a10 = (self._p1 - self._p0).orientation
self._a21 = (self._p2 - self._p1).orientation
self._a02 = (self._p0 - self._p2).orientation
##############################################
@property
def perimeter(self):
self._cache_length()
return self._p10 + self._p21 + self._p02
##############################################
@property
def area(self):
# using height
# = base * height / 2
# using edge length
# = \frac{1}{4} \sqrt{(a+b+c)(-a+b+c)(a-b+c)(a+b-c)} = \sqrt{p(p-a)(p-b)(p-c)}
# using sinus law
# = \frac{1}{2} a b \sin\gamma
# using coordinate
# = \frac{1}{2} \left\|{ \overrightarrow{AB} \wedge \overrightarrow{AC}}
# = \dfrac{1}{2} \big| x_A y_C - x_A y_B + x_B y_A - x_B y_C + x_C y_B - x_C y_A \big|
return .5 * math.fabs((self._p1 - self._p0).cross(self._p2 - self._p0))
##############################################
@property
def is_equilateral(self):
self._cache_length()
# all sides have the same length and angle = 60
return (self._p10 == self._p21 and
self._p21 == self._p02)
##############################################
@property
def is_scalene(self):
self._cache_length()
# all sides have different lengths
return (self._p10 != self._p21 and
self._p21 != self._p02 and
self._p02 != self._p10)
##############################################
@property
def is_isosceles(self):
self._cache_length()
# two sides of equal length
return not(self.is_equilateral) and not(self.is_scalene)
##############################################
@property
def is_right(self):
self._cache_angle()
# one angle = 90
raise NotImplementedError
##############################################
@property
def is_obtuse(self):
self._cache_angle()
# one angle > 90
return max(self._a10, self._a21, self._a02) > 90
##############################################
@property
def is_acute(self):
self._cache_angle()
# all angle < 90
return max(self._a10, self._a21, self._a02) < 90
##############################################
@property
def is_oblique(self):
return not self.is_equilateral
##############################################
@property
def orthocenter(self):
# intersection of the altitudes
raise NotImplementedError
##############################################
@property
def centroid(self):
# intersection of the medians
raise NotImplementedError
##############################################
@property
def circumcenter(self):
# intersection of the perpendiculars at middle
raise NotImplementedError
##############################################
@property
def in_circle(self):
# intersection of the bisectors
raise NotImplementedError # return circle
##############################################
def is_point_inside(self, point):
# Reference:
# http://mathworld.wolfram.com/TriangleInterior.html
return (
same_side(point, self._p0, self._p1, self._p2) and
same_side(point, self._p1, self._p0, self._p2) and
same_side(point, self._p2, self._p0, self._p1)
)