119 lines
3.0 KiB
Python
119 lines
3.0 KiB
Python
# Copyright (C) 2013-2014 Florian Festi
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#
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# This program is free software: you can redistribute it and/or modify
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# it under the terms of the GNU General Public License as published by
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# the Free Software Foundation, either version 3 of the License, or
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# (at your option) any later version.
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#
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# This program is distributed in the hope that it will be useful,
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# but WITHOUT ANY WARRANTY; without even the implied warranty of
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# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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# GNU General Public License for more details.
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#
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# You should have received a copy of the GNU General Public License
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# along with this program. If not, see <http://www.gnu.org/licenses/>.
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import math
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def normalize(v):
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"set lenght of vector to one"
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l = (v[0] ** 2 + v[1] ** 2) ** 0.5
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if l == 0.0:
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return (0.0, 0.0)
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return (v[0] / l, v[1] / l)
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def vlength(v):
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return (v[0] ** 2 + v[1] ** 2) ** 0.5
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def vclip(v, length):
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l = vlength(v)
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if l > length:
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return vscalmul(v, length / l)
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return v
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def vdiff(p1, p2):
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"vector from point1 to point2"
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return (p2[0] - p1[0], p2[1] - p1[1])
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def vadd(v1, v2):
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"Sum of two vectors"
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return (v1[0] + v2[0], v1[1] + v2[1])
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def vorthogonal(v):
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"orthogonal vector"
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"Orthogonal vector"
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return (-v[1], v[0])
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def vscalmul(v, a):
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"scale vector by a"
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return (a * v[0], a * v[1])
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def dotproduct(v1, v2):
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"Dot product"
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return v1[0] * v2[0] + v1[1] * v2[1]
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def circlepoint(r, a):
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return (r * math.cos(a), r * math.sin(a))
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def tangent(x, y, r):
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"angle and length of a tangent to a circle at x,y with raduis r"
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l1 = vlength((x, y))
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a1 = math.atan2(y, x)
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a2 = math.asin(r / l1)
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l2 = math.cos(a2) * l1
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return (a1+a2, l2)
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def rotm(angle):
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"Rotation matrix"
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return [[math.cos(angle), -math.sin(angle), 0],
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[math.sin(angle), math.cos(angle), 0]]
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def vtransl(v, m):
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m0, m1 = m
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return [m0[0] * v[0] + m0[1] * v[1] + m0[2],
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m1[0] * v[0] + m1[1] * v[1] + m1[2]]
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def mmul(m0, m1):
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result = [[0, ] * len(m0[0]) for i in range(len(m0))]
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for i in range(len(m0[0])):
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for j in range(len(m0)):
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for k in range(len(m0)):
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result[j][i] += m0[k][i] * m1[j][k]
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return result
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def kerf(points, k, closed=True):
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"""Outset points by k
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Assumes a closed loop of points
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"""
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result = []
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lp = len(points)
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for i in range(len(points)):
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# get normalized orthogonals of both segments
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v1 = vorthogonal(normalize(vdiff(points[i - 1], points[i])))
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v2 = vorthogonal(normalize(vdiff(points[i], points[(i + 1) % lp])))
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if not closed:
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if i == 0:
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v1 = v2
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if i == lp-1:
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v2 = v1
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# direction the point has to move
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d = normalize(vadd(v1, v2))
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# cos of the half the angle between the segments
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cos_alpha = dotproduct(v1, d)
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result.append(vadd(points[i], vscalmul(d, -k / cos_alpha)))
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return result
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