# Source code for boxes.vectors

```# Copyright (C) 2013-2014 Florian Festi
#
#   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/>.
import math

[docs]def normalize(v):
"""set length of vector to one"""
l = (v[0] ** 2 + v[1] ** 2) ** 0.5
if l == 0.0:
return (0.0, 0.0)
return (v[0] / l, v[1] / l)

[docs]def vlength(v):
return (v[0] ** 2 + v[1] ** 2) ** 0.5

[docs]def vclip(v, length):
l = vlength(v)
if l > length:
return vscalmul(v, length / l)
return v

[docs]def vdiff(p1, p2):
"""vector from point1 to point2"""
return (p2[0] - p1[0], p2[1] - p1[1])

[docs]def vadd(v1, v2):
"""Sum of two vectors"""
return (v1[0] + v2[0], v1[1] + v2[1])

[docs]def vorthogonal(v):
"""Orthogonal vector"""
return (-v[1], v[0])

[docs]def vscalmul(v, a):
"""scale vector by a"""
return (a * v[0], a * v[1])

[docs]def dotproduct(v1, v2):
"""Dot product"""
return v1[0] * v2[0] + v1[1] * v2[1]

[docs]def circlepoint(r, a):
return (r * math.cos(a), r * math.sin(a))

[docs]def tangent(x, y, r):
"""angle and length of a tangent to a circle at x,y with radius r"""
l1 = vlength((x, y))
a1 = math.atan2(y, x)
a2 = math.asin(r / l1)
l2 = math.cos(a2) * l1

return (a1+a2, l2)

[docs]def rotm(angle):
"""Rotation matrix"""
return [[math.cos(angle), -math.sin(angle), 0],
[math.sin(angle), math.cos(angle), 0]]

[docs]def vtransl(v, m):
m0, m1 = m
return [m0[0] * v[0] + m0[1] * v[1] + m0[2],
m1[0] * v[0] + m1[1] * v[1] + m1[2]]

[docs]def mmul(m0, m1):
result = [[0, ] * len(m0[0]) for i in range(len(m0))]
for i in range(len(m0[0])):
for j in range(len(m0)):
for k in range(len(m0)):
result[j][i] += m0[k][i] * m1[j][k]
return result

[docs]def kerf(points, k, closed=True):
"""Outset points by k
Assumes a closed loop of points
"""
result = []
lp = len(points)

for i in range(len(points)):
# get normalized orthogonals of both segments
v1 = vorthogonal(normalize(vdiff(points[i - 1], points[i])))
v2 = vorthogonal(normalize(vdiff(points[i], points[(i + 1) % lp])))

if not closed:
if i == 0:
v1 = v2
if i == lp-1:
v2 = v1
# direction the point has to move
d = normalize(vadd(v1, v2))
# cos of the half the angle between the segments
cos_alpha = dotproduct(v1, d)
result.append(vadd(points[i], vscalmul(d, -k / cos_alpha)))

return result
```