boxespy/boxes/vectors.py

102 lines
2.6 KiB
Python

# 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
def normalize(v):
"set lenght of vector to one"
l = (v[0] ** 2 + v[1] ** 2) ** 0.5
return (v[0] / l, v[1] / l)
def vlength(v):
return (v[0] ** 2 + v[1] ** 2) ** 0.5
def vclip(v, length):
l = vlength(v)
if l > length:
return vscalmul(v, length / l)
return v
def vdiff(p1, p2):
"vector from point1 to point2"
return (p2[0] - p1[0], p2[1] - p1[1])
def vadd(v1, v2):
"Sum of two vectors"
return (v1[0] + v2[0], v1[1] + v2[1])
def vorthogonal(v):
"orthogonal vector"
"Orthogonal vector"
return (-v[1], v[0])
def vscalmul(v, a):
"scale vector by a"
return (a * v[0], a * v[1])
def dotproduct(v1, v2):
"Dot product"
return v1[0] * v2[0] + v1[1] * v2[1]
def circlepoint(r, a):
return (r * math.cos(a), r * math.sin(a))
def rotm(angle):
"Rotation matrix"
return [[math.cos(angle), -math.sin(angle), 0],
[math.sin(angle), math.cos(angle), 0]]
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]]
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
def kerf(points, k):
"""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])))
# 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