boxespy/boxes/vectors.py

86 lines
2.5 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 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