Как равномерно перераспределить точки по кривой ⇐ Python

[Anonymous]

У меня есть произвольная трехмерная кривая, состоящая из списка декартовых точек XYZ. Очки распределены неравномерно (есть временной фактор). Как я могу «перестроить» кривую с заданным количеством точек, которые должны составлять кривую. Я вижу это в программах 3D-моделирования, поэтому я почти уверен, что это возможно, просто не знаю как.



Основываясь на ответе, мне это нужно было в Python, поэтому я начал работать над преобразованием interparc в Python. Я дошёл до линейной интерполяции. Вероятно, он неэффективен и имеет избыточность, но, возможно, кому-то будет полезен:
import numpy as np
import scipy.interpolate as sp
import math
import csv

def diffCOL(matrix):
newMAT = []
newROW = []
for i in range(len(matrix)-1):
for j in range(len(matrix)):
diff = matrix[i+1][j]-matrix[j]
newROW.append(diff)
newMAT.append(newROW)
newROW = []
#Stack the matrix to get xyz in columns
newMAT = np.vstack(newMAT)
return newMAT

def squareELEM(matrix):
for i in range(len(matrix)):
for j in range(len(matrix)):
matrix[j] = matrix[j]*matrix[j]
return matrix

def sumROW(matrix):
newMAT = []
for j in range(len(matrix)):
rowSUM = 0
for k in range(len(matrix[j])):
rowSUM = rowSUM + matrix[j][k]
newMAT.append(rowSUM)
return newMAT

def sqrtELEM(matrix):
for i in range(len(matrix)):
matrix = math.sqrt(matrix)
return matrix

def sumELEM(matrix):
sum = 0
for i in range(len(matrix)):
sum = sum + matrix
return sum

def diffMAT(matrix,denom):
newMAT = []
for i in range(len(matrix)):
newMAT.append(matrix/denom)
return newMAT

def cumsumMAT(matrix):
first = 0
newmat = []
newmat.append(first)
#newmat.append(matrix)
for i in range(len(matrix)):
newmat.append(matrix[i])
cum = 0
for i in range(len(newmat)):
cum = cum + newmat[i]
newmat[i] = cum
return newmat

def divMAT(A,B):
newMAT = []
for i in range(len(A)):
newMAT.append(A[i] / B[i])
return newMAT

def minusVector(t,cumarc):
newMAT = []
for i in range(len(t)):
newMAT.append(t[i] - cumarc[i])
return newMAT

def replaceIndex(A,B):
newMAT = []
print "A: ,",A
print "LENA: ",len(A)
print "B: ,",B
print "LENB: ",len(B)
for i in range(len(B)):
index = B[i]
newMAT.append(A[index])
return newMAT

def matSUB(first,second):
newMAT = []
newCOL = []
for i in range(len(first)):
for j in range(len(first[i])):
newMAT.append(first[i][j] - second[i][j])
#newMAT.append(newCOL)
return newMAT

def matADD(first,second):
newMAT = []
newCOL = []
#print "F: ",first
#print "S: ",second
for i in range(len(first)):
for j in range(len(first[i])):
newMAT.append(first[i][j]+second[i][j])
#newMAT.append(newCOL)
return newMAT

def matMULTI(first,second):
"""
Take in two matrix
multiply each element against the other at the same index
return a new matrix
"""
#print "FIRST: ",first
#print "SECOND: ",second
newMAT = []
newCOL = []
for i in range(len(first)):
for j in range(len(first[i])):
newMAT.append(first[i][j]*second[i][j])
#newMAT.append(newCOL)
return newMAT

def matDIV(first,second):
"""
Take in two matrix
multiply each element against the other at the same index
return a new matrix
"""
newMAT = []
newCOL = []
for i in range(len(first)):
for j in range(len(first[i])):
newMAT.append(first[i][j]/second[i][j])
#newMAT.append(newCOL)
return newMAT

def vecDIV(first,second):
"""
Take in two arrays
multiply each element against the other at the same index
return a new array
"""
newMAT = []
for i in range(len(first)):
newMAT.append(first[i]/second[i])
return newMAT

def replaceROW(matrix,replacer,adder):
newMAT = []
#print "MAT: ",matrix
#print "REP: ",replacer
if adder != 0:
for i in range(len(replacer)):
newMAT.append(matrix[replacer[i]+adder])
else:
for i in range(len(replacer)):
newMAT.append(matrix[replacer[i]])
return np.vstack(newMAT)

def interparc(t,px,py,*args):
inputs = [t,px,py,args]
#print "T: ",t
#print "X: ",px
#print "Y: ",py
#print "Z: ",varargin

#If we dont get at least a t, x, and y value we error
if len(inputs)1) and (t%1==0):
t = np.linspace(0,1,t)
elif t1:
print "Error: STEP SIZE t IS NOT ALLOWED"

nt = len(t)

px = px
py = py
n = len(px)

if len(px) != len(py):
print "ERROR: MUST BE SAME LENGTH"
elif n < 2:
print "ERROR: MUST BE OF LENGTH 2"

pxy = [px,py]
#pxy = np.transpose(pxy)
ndim = 2

method = 'linear'

if len(args) > 1:
if isinstance(args[len(args)-1], basestring) == True:
method = args[len(args)-1]
if method != 'linear' and method != 'pchip' and method != 'spline':
print "ERROR: INVALID METHOD"
elif len(args)==1:
method = args[0]
print method
method = 'linear'
# Try to append all the arguments together
for i in range(len(args)):
if isinstance(args[i], basestring) != True:
pz = args[i]
print "Z",len(pz)
if len(pz) != n:
print "ERROR: LENGTH MUST BE SAME AS OTHER INPUT"
pxy.append(pz)
print "DIM LEN: ",len(pxy)
ndim = len(pxy)

pt = np.zeros((nt,ndim))
#Check for rounding errors here
# Transpose the matrix to align with matlab codes method
pxy = np.transpose(pxy)
chordlen = sqrtELEM(sumROW(squareELEM(diffCOL(pxy))))
chordlen = diffMAT(chordlen,sumELEM(chordlen))
cumarc = cumsumMAT(chordlen)
print ""
print ""
print "Third operation (CUMARC): \n",np.vstack(cumarc)
print ""

if method == 'linear':
inter = np.histogram(bins=t,a=cumarc)
tbins = inter[1]
hist= inter[0]
tbinset=[]
index=0
tbinset.append(index)
print "ORIGINAL TBIN: \n",hist
print "LEN: \n",len(hist)
print ""

for i in range(len(hist)):
if hist[i]>0:
index=index+hist[i]
tbinset.append(index)
else:
tbinset.append(index)

for i in range(len(tbinset)):
if tbinset[i]=1:
tbinset[i] = n-1
print ""
print "TBINSET: ",tbinset
print "LEN: ",len(tbinset)
#Take off one value to match the way matlab does indexing
for i in range(len(tbinset)):
tbinset[i]=tbinset[i]-1

s = divMAT(minusVector(t,replaceIndex(cumarc,tbinset)),replaceIndex(chordlen,tbinset) )

#Breakup the parts of pt
repmat = np.transpose(np.reshape(np.vstack(np.tile(s,(1,ndim))[0]),(ndim,-1)))
sub = np.reshape( np.vstack( matSUB( replaceROW(pxy,tbinset,1) , replaceROW(pxy,tbinset,0) ) ) , (-1,ndim) )
multi = np.reshape( np.vstack(matMULTI( sub , repmat )) ,(-1,ndim) )
pt = np.reshape( np.vstack( matADD( replaceROW(pxy,tbinset,0) , multi ) ) ,(-1,ndim) )
return pt