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import math
import torch
class GeometryLoss:
def __init__(self, pathObj, xyalign=True, parallel=True, smooth_node=True):
self.pathObj=pathObj
self.pathId=pathObj.id
self.get_segments(pathObj)
if xyalign:
self.make_hor_ver_constraints(pathObj)
self.xyalign=xyalign
self.parallel=parallel
self.smooth_node=smooth_node
if parallel:
self.make_parallel_constraints(pathObj)
if smooth_node:
self.make_smoothness_constraints(pathObj)
def make_smoothness_constraints(self,pathObj):
self.smooth_nodes=[]
for idx, node in enumerate(self.iterate_nodes()):
sm, t0, t1=self.node_smoothness(node,pathObj)
if abs(sm)<1e-2:
self.smooth_nodes.append((node,((t0.norm()/self.segment_approx_length(node[0],pathObj)).item(),(t1.norm()/self.segment_approx_length(node[1],pathObj)).item())))
#print("Node {} is smooth (smoothness {})".format(idx,sm))
else:
#print("Node {} is not smooth (smoothness {})".format(idx, sm))
pass
def node_smoothness(self,node,pathObj):
t0=self.tangent_out(node[0],pathObj)
t1=self.tangent_in(node[1],pathObj)
t1rot=torch.stack((-t1[1],t1[0]))
smoothness=t0.dot(t1rot)/(t0.norm()*t1.norm())
return smoothness, t0, t1
def segment_approx_length(self,segment,pathObj):
if segment[0]==0:
#line
idxs=self.segList[segment[0]][segment[1]]
#should have a pair of indices now
length=(pathObj.points[idxs[1],:]-pathObj.points[idxs[0],:]).norm()
return length
elif segment[0]==1:
#quadric
idxs = self.segList[segment[0]][segment[1]]
# should have a pair of indices now
length = (pathObj.points[idxs[1],:] - pathObj.points[idxs[0],:]).norm()+(pathObj.points[idxs[2],:] - pathObj.points[idxs[1],:]).norm()
return length
elif segment[0]==2:
#cubic
idxs = self.segList[segment[0]][segment[1]]
# should have a pair of indices now
length = (pathObj.points[idxs[1],:] - pathObj.points[idxs[0],:]).norm()+(pathObj.points[idxs[2],:] - pathObj.points[idxs[1],:]).norm()+(pathObj.points[idxs[3],:] - pathObj.points[idxs[2],:]).norm()
return length
def tangent_in(self, segment,pathObj):
if segment[0]==0:
#line
idxs=self.segList[segment[0]][segment[1]]
#should have a pair of indices now
tangent=(pathObj.points[idxs[1],:]-pathObj.points[idxs[0],:])/2
return tangent
elif segment[0]==1:
#quadric
idxs = self.segList[segment[0]][segment[1]]
# should have a pair of indices now
tangent = (pathObj.points[idxs[1],:] - pathObj.points[idxs[0],:])
return tangent
elif segment[0]==2:
#cubic
idxs = self.segList[segment[0]][segment[1]]
# should have a pair of indices now
tangent = (pathObj.points[idxs[1],:] - pathObj.points[idxs[0],:])
return tangent
assert(False)
def tangent_out(self, segment, pathObj):
if segment[0] == 0:
# line
idxs = self.segList[segment[0]][segment[1]]
# should have a pair of indices now
tangent = (pathObj.points[idxs[0],:] - pathObj.points[idxs[1],:]) / 2
return tangent
elif segment[0] == 1:
# quadric
idxs = self.segList[segment[0]][segment[1]]
# should have a pair of indices now
tangent = (pathObj.points[idxs[1],:] - pathObj.points[idxs[2],:])
return tangent
elif segment[0] == 2:
# cubic
idxs = self.segList[segment[0]][segment[1]]
# should have a pair of indices now
tangent = (pathObj.points[idxs[2],:] - pathObj.points[idxs[3],:])
return tangent
assert (False)
def get_segments(self, pathObj):
self.segments=[]
self.lines = []
self.quadrics=[]
self.cubics=[]
self.segList =(self.lines,self.quadrics,self.cubics)
idx=0
total_points=pathObj.points.shape[0]
for ncp in pathObj.num_control_points.numpy():
if ncp==0:
self.segments.append((0,len(self.lines)))
self.lines.append((idx, (idx + 1) % total_points))
idx+=1
elif ncp==1:
self.segments.append((1, len(self.quadrics)))
self.quadrics.append((idx, (idx + 1), (idx+2) % total_points))
idx+=ncp+1
elif ncp==2:
self.segments.append((2, len(self.cubics)))
self.cubics.append((idx, (idx + 1), (idx+2), (idx + 3) % total_points))
idx += ncp + 1
def iterate_nodes(self):
for prev, next in zip([self.segments[-1]]+self.segments[:-1],self.segments):
yield (prev, next)
def make_hor_ver_constraints(self, pathObj):
self.horizontals=[]
self.verticals=[]
for idx, line in enumerate(self.lines):
startPt=pathObj.points[line[0],:]
endPt=pathObj.points[line[1],:]
dif=endPt-startPt
if abs(dif[0])<1e-6:
#is horizontal
self.horizontals.append(idx)
if abs(dif[1])<1e-6:
#is vertical
self.verticals.append(idx)
def make_parallel_constraints(self,pathObj):
slopes=[]
for lidx, line in enumerate(self.lines):
startPt = pathObj.points[line[0], :]
endPt = pathObj.points[line[1], :]
dif = endPt - startPt
slope=math.atan2(dif[1],dif[0])
if slope<0:
slope+=math.pi
minidx=-1
for idx, s in enumerate(slopes):
if abs(s[0]-slope)<1e-3:
minidx=idx
break
if minidx>=0:
slopes[minidx][1].append(lidx)
else:
slopes.append((slope,[lidx]))
self.parallel_groups=[sgroup[1] for sgroup in slopes if len(sgroup[1])>1 and (not self.xyalign or (sgroup[0]>1e-3 and abs(sgroup[0]-(math.pi/2))>1e-3))]
def make_line_diff(self,pathObj,lidx):
line = self.lines[lidx]
startPt = pathObj.points[line[0], :]
endPt = pathObj.points[line[1], :]
dif = endPt - startPt
return dif
def calc_hor_ver_loss(self,loss,pathObj):
for lidx in self.horizontals:
dif = self.make_line_diff(pathObj,lidx)
loss+=dif[0].pow(2)
for lidx in self.verticals:
dif = self.make_line_diff(pathObj,lidx)
loss += dif[1].pow(2)
def calc_parallel_loss(self,loss,pathObj):
for group in self.parallel_groups:
diffs=[self.make_line_diff(pathObj,lidx) for lidx in group]
difmat=torch.stack(diffs,1)
lengths=difmat.pow(2).sum(dim=0).sqrt()
difmat=difmat/lengths
difmat=torch.cat((difmat,torch.zeros(1,difmat.shape[1])))
rotmat=difmat[:,list(range(1,difmat.shape[1]))+[0]]
cross=difmat.cross(rotmat)
ploss=cross.pow(2).sum()*lengths.sum()*10
loss+=ploss
def calc_smoothness_loss(self,loss,pathObj):
for node, tlengths in self.smooth_nodes:
sl,t0,t1=self.node_smoothness(node,pathObj)
#add smoothness loss
loss+=sl.pow(2)*t0.norm().sqrt()*t1.norm().sqrt()
tl=((t0.norm()/self.segment_approx_length(node[0],pathObj))-tlengths[0]).pow(2)+((t1.norm()/self.segment_approx_length(node[1],pathObj))-tlengths[1]).pow(2)
loss+=tl*10
def compute(self, pathObj):
if pathObj.id != self.pathId:
raise ValueError("Path ID {} does not match construction-time ID {}".format(pathObj.id,self.pathId))
loss=torch.tensor(0.)
if self.xyalign:
self.calc_hor_ver_loss(loss,pathObj)
if self.parallel:
self.calc_parallel_loss(loss, pathObj)
if self.smooth_node:
self.calc_smoothness_loss(loss,pathObj)
#print(loss.item())
return loss
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