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pc.jl
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pc.jl
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using LinearAlgebraicRepresentation, ViewerGL,AlphaStructures
Lar = LinearAlgebraicRepresentation
GL = ViewerGL
V,(VV,EV,FV,CV) = Lar.cuboid([5,3,2],true)
V1,(VV1,EV1,FV1,CV1) = Lar.cuboid([10,6,9],true)
model = Lar.apply(Lar.t(1,2,3),Lar.apply(Lar.r(pi/4,0,0),(V,FV)))
model1 = Lar.apply(Lar.t(5,6,7),Lar.apply(Lar.r(0,-pi/6,0),(V1,FV1)))
GL.VIEW([
GL.GLPoints(convert(Lar.Points,model[1]'))
GL.GLPoints(convert(Lar.Points,model1[1]'))
GL.GLGrid(model...)
GL.GLGrid(model1...)
GL.GLAxis(GL.Point3d(0,0,0),GL.Point3d(1,1,1))
]);
# prendo le due origini
O = model[1][:,1]
O1 = model1[1][:,1]
# e tutti i punti degli assi
assex=model[1][:,5]-O
assey=model[1][:,3]-O
assez=model[1][:,2]-O
asse1x=model1[1][:,5]-O1
asse1y=model1[1][:,3]-O1
asse1z=model1[1][:,2]-O1
# Assi normalizzati per creare le rotazioni
nassex = assex/Lar.norm(assex)
nassey = assey/Lar.norm(assey)
nassez = assez/Lar.norm(assez)
nassex1 = asse1x/Lar.norm(asse1x)
nassey1 = asse1y/Lar.norm(asse1y)
nassez1 = asse1z/Lar.norm(asse1z)
R=[nassex[1] nassex[2] nassex[3]; nassey[1] nassey[2] nassey[3];nassez[1] nassez[2] nassez[3]]
R1=[nassex1[1] nassex1[2] nassex1[3]; nassey1[1] nassey1[2] nassey1[3]; nassez1[1] nassez1[2] nassez1[3]]
#V2 = R*(model[1].-O)
# calcolo la matrice di scala lunghezza asse pc1 fratto lunghezza asse pc2
S = Lar.Diagonal([Lar.norm(assex)/Lar.norm(asse1x),Lar.norm(assey)/Lar.norm(asse1y),Lar.norm(assez)/Lar.norm(asse1z)])
##### applico la rotazione per portarla nell 'origine e scalarla
V12 = S*R1*(model1[1].-O1)
# la sovrappongo sulla pc1 con la trasformazione inversa di pc1
V1finale = (Lar.inv(R)*V12).+O
GL.VIEW([
GL.GLPoints(convert(Lar.Points,model[1]'))
GL.GLPoints(convert(Lar.Points,V1finale'))
GL.GLGrid(model[1],FV,GL.COLORS[3],0.5)
GL.GLGrid(V1finale,FV1,GL.COLORS[2],0.5)
GL.GLAxis(GL.Point3d(0,0,0),GL.Point3d(1,1,1))
]);
"""
Y è la reference cloud
X la source cloud
"""
function ICP(X,Y)
x=X[1,:]
y=X[2,:]
u=Y[1,:]
v=Y[2,:]
sx2=Lar.norm(x)^2
sxy=Lar.dot(x,y)
sx=sum(x)
sy2=Lar.norm(y)^2
sy=sum(y)
n=size(X,2)
sux=Lar.dot(u,x)
suy=Lar.dot(u,y)
su=sum(u)
svx=Lar.dot(v,x)
svy=Lar.dot(v,y)
sv=sum(v)
A=[ sx2 sxy sx 0 0 0;
sxy sy2 sy 0 0 0;
sx sy n 0 0 0;
0 0 0 sx2 sxy sx;
0 0 0 sxy sy2 sy;
0 0 0 sx sy n]
b=[sux, suy, su, svx, svy, sv]
params=A\b
R=[ params[1] params[2];
params[4] params[5]]
t=[params[3], params[6]]
return R,t
end
function iterativeICP(X,Y,itermax)
x=copy(X)
iter=1
R=Matrix(Lar.I,2,2)
T=[0,0]
error=diff=Inf
while diff>1.e-8 && iter<itermax
r,t = ICP(x,Y)
R=r*R
T=r*T+t
diff=Lar.abs(error-residuo(R,T,X,Y))
error=residuo(R,T,X,Y)
@show diff
x=r*x.+t
iter+=1
end
return R,T,iter,error
end
function residuo(R,T,X,Y)
error = Lar.abs(Lar.norm(R*X.+T.-Y)^2)
return error
end
X=rand(2,1000)
# R = [0.5 0 0.866025; 0.866025 0 -0.5; 0 1 0]
# t = [1,1,1]
r = [0.5 -sqrt(3)/2; sqrt(3)/2 0.5]
t = [1,2]
s=[1.4 0;0 0.5]
Y = r*s*X.+t
Y = AlphaStructures.matrixPerturbation(Y,atol=0.01)
GL.VIEW([
GL.GLPoints(convert(Lar.Points,X'))
GL.GLPoints(convert(Lar.Points,Y'), GL.COLORS[2])
GL.GLFrame2
]);
R,T=ICP(X,Y)
X2 = R*X.+T
residuo(R,T,X,Y)
GL.VIEW([
GL.GLPoints(convert(Lar.Points,X2'))
GL.GLPoints(convert(Lar.Points,Y'), GL.COLORS[2])
GL.GLFrame2
]);
R,T,iter,er=iterativeICP(X,Y,1000)
residuo(R,T,X,Y)
X2 = R*X.+T
GL.VIEW([
GL.GLPoints(convert(Lar.Points,X2'))
GL.GLPoints(convert(Lar.Points,Y'), GL.COLORS[2])
GL.GLFrame2
]);