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//
// GetMobius3DCoeffs.h
// testigl
//
// Created by Amir Vaxman on 26/12/14.
// Copyright (c) 2014 Amir Vaxman. All rights reserved.
//
#ifndef MoebiusCode_GetMobius3DCoeffs_h
#define MoebiusCode_GetMobius3DCoeffs_h
#include <hedra/quaternionic_operations.h>
//both meshes have to be on the same unit sphere, 3 points interpolating, and the rest have the same radius
class UnitSphereMoebiusTraitsTraits{
public:
Matrix4d SourceVq;
Matrix4d TargetVq;
VectorXd InitSolution;
double SolutionSize;
double CloseFactor;
double ConstTolerance;
double ValueTolerance;
RowVector4d UnitQuat;
VectorXd CloseVec;
VectorXd ImagVec;
VectorXd PointVec;
VectorXd UnitVec;
VectorXd TotalVec;
VectorXd ConstVec;
VectorXi GradRows, GradCols;
VectorXd GradValues;
double CloseTriOffset, CloseRowOffset;
double ImagTriOffset, ImagRowOffset;
double PosTriOffset, PosRowOffset;
double UnitTriOffset, UnitRowOffset;
void Initialize(const Matrix4d& inSourceVq, const Matrix4d& inTargetVq, const VectorXd& inInitSolution){
InitSolution=inInitSolution;
SourceVq=inSourceVq;
TargetVq=inTargetVq;
UnitQuat<<1.0,0.0,0.0,0.0;
SolutionSize=16;
CloseFactor=10e-6;
ConstTolerance=10e-11;
ImagVec.resize(6);
PointVec.resize(4*3);
UnitVec.resize(1);
CloseVec.resize(SolutionSize);
TotalVec.resize(CloseVec.size()+ImagVec.size()+PointVec.size()+UnitVec.size());
ConstVec.resize(ImagVec.size()+PointVec.size()+UnitVec.size());
//createing gradient pattern
GradRows.resize(SolutionSize+(64+8+8)+64*3+SolutionSize);
GradCols.resize(GradRows.size());
GradValues.resize(GradRows.size());
/*******************Closeness energy*************/
CloseTriOffset=0;
CloseRowOffset=0;
for (int i=0;i<SolutionSize;i++){
GradRows(CloseTriOffset+i)=CloseRowOffset+i;
GradCols(CloseTriOffset+i)=i;
GradValues(CloseTriOffset+i)=CloseFactor;
}
/*******************Imaginarity Constraints************/
ImagTriOffset=CloseTriOffset+SolutionSize;
ImagRowOffset=CloseRowOffset+SolutionSize;
//a*conj(c) in imH
for (int j=0;j<4;j++){
GradRows(ImagTriOffset+j)=ImagRowOffset;
GradCols(ImagTriOffset+j)=j;
GradRows(ImagTriOffset+j+4)=ImagRowOffset;
GradCols(ImagTriOffset+j+4)=8+j;
}
//b*conj(d) in imH
for (int j=0;j<4;j++){
GradRows(ImagTriOffset+8+j)=ImagRowOffset+1;
GradCols(ImagTriOffset+8+j)=j+4;
GradRows(ImagTriOffset+8+j+4)=ImagRowOffset+1;
GradCols(ImagTriOffset+8+j+4)=12+j;
}
//conj(a)*d-conj(b)*c = (1,0,0,0) derivatives
Vector4i aTriPoses; aTriPoses<<0,16,32,48;
Vector4i bTriPoses; bTriPoses<<4,20,36,52;
Vector4i cTriPoses; cTriPoses<<8,24,40,56;
Vector4i dTriPoses; dTriPoses<<12,28,44,60;
hedra::quatDerivativeIndices(GradRows, GradCols, ImagTriOffset+16, aTriPoses, ImagRowOffset+2, 0);
hedra::quatDerivativeIndices(GradRows, GradCols, ImagTriOffset+16, bTriPoses, ImagRowOffset+2, 4);
hedra::quatDerivativeIndices(GradRows, GradCols, ImagTriOffset+16, cTriPoses, ImagRowOffset+2, 8);
hedra::quatDerivativeIndices(GradRows, GradCols, ImagTriOffset+16, dTriPoses, ImagRowOffset+2, 12);
/****************************Positional Constraints******************************/
PosTriOffset=ImagTriOffset+64+8+8;
PosRowOffset=ImagRowOffset+6;
for (int i=0;i<3;i++){
//a*q+b-w*c*q-w*d
hedra::quatDerivativeIndices(GradRows, GradCols, PosTriOffset+64*i, aTriPoses, PosRowOffset+4*i, 0);
hedra::quatDerivativeIndices(GradRows, GradCols, PosTriOffset+64*i, bTriPoses, PosRowOffset+4*i, 4);
hedra::quatDerivativeIndices(GradRows, GradCols, PosTriOffset+64*i, cTriPoses, PosRowOffset+4*i, 8);
hedra::quatDerivativeIndices(GradRows, GradCols, PosTriOffset+64*i, dTriPoses, PosRowOffset+4*i, 12);
}
/********************Unit Constraints***********************************************/
UnitTriOffset=PosTriOffset+64*3;
UnitRowOffset=PosRowOffset+4*3;
for (int i=0;i<SolutionSize;i++){
GradRows(UnitTriOffset+i)=UnitRowOffset;
GradCols(UnitTriOffset+i)=i;
}
}
void UpdateEnergy(const VectorXd& CurrSolution)
{
CloseVec<<CloseFactor*(CurrSolution-InitSolution);
UpdateConstraints(CurrSolution);
TotalVec<<CloseVec, ConstVec;
}
void UpdateGradient(const VectorXd& CurrSolution)
{
RowVector4d a=CurrSolution.segment(0,4);
RowVector4d b=CurrSolution.segment(4,4);
RowVector4d c=CurrSolution.segment(8,4);
RowVector4d d=CurrSolution.segment(12,4);
//closeness is constant
/****************Imaginarity Gradient***********************/
//a*conj(c)
for (int j=0;j<4;j++){
GradValues(ImagTriOffset+j)=c(j);
GradValues(ImagTriOffset+j+4)=a(j);
}
//b*conj(d)
for (int j=0;j<4;j++){
GradValues(ImagTriOffset+8+j)=d(j);
GradValues(ImagTriOffset+12+j)=b(j);
}
//conj(a)*d-conj(b)*c derivatives
Vector4i aTriPoses; aTriPoses<<0,16,32,48;
Vector4i bTriPoses; bTriPoses<<4,20,36,52;
Vector4i cTriPoses; cTriPoses<<8,24,40,56;
Vector4i dTriPoses; dTriPoses<<12,28,44,60;
hedra::quatDerivativeValues(GradValues, ImagTriOffset+16, aTriPoses, UnitQuat, d, true, false);
hedra::quatDerivativeValues(GradValues, ImagTriOffset+16, bTriPoses, -UnitQuat, c, true, false);
hedra::quatDerivativeValues(GradValues, ImagTriOffset+16, cTriPoses, -QConj(b), UnitQuat, false, false);
hedra::quatDerivativeValues(GradValues, ImagTriOffset+16, dTriPoses, QConj(a), UnitQuat, false, false);
/****************************Point Constraints******************************/
for (int i=0;i<3;i++){
//a*q+b-w*c*q-w*d
RowVector4d q=SourceVq.row(i);
RowVector4d w=TargetVq.row(i);
hedra::quatDerivativeValues(GradValues, PosTriOffset+64*i, aTriPoses, UnitQuat, q, false, false);
hedra::quatDerivativeValues(GradValues, PosTriOffset+64*i, bTriPoses, UnitQuat, UnitQuat, false, false);
hedra::quatDerivativeValues(GradValues, PosTriOffset+64*i, cTriPoses, -w,q, false, false);
hedra::quatDerivativeValues(GradValues, PosTriOffset+64*i, dTriPoses, -w, UnitQuat, false, false);
}
/*****************************Unit Constraints******************************/
//(diff(|aq+b|^2)/da=2*a*sum(q.^2)-2*QMult(b,q)
RowVector4d diffa=2*a*SourceVq.row(3).squaredNorm()-2*QMult(b,SourceVq.row(3));
//(diff(|aq+b|^2)/db=2*b+2*QMult(a,q)
RowVector4d diffb=2*b+2*QMult(a,SourceVq.row(3));
//(diff(|cq+d|^2)/dc=2*c*sum(q.^2)-2*QMult(d,q)
RowVector4d diffc=2*c*SourceVq.row(3).squaredNorm()-2*QMult(d,SourceVq.row(3));
//(diff(|cq+d|^2)/dd=2*d+2*QMult(c,q)
RowVector4d diffd=2*d+2*QMult(c,SourceVq.row(3));
for (int j=0;j<4;j++){
GradValues(UnitTriOffset+j)=diffa(j);
GradValues(UnitTriOffset+4+j)=diffb(j);
GradValues(UnitTriOffset+8+j)=-diffc(j);
GradValues(UnitTriOffset+12+j)=-diffd(j);
}
}
void Reformulate(int NumIteration, int MaxIteration, VectorXd& CurrSolution, double PrevError)
{
InitSolution=CurrSolution;
}
void UpdateConstraints(const VectorXd& CurrSolution)
{
RowVector4d a=CurrSolution.segment(0,4);
RowVector4d b=CurrSolution.segment(4,4);
RowVector4d c=CurrSolution.segment(8,4);
RowVector4d d=CurrSolution.segment(12,4);
//a*conj(c) in imH
RowVector4d ac=QMult(a,QConj(c));
ImagVec(0)=ac(0);
//b*conj(d) in imH
RowVector4d bd=QMult(b,QConj(d));
ImagVec(1)=bd(0);
//conj(a)*d-conj(b)*c = UnitQuat
RowVector4d adcb=QMult(QConj(a), d)-QMult(QConj(b), c)-UnitQuat;
ImagVec.segment(2,4)=adcb.transpose();
for (int i=0;i<3;i++){
RowVector4d Res=QMult(a,SourceVq.row(i))+b-QMult(TargetVq.row(i),QMult(c,SourceVq.row(i))+d);
PointVec.segment(4*i,4)=Res.transpose();
}
//unit-preserving
UnitVec(0)=(QMult(a,SourceVq.row(3))+b).squaredNorm()-(QMult(c,SourceVq.row(3))+d).squaredNorm();
ConstVec<<ImagVec, PointVec, UnitVec;
}
bool isTerminate(){
return (ConstVec.lpNorm<Infinity>()<ConstTolerance);
}
};
#endif