129 lines
6.0 KiB
C++
129 lines
6.0 KiB
C++
// This file is part of libigl, a simple c++ geometry processing library.
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//
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// Copyright (C) 2017 Amir Vaxman <avaxman@gmail.com>
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//
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// This Source Code Form is subject to the terms of the Mozilla Public License
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// v. 2.0. If a copy of the MPL was not distributed with this file, You can
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// obtain one at http://mozilla.org/MPL/2.0/.
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#ifndef IGL_SHAPEUP_H
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#define IGL_SHAPEUP_H
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#include <igl/min_quad_with_fixed.h>
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#include <igl/igl_inline.h>
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#include <igl/setdiff.h>
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#include <igl/cat.h>
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#include <Eigen/Core>
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#include <vector>
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#include <igl/PI.h>
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//This file implements the following algorithm:
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//Boaziz et al.
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//Shape-Up: Shaping Discrete Geometry with Projections
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//Computer Graphics Forum (Proc. SGP) 31(5), 2012
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namespace igl
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{
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struct ShapeupData{
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//input data
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Eigen::MatrixXd P;
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Eigen::VectorXi SC;
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Eigen::MatrixXi S;
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Eigen::VectorXi b;
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int maxIterations; //referring to number of local-global pairs.
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double pTolerance; //algorithm stops when max(|P_k-P_{k-1}|)<pTolerance.
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double shapeCoeff, closeCoeff, smoothCoeff;
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//Internally-used matrices
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Eigen::SparseMatrix<double> DShape, DClose, DSmooth, Q, A, At, W;
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min_quad_with_fixed_data<double> solver_data;
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ShapeupData():
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maxIterations(50),
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pTolerance(10e-6),
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shapeCoeff(1.0),
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closeCoeff(100.0),
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smoothCoeff(0.0){}
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};
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//Every function here defines a local projection for ShapeUp, and must have the following structure to qualify:
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//Input:
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// P #P by 3 the set of points, either the initial solution, or from previous iteration.
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// SC #Set by 1 cardinalities of sets in S
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// S #Sets by max(SC) independent sets where the local projection applies. Values beyond column SC(i)-1 in row S(i,:) are "don't care"
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//Output:
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// projP #S by 3*max(SC) in format xyzxyzxyz, where the projected points correspond to each set in S in the same order.
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typedef std::function<bool(const Eigen::PlainObjectBase<Eigen::MatrixXd>&, const Eigen::PlainObjectBase<Eigen::VectorXi>&, const Eigen::PlainObjectBase<Eigen::MatrixXi>&, Eigen::PlainObjectBase<Eigen::MatrixXd>&)> shapeup_projection_function;
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//This projection does nothing but render points into projP. Mostly used for "echoing" the global step
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IGL_INLINE bool shapeup_identity_projection(const Eigen::PlainObjectBase<Eigen::MatrixXd>& P, const Eigen::PlainObjectBase<Eigen::VectorXi>& SC, const Eigen::PlainObjectBase<Eigen::MatrixXi>& S, Eigen::PlainObjectBase<Eigen::MatrixXd>& projP);
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//the projection assumes that the sets are vertices of polygons in cyclic order
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IGL_INLINE bool shapeup_regular_face_projection(const Eigen::PlainObjectBase<Eigen::MatrixXd>& P, const Eigen::PlainObjectBase<Eigen::VectorXi>& SC, const Eigen::PlainObjectBase<Eigen::MatrixXi>& S, Eigen::PlainObjectBase<Eigen::MatrixXd>& projP);
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//This function precomputation the necessary matrices for the ShapeUp process, and prefactorizes them.
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//input:
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// P #P by 3 point positions
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// SC #Set by 1 cardinalities of sets in S
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// S #Sets by max(SC) independent sets where the local projection applies. Values beyond column SC(i)-1 in row S(i,:) are "don't care"
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// E #E by 2 the "edges" of the set P; used for the smoothness energy.
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// b #b by 1 boundary (fixed) vertices from P.
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// wShape, #Set by 1
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// wSmooth #b by 1 weights for constraints from S and positional constraints (used in the global step)
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// Output:
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// sudata struct ShapeupData the data necessary to solve the system in shapeup_solve
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template <
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typename DerivedP,
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typename DerivedSC,
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typename DerivedS,
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typename Derivedw>
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IGL_INLINE bool shapeup_precomputation(const Eigen::PlainObjectBase<DerivedP>& P,
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const Eigen::PlainObjectBase<DerivedSC>& SC,
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const Eigen::PlainObjectBase<DerivedS>& S,
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const Eigen::PlainObjectBase<DerivedS>& E,
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const Eigen::PlainObjectBase<DerivedSC>& b,
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const Eigen::PlainObjectBase<Derivedw>& wShape,
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const Eigen::PlainObjectBase<Derivedw>& wSmooth,
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ShapeupData & sudata);
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//This function solve the shapeup project optimization. shapeup_precompute must be called before with the same sudata, or results are unpredictable
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//Input:
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//bc #b by 3 fixed point values corresonding to "b" in sudata
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//local_projection function pointer taking (P,SC,S,projP),
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// where the first three parameters are as defined, and "projP" is the output, as a #S by 3*max(SC) function in format xyzxyzxyz, and where it returns the projected points corresponding to each set in S in the same order.
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//NOTE: the input values in P0 don't need to correspond to prescribed values in bc; the iterations will project them automatically (by design).
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//P0 #P by 3 initial solution (point positions)
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//sudata the ShapeUpData structure computed in shapeup_precomputation()
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//quietIterations flagging if to output iteration information.
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//Output:
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//P the solution to the problem, indices corresponding to P0.
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template <
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typename DerivedP,
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typename DerivedSC,
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typename DerivedS>
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IGL_INLINE bool shapeup_solve(const Eigen::PlainObjectBase<DerivedP>& bc,
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const std::function<bool(const Eigen::PlainObjectBase<DerivedP>&, const Eigen::PlainObjectBase<DerivedSC>&, const Eigen::PlainObjectBase<DerivedS>&, Eigen::PlainObjectBase<DerivedP>&)>& local_projection,
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const Eigen::PlainObjectBase<DerivedP>& P0,
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const ShapeupData & sudata,
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const bool quietIterations,
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Eigen::PlainObjectBase<DerivedP>& P);
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}
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#ifndef IGL_STATIC_LIBRARY
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#include "shapeup.cpp"
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#endif
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#endif
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