barycenter.h

/*****************************************************************************
 * VCLib                                                                     *
 * Visual Computing Library                                                  *
 *                                                                           *
 * Copyright(C) 2021-2025                                                    *
 * Visual Computing Lab                                                      *
 * ISTI - Italian National Research Council                                  *
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 * it under the terms of the Mozilla Public License Version 2.0 as published *
 * by the Mozilla Foundation; either version 2 of the License, or            *
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 * This program is distributed in the hope that it will be useful,           *
 * but WITHOUT ANY WARRANTY; without even the implied warranty of            *
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the              *
 * Mozilla Public License Version 2.0                                        *
 * (https://www.mozilla.org/en-US/MPL/2.0/) for more details.                *
 ****************************************************************************/
 
#ifndef VCL_ALGORITHMS_MESH_STAT_BARYCENTER_H
#define VCL_ALGORITHMS_MESH_STAT_BARYCENTER_H
 
#include <vclib/mesh.h>
 
namespace vcl {
 
template<MeshConcept MeshType>
auto barycenter(const MeshType& m) -> MeshType::VertexType::PositionType
{
    using VertexType   = MeshType::VertexType;
    using PositionType = VertexType::PositionType;
 
    PositionType bar;
 
    for (const VertexType& v : m.vertices()) {
        bar += v.position();
    }
 
    return bar / m.vertexNumber();
}
 
template<MeshConcept MeshType>
auto weightedBarycenter(const MeshType& m, Range auto&& weights)
    -> MeshType::VertexType::PositionType
{
    using VertexType   = MeshType::VertexType;
    using PositionType = VertexType::PositionType;
    using RType        = std::ranges::range_value_t<decltype(weights)>;
 
    assert(std::ranges::size(weights) == m.vertexNumber());
 
    PositionType bar;
    RType        weightedSum = 0;
 
    for (const auto& [v, w] : std::views::zip(m.vertices(), weights)) {
        bar += v.position() * w;
        weightedSum += w;
    }
 
    return bar / weightedSum;
}
 
template<MeshConcept MeshType>
auto qualityWeightedBarycenter(const MeshType& m)
    -> MeshType::VertexType::PositionType
{
    requirePerVertexQuality(m);
 
    return weightedBarycenter(m, m.vertices() | views::quality);
}
 
template<FaceMeshConcept MeshType>
auto shellBarycenter(const MeshType& m) -> MeshType::VertexType::PositionType
{
    using VertexType   = MeshType::VertexType;
    using FaceType     = MeshType::FaceType;
    using PositionType = VertexType::PositionType;
    using ScalarType   = PositionType::ScalarType;
 
    PositionType bar;
    bar.setZero();
    ScalarType areaSum = 0;
 
    for (const FaceType& f : m.faces()) {
        ScalarType area = faceArea(f);
        bar += faceBarycenter(f) * area;
        areaSum += area;
    }
 
    return bar / areaSum;
}
 
} // namespace vcl
 
#endif // VCL_ALGORITHMS_MESH_STAT_BARYCENTER_H