metaforce/DataSpec/DNACommon/OBBTreeBuilder.cpp

#include <athena/Types.hpp>
#include "OBBTreeBuilder.hpp"
#include "zeus/CTransform.hpp"
#include "DataSpec/DNAMP1/DCLN.hpp"
#include "gmm/gmm.h"
#include "hecl/Blender/Connection.hpp"

namespace DataSpec
{

using ColMesh = hecl::blender::ColMesh;

struct FittedOBB
{
    zeus::CTransform xf;
    zeus::CVector3f he;
};

static std::vector<int> MakeRootTriangleIndex(const ColMesh& mesh)
{
    std::vector<int> ret;
    ret.reserve(mesh.trianges.size());
    for (int i = 0; i < mesh.trianges.size(); ++i)
        ret.push_back(i);
    return ret;
}

static std::unordered_set<uint32_t> GetTriangleVerts(const ColMesh& mesh, int triIdx)
{
    const ColMesh::Triangle& T = mesh.trianges[triIdx];
    std::unordered_set<uint32_t> verts;
    verts.insert(mesh.edges[T.edges[0]].verts[0]);
    verts.insert(mesh.edges[T.edges[0]].verts[1]);
    verts.insert(mesh.edges[T.edges[1]].verts[0]);
    verts.insert(mesh.edges[T.edges[1]].verts[1]);
    verts.insert(mesh.edges[T.edges[2]].verts[0]);
    verts.insert(mesh.edges[T.edges[2]].verts[1]);
    return verts;
}

// method to set the OBB parameters which produce a box oriented according to
// the covariance matrix C, which just containts the points pnts
static FittedOBB BuildFromCovarianceMatrix(gmm::dense_matrix<float>& C,
                                           const ColMesh& mesh, const std::vector<int>& index)
{
    FittedOBB ret;

    // extract the eigenvalues and eigenvectors from C
    gmm::dense_matrix<float> eigvec(3,3);
    std::vector<float> eigval(3);
    gmm::symmetric_qr_algorithm(C, eigval, eigvec);

    // find the right, up and forward vectors from the eigenvectors
    zeus::CVector3f r(eigvec(0,0), eigvec(1,0), eigvec(2,0));
    zeus::CVector3f u(eigvec(0,1), eigvec(1,1), eigvec(2,1));
    zeus::CVector3f f(eigvec(0,2), eigvec(1,2), eigvec(2,2));
    r.normalize(); u.normalize(), f.normalize();

    // set the rotation matrix using the eigvenvectors
    ret.xf.basis[0][0]=r.x; ret.xf.basis[1][0]=u.x; ret.xf.basis[2][0]=f.x;
    ret.xf.basis[0][1]=r.y; ret.xf.basis[1][1]=u.y; ret.xf.basis[2][1]=f.y;
    ret.xf.basis[0][2]=r.z; ret.xf.basis[1][2]=u.z; ret.xf.basis[2][2]=f.z;

    // now build the bounding box extents in the rotated frame
    zeus::CVector3f minim(1e10f, 1e10f, 1e10f), maxim(-1e10f, -1e10f, -1e10f);
    for (int triIdx : index)
    {
        std::unordered_set<uint32_t> verts = GetTriangleVerts(mesh, triIdx);
        for (uint32_t v : verts)
        {
            const zeus::CVector3f& p = mesh.verts[v].val;
            zeus::CVector3f p_prime(r.dot(p), u.dot(p), f.dot(p));
            minim = zeus::min(minim, p_prime);
            maxim = zeus::max(maxim, p_prime);
        }
    }

    // set the center of the OBB to be the average of the
    // minimum and maximum, and the extents be half of the
    // difference between the minimum and maximum
    zeus::CVector3f center = (maxim + minim) * 0.5f;
    ret.xf.origin = ret.xf.basis * center;
    ret.he = (maxim - minim) * 0.5f;

    return ret;
}

// builds an OBB from triangles specified as an array of
// points with integer indices into the point array. Forms
// the covariance matrix for the triangles, then uses the
// method build_from_covariance_matrix() method to fit
// the box.  ALL points will be fit in the box, regardless
// of whether they are indexed by a triangle or not.
static FittedOBB FitOBB(const ColMesh& mesh, const std::vector<int>& index)
{
    float Ai, Am=0.0;
    zeus::CVector3f mu, mui;
    gmm::dense_matrix<float> C(3,3);
    float cxx=0.0, cxy=0.0, cxz=0.0, cyy=0.0, cyz=0.0, czz=0.0;

    // loop over the triangles this time to find the
    // mean location
    for (int i : index)
    {
        std::unordered_set<uint32_t> verts = GetTriangleVerts(mesh, i);
        auto it = verts.begin();
        zeus::CVector3f p = mesh.verts[*it++].val;
        zeus::CVector3f q = mesh.verts[*it++].val;
        zeus::CVector3f r = mesh.verts[*it++].val;
        mui = (p+q+r)/3.f;
        Ai = (q-p).cross(r-p).magnitude() / 2.f;
        mu += mui*Ai;
        Am += Ai;

        // these bits set the c terms to Am*E[xx], Am*E[xy], Am*E[xz]....
        cxx += ( 9.0*mui.x*mui.x + p.x*p.x + q.x*q.x + r.x*r.x )*(Ai/12.0);
        cxy += ( 9.0*mui.x*mui.y + p.x*p.y + q.x*q.y + r.x*r.y )*(Ai/12.0);
        cxz += ( 9.0*mui.x*mui.z + p.x*p.z + q.x*q.z + r.x*r.z )*(Ai/12.0);
        cyy += ( 9.0*mui.y*mui.y + p.y*p.y + q.y*q.y + r.y*r.y )*(Ai/12.0);
        cyz += ( 9.0*mui.y*mui.z + p.y*p.z + q.y*q.z + r.y*r.z )*(Ai/12.0);
    }

    if (zeus::close_enough(Am, 0.f))
        return {};

    // divide out the Am fraction from the average position and
    // covariance terms
    mu = mu / Am;
    cxx /= Am; cxy /= Am; cxz /= Am; cyy /= Am; cyz /= Am; czz /= Am;

    // now subtract off the E[x]*E[x], E[x]*E[y], ... terms
    cxx -= mu.x*mu.x; cxy -= mu.x*mu.y; cxz -= mu.x*mu.z;
    cyy -= mu.y*mu.y; cyz -= mu.y*mu.z; czz -= mu.z*mu.z;

    // now build the covariance matrix
    C(0,0)=cxx; C(0,1)=cxy; C(0,2)=cxz;
    C(1,0)=cxy; C(1,1)=cyy; C(1,2)=cyz;
    C(2,0)=cxz; C(2,1)=cyz; C(2,2)=czz;

    // set the obb parameters from the covariance matrix
    return BuildFromCovarianceMatrix(C, mesh, index);
}

template <typename Node>
static void MakeLeaf(const ColMesh& mesh, const std::vector<int>& index, Node& n)
{
    n.left.reset();
    n.right.reset();
    n.isLeaf = true;
    n.leafData = std::make_unique<typename Node::LeafData>();
    n.leafData->triangleIndexCount = atUint32(index.size());
    n.leafData->triangleIndices.reserve(n.leafData->triangleIndexCount);
    for (int i : index)
        n.leafData->triangleIndices.push_back(i);
}

template <typename Node>
static std::unique_ptr<Node> RecursiveMakeNode(const ColMesh& mesh, const std::vector<int>& index)
{
    // calculate root OBB
    FittedOBB obb = FitOBB(mesh, index);

    // make results row-major and also invert the rotation basis
    obb.xf.basis.transpose();

    std::unique_ptr<Node> n = std::make_unique<Node>();
    for (int i = 0; i < 3; ++i)
    {
        n->xf[i] = zeus::CVector4f{obb.xf.basis[i]};
        n->xf[i].vec[3] = obb.xf.origin[i];
    }
    n->halfExtent = obb.he;

    // terminate branch when volume < 1.0
    if (obb.he[0] * obb.he[1] * obb.he[2] < 1.f)
    {
        MakeLeaf(mesh, index, *n);
        return n;
    }

    n->isLeaf = false;

    std::vector<int> indexNeg[3];
    std::vector<int> indexPos[3];
    for (int c = 0; c < 3; ++c)
    {
        // subdivide negative side
        indexNeg[c].reserve(index.size());
        for (int i : index)
        {
            std::unordered_set<uint32_t> verts = GetTriangleVerts(mesh, i);
            for (uint32_t vtx : verts)
            {
                zeus::CVector3f v = mesh.verts[vtx].val;
                v = obb.xf.basis * (v - obb.xf.origin);
                if (v[c] < 0.f)
                {
                    indexNeg[c].push_back(i);
                    break;
                }
            }
        }

        // subdivide positive side
        indexPos[c].reserve(index.size());
        for (int i : index)
        {
            std::unordered_set<uint32_t> verts = GetTriangleVerts(mesh, i);
            for (uint32_t vtx : verts)
            {
                zeus::CVector3f v = mesh.verts[vtx].val;
                v = obb.xf.basis * (v - obb.xf.origin);
                if (v[c] >= 0.f)
                {
                    indexPos[c].push_back(i);
                    break;
                }
            }
        }
    }

    size_t idxMin = index.size();
    int minComp = -1;
    for (int c = 0; c < 3; ++c)
    {
        size_t test = std::max(indexNeg[c].size(), indexPos[c].size());
        if (test < idxMin && test < index.size() * 3 / 4)
        {
            minComp = c;
            idxMin = test;
        }
    }

    if (minComp == -1)
    {
        MakeLeaf(mesh, index, *n);
        return n;
    }

    n->left = RecursiveMakeNode<Node>(mesh, indexNeg[minComp]);
    n->right = RecursiveMakeNode<Node>(mesh, indexPos[minComp]);

    return n;
}

template <typename Node>
std::unique_ptr<Node> OBBTreeBuilder::buildCol(const ColMesh& mesh)
{
    std::vector<int> root = MakeRootTriangleIndex(mesh);
    return RecursiveMakeNode<Node>(mesh, root);
}

template std::unique_ptr<DNAMP1::DCLN::Collision::Node>
OBBTreeBuilder::buildCol<DNAMP1::DCLN::Collision::Node>(const ColMesh& mesh);

}