Function computeTriangleTransform

src/aliceVision/mesh/Texturing.cpp:232–261

* @brief Compute a transformation matrix to convert coordinates in world space coordinates into the triangle space. * The triangle space is define by the Z-axis as the normal of the triangle, * the X-axis aligned with the horizontal line in the texture file (using texture/UV coordinates). * * @param[in] mesh: input mesh * @param[in] f: facet/triangle index * @param[in] triPts: UV Coordinates

 * @return Rotation matrix to convert from world space coordinates in the triangle space
 */
inline Eigen::Matrix3d computeTriangleTransform(const Mesh& mesh, int f, const Point2d* triPts)
{
    const Eigen::Vector3d p0 = toEigen((mesh.pts)[(mesh.tris)[f].v[0]]);
    const Eigen::Vector3d p1 = toEigen((mesh.pts)[(mesh.tris)[f].v[1]]);
    const Eigen::Vector3d p2 = toEigen((mesh.pts)[(mesh.tris)[f].v[2]]);

    const Eigen::Vector3d tX = (p1 - p0).normalized();                        // edge0 => local triangle X-axis
    const Eigen::Vector3d N = tX.cross((p2 - p0).normalized()).normalized();  // cross(edge0, edge1) => Z-axis

    // Correct triangle X-axis to be align with X-axis in the texture
    const GEO::vec2 t0 = GEO::vec2(triPts[0].m);
    const GEO::vec2 t1 = GEO::vec2(triPts[1].m);
    const GEO::vec2 tV = GEO::normalize(t1 - t0);
    const GEO::vec2 origNormal(1.0, 0.0);  // X-axis in the texture
    const double tAngle = GEO::Geom::angle(tV, origNormal);
    Eigen::Matrix3d transform(Eigen::AngleAxisd(tAngle, N).toRotationMatrix());
    // Rotate triangle v0v1 axis around Z-axis, to get a X axis aligned with the 2d texture
    Eigen::Vector3d X = (transform * tX).normalized();

    const Eigen::Vector3d Y = N.cross(X).normalized();  // Y-axis

    Eigen::Matrix3d m;
    m.col(0) = X;
    m.col(1) = Y;
    m.col(2) = N;
    // const Eigen::Matrix3d mInv = m.inverse();
    const Eigen::Matrix3d mT = m.transpose();

    return mT;
}

inline void computeNormalHeight(const GEO::Mesh& mesh,
                                double orientation,