Slic3r::Geometry::ArcWelder Namespace Reference

Functions
template<typename Derived, typename Derived2, typename Float>
Eigen::Matrix< Float, 2, 1, Eigen::DontAlign >	arc_center (const Eigen::MatrixBase< Derived > &start_pos, const Eigen::MatrixBase< Derived2 > &end_pos, const Float radius, const bool is_ccw)
template<typename FloatType>
size_t	arc_discretization_steps (const FloatType radius, const FloatType angle, const FloatType deviation)

Function Documentation

arc_center()

template<typename Derived, typename Derived2, typename Float>

Eigen::Matrix< Float, 2, 1, Eigen::DontAlign > Slic3r::Geometry::ArcWelder::arc_center ( const Eigen::MatrixBase< Derived > & start_pos, const Eigen::MatrixBase< Derived2 > & end_pos, const Float radius, const bool is_ccw )

inline

{
    static_assert(Derived::IsVectorAtCompileTime && int(Derived::SizeAtCompileTime) == 2, "arc_center(): first parameter is not a 2D vector");
    static_assert(Derived2::IsVectorAtCompileTime && int(Derived2::SizeAtCompileTime) == 2, "arc_center(): second parameter is not a 2D vector");
    static_assert(std::is_same<typename Derived::Scalar, typename Derived2::Scalar>::value, "arc_center(): Both vectors must be of the same type.");
    static_assert(std::is_same<typename Derived::Scalar, Float>::value, "arc_center(): Radius must be of the same type as the vectors.");
    assert(radius != 0);
    using Vector = Eigen::Matrix<Float, 2, 1, Eigen::DontAlign>;
    auto  v  = end_pos - start_pos;
    Float q2 = v.squaredNorm();
    assert(q2 > 0);
    Float t2 = sqr(radius) / q2 - Float(.25f);
    // If the start_pos and end_pos are nearly antipodal, t2 may become slightly negative.
    // In that case return a centroid of start_point & end_point.
    Float t = t2 > 0 ? sqrt(t2) : Float(0);
    auto mid = Float(0.5) * (start_pos + end_pos);
    Vector vp{ -v.y() * t, v.x() * t };
    return (radius > Float(0)) == is_ccw ? (mid + vp).eval() : (mid - vp).eval();
}

References Slic3r::Geometry::is_ccw(), and Slic3r::sqr().

Referenced by Slic3r::GCodeProcessor::process_G2_G3().

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arc_discretization_steps()

template<typename FloatType>

size_t Slic3r::Geometry::ArcWelder::arc_discretization_steps	(	const FloatType	radius,
		const FloatType	angle,
		const FloatType	deviation )

{
    assert(radius > 0);
    assert(angle > 0);
    assert(angle <= FloatType(2. * M_PI));
    assert(deviation > 0);
 
    FloatType d = radius - deviation;
    return d < EPSILON ?
        // Radius smaller than deviation.
        (   // Acute angle: a single segment interpolates the arc with sufficient accuracy.
            angle < M_PI || 
            // Obtuse angle: Test whether the furthest point (center) of an arc is closer than deviation to the center of a line segment.
            radius * (FloatType(1.) + cos(M_PI - FloatType(.5) * angle)) < deviation ?
            // Single segment is sufficient
            1 :
            // Two segments are necessary, the middle point is at the center of the arc.
            2) :
        size_t(ceil(angle / (2. * acos(d / radius))));
}

References Slic3r::angle(), EPSILON, and M_PI.

Referenced by Slic3r::GCodeWriter::_spiral_travel_to_z(), and Slic3r::GCodeProcessor::process_G2_G3().

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