Import PrusaSlicer G2/G3 arc discretization code

src/libslic3r/Geometry/ArcWelder.cpp

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+// The following code for merging circles into arches originates from https://github.com/FormerLurker/ArcWelderLib
+
+////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+// Arc Welder: Anti-Stutter Library
+//
+// Compresses many G0/G1 commands into G2/G3(arc) commands where possible, ensuring the tool paths stay within the specified resolution.
+// This reduces file size and the number of gcodes per second.
+//
+// Uses the 'Gcode Processor Library' for gcode parsing, position processing, logging, and other various functionality.
+//
+// Copyright(C) 2021 - Brad Hochgesang
+////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+// This program is free software : you can redistribute it and/or modify
+// it under the terms of the GNU Affero General Public License as published
+// by the Free Software Foundation, either version 3 of the License, or
+// (at your option) any later version.
+//
+// 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
+// GNU Affero General Public License for more details.
+//
+//
+// You can contact the author at the following email address: 
+// FormerLurker@pm.me
+////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+
+#include "ArcWelder.hpp"
+
+namespace Slic3r { namespace Geometry { namespace ArcWelder {
+
+} } } // namespace Slic3r::Geometry::ArcWelder

src/libslic3r/Geometry/ArcWelder.hpp

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+#ifndef slic3r_Geometry_ArcWelder_hpp_
+#define slic3r_Geometry_ArcWelder_hpp_
+
+#include <assert.h>
+#include <stddef.h>
+#include <stdint.h>
+#include <Eigen/Geometry>
+#include <type_traits>
+#include <cassert>
+
+#include "libslic3r/libslic3r.h"
+
+namespace Slic3r { namespace Geometry { namespace ArcWelder {
+
+// Calculate center point (center of a circle) of an arc given two points and a radius.
+// positive radius: take shorter arc
+// negative radius: take longer arc
+// radius must NOT be zero!
+template<typename Derived, typename Derived2, typename Float>
+inline 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)
+{
+    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();
+}
+
+
+// Return number of linear segments necessary to interpolate arc of a given positive radius and positive angle to satisfy
+// maximum deviation of an interpolating polyline from an analytic arc.
+template<typename FloatType>
+size_t 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))));
+}
+
+} } } // namespace Slic3r::Geometry::ArcWelder
+
+#endif // slic3r_Geometry_ArcWelder_hpp_