src/Mod/CAM/libarea/Arc.cpp

// SPDX-License-Identifier: BSD-3-Clause

// Arc.cpp

// Copyright 2011, Dan Heeks
// This program is released under the BSD license. See the file COPYING for details.

#include "Arc.h"
#include "Curve.h"

void CArc::SetDirWithPoint(const Point& p)
{
    double angs = atan2(m_s.y - m_c.y, m_s.x - m_c.x);
    double ange = atan2(m_e.y - m_c.y, m_e.x - m_c.x);
    double angp = atan2(p.y - m_c.y, p.x - m_c.x);
    if (ange < angs) {
        ange += 6.2831853071795864;
    }
    if (angp < angs - 0.0000000000001) {
        angp += 6.2831853071795864;
    }
    if (angp > ange + 0.0000000000001) {
        m_dir = false;
    }
    else {
        m_dir = true;
    }
}

double CArc::IncludedAngle() const
{
    double angs = atan2(m_s.y - m_c.y, m_s.x - m_c.x);
    double ange = atan2(m_e.y - m_c.y, m_e.x - m_c.x);
    if (m_dir) {
        // make sure ange > angs
        if (ange < angs) {
            ange += 6.2831853071795864;
        }
    }
    else {
        // make sure angs > ange
        if (angs < ange) {
            angs += 6.2831853071795864;
        }
    }

    return fabs(ange - angs);
}

bool CArc::AlmostALine() const
{
    Point mid_point = MidParam(0.5);
    if (Line(m_s, m_e - m_s).Dist(mid_point) <= Point::tolerance) {
        return true;
    }

    const double max_arc_radius = 1.0 / Point::tolerance;
    double radius = m_c.dist(m_s);
    if (radius > max_arc_radius) {
        return true;  // We don't want to produce an arc whose radius is too large.
    }

    return false;
}

Point CArc::MidParam(double param) const
{
    /// returns a point which is 0-1 along arc
    if (fabs(param) < 0.00000000000001) {
        return m_s;
    }
    if (fabs(param - 1.0) < 0.00000000000001) {
        return m_e;
    }

    Point p;
    Point v = m_s - m_c;
    v.Rotate(param * IncludedAngle());
    p = v + m_c;

    return p;
}

// segments - number of segments per full revolution!
// d_angle - determines the direction and the amount of the arc to draw
void CArc::GetSegments(void (*callbackfunc)(const double* p), double pixels_per_mm) const
{
    if (m_s == m_e) {
        return;
    }

    Point Va = m_s - m_c;
    Point Vb = m_e - m_c;

    double start_angle = atan2(Va.y, Va.x);
    double end_angle = atan2(Vb.y, Vb.x);

    if (m_dir) {
        if (start_angle > end_angle) {
            end_angle += 6.28318530717958;
        }
    }
    else {
        if (start_angle < end_angle) {
            end_angle -= 6.28318530717958;
        }
    }

    double radius = m_c.dist(m_s);
    double d_angle = end_angle - start_angle;
    int segments = (int)(fabs(pixels_per_mm * radius * d_angle / 6.28318530717958 + 1));

    double theta = d_angle / (double)segments;
    while (theta > 1.0) {
        segments *= 2;
        theta = d_angle / (double)segments;
    }
    double tangential_factor = tan(theta);
    double radial_factor = 1 - cos(theta);

    double x = radius * cos(start_angle);
    double y = radius * sin(start_angle);

    double pp[3] = {0.0, 0.0, 0.0};

    for (int i = 0; i < segments + 1; i++) {
        Point p = m_c + Point(x, y);
        pp[0] = p.x;
        pp[1] = p.y;
        (*callbackfunc)(pp);

        double tx = -y;
        double ty = x;

        x += tx * tangential_factor;
        y += ty * tangential_factor;

        double rx = -x;
        double ry = -y;

        x += rx * radial_factor;
        y += ry * radial_factor;
    }
}