QCAD Bugtracker

This is a complex problem. QCAD uses the Apollonius algorithm and an alternative algorithm to come up with as many solutions as possible. However, it is a best effort type algorithm. There are very likely other scenarios where not all solution can be found (hence "no solution found").

There is but one solution inside the area of interest and its mirror.
Both their centers are on the Centerline.
There are indeed four more outside area of interest.

I am coding the locus of equidistant points between:
- 2 Points ⇒ RXline (Too easy )
- Point vs Line segment ⇒ Up to 4 shapes (2 Quadratic RSpline's, 2RRay's)
- Point vs Arc segment ... Circle ⇒ ... Includes Hyperbola and former
- 2 Line segments ⇒ Up to 6 shapes (2 RLine's, 2 Quadratic RSpline's, 2RRay's)
- 2 Arc segments ... Circles ⇒ ... Includes Hyperbola and former

Work in process, the hyperbola is fairly good approximated by a cubic RSpline.
Fairly good but I store the coefficients of the implicit conic equation.
Regards,
CVH

Reviewing Apollonius.getSolutionsCCC
I read: special case: at least two circles are concentric: no solution:

When two circles are concentric there are an infinite amount of circles with radius rx=abs(r1-r2)/2 tangent to both.
The locus of the center points is itself a circle with r1+(r1-r2)/2.
All intersections of the locus and circles with radius r3-rx or r3+rx are solutions for centers of tangent circles with radius rx.

Simply a question to enhance Apollonius.getSolutionsCCC

If all three are concentric with different radii then there is no solution.
If 2 of them have the same radii then there are infinite solutions.

Regards,
CVH

Andrew,

I replaced in Apollonius.getSolutionsCCC:

    // special case: at least two circles are concentric: no solution:
    if (c1.center.equalsFuzzy(c2.center) ||
        c1.center.equalsFuzzy(c3.center) ||
        c2.center.equalsFuzzy(c3.center)) {

        return [];
    }

With the code below with good and stable results.

    // special case: at least two circles are concentric: no solution:
    // # Enhanced by CVH #
    // Verify if circle 1 is concentric with circle 2:
    if (c1.center.equalsFuzzy(c2.center)) {
        if (c1.center.equalsFuzzy(c3.center)) {
            // Failed: 3 concentric circles
            return [];    // No or infinite solutions
        }
        var rDiff = c1.getRadius() - c2.getRadius();
        var locus = c1.clone();
        circle1 = c3.clone();
    }
    // Verify if circle 1 is concentric with circle 3:
    else if (c1.center.equalsFuzzy(c3.center)) {
        if (c1.center.equalsFuzzy(c2.center)) {
            // Failed: 3 concentric circles
            return [];    // No or infinite solutions
        }
        var rDiff = c1.getRadius() - c3.getRadius();
        var locus = c1.clone();
        circle1 = c2.clone();
    }
    // Verify if circle 2 is concentric with circle 3:
    else if (c2.center.equalsFuzzy(c3.center)) {
        if (c2.center.equalsFuzzy(c1.center)) {
            // Failed: 3 concentric circles
            return [];    // No or infinite solutions
        }
        var rDiff = c2.getRadius() - c3.getRadius();
        var locus = c2.clone();
        circle1 = c1.clone();
    }

    // Handle two concentric circles:
    if (!isNull(locus)) {
        if (!isNumber(rDiff)) {
            return [];    // No solutions
        }
        if (RMath.fuzzyCompare(rDiff, 0.0)) {
            return [];    // Infinite solutions
        }

        // Get intersections of two concentric with the other circle and the locus:
        locus.setRadius(locus.getRadius() - rDiff / 2);
        circle1.setRadius(circle1.getRadius() - Math.abs(rDiff / 2));
        circle2 = circle1.clone();
        circle2.setRadius(circle1.getRadius() + Math.abs(rDiff));
        var ips = locus.getIntersectionPoints(circle1);
        ips = ips.concat(locus.getIntersectionPoints(circle2));

        // If any, create tangent circles at intersections;
        if (ips.length === 0) {
            return [];    // No solutions
        }
        for (var i=0; i<ips.length; i++) {
            ret.push(new RCircle(ips[i], Math.abs(rDiff / 2)));
        }

        ret = Apollonius.removeDuplicates(ret);    // Most likely none
        return ret;
    }

Newer art see PM Sat Nov 04, 2023 9:41 am
Avoid negative radii for intersections of locus/circle:

      // Get intersections of two concentric with the other circle and the locus:
      locus.setRadius(locus.getRadius() - rDiff / 2);
      circle1.setRadius(circle1.getRadius() + Math.abs(rDiff / 2));
      var ips = locus.getIntersectionPoints(circle1);
      circle1.setRadius(circle1.getRadius() - Math.abs(rDiff));
      // Avoid inversion through the center with negative radii:
      if (circle1.getRadius() > 0) {
          ips = ips.concat(locus.getIntersectionPoints(circle1));
      }

Regards,
CVH