[Bug]This polyline cannot be offset outside

[FishOrBear]

https://user-images.githubusercontent.com/19372111/122493643-a4f24500-d01a-11eb-97f8-f2e26873c0cd.mp4

This polyline cannot be offset outside

{"vertexes":[[0,0,2.9239855509708432],[422.7001801508977,-2181.678349165927,0.21373279590439873],[1217.850643134374,-1733.2038795014323,4.472986753391631],[961.0754444813574,-155.87051634718955,0.22947158823257166]],"isClosed":true}

[jbuckmccready]

The json text representation has vertexes with bulge > 1, bulge must always be between -1 and 1 (inputs are not sanitized by the library currently).

[jbuckmccready]

I need a working polyline (with bulge values between -1 and 1) to be able to reproduce and fix the issue.

[FishOrBear]

I interrupted it, do you think this is okay?

{"vertexes":[[0,0,0.39225530213565374],[-2466.3785800210244,-67.26296602434104,0.484923954116067],[-2161.7248988609135,-2900.376762550583,0.44171257084882926],[422.7001801508977,-2181.678349165927,0.21373279590439873],[1217.850643134374,-1733.2038795014323,0.47915321276268247],[4134.244054592013,-1954.8763015675465,0.5643966953535755],[3262.8872828398416,1137.416074109292,0.41127495953982673],[961.0754444813574,-155.87051634718955,0.22947158823257166]],"isClosed":true}

[jbuckmccready]

That json works and looks like the one in the video. I am able to offset outward OK with the latest commit on master (I may have fixed it in the process of fixing the overlap bug), are you using the latest commit?

[FishOrBear]

The offset can be normal after interruption The one before the interruption cannot be offset.

I use Google Translate, it may not be very precise

[jbuckmccready]

The library only supports bulge values between -1 and 1. Functions could be added to convert other things (although I'm not sure based on the definition of a vertex bulge what a value greater than 1 means), how are you interpreting bulge values greater than 1?

[FishOrBear]

So when bul=1, the arc is a semicircle, and when bul is greater than 1, the arc is larger than the semicircle.

bul= <Tangent value of (quarter central angle)>

    /**
     * 解析两点和凸度所构成的圆弧
     *
     * @param {Vector2} p1
     * @param {Vector2} p2
     * @param {number} bul 凸度,在cad中,凸度为 <(四分之一圆心角)的正切值> 
     */
    ParseFromBul(p1: Vector3 | Vector2, p2: Vector3 | Vector2, bul: number): Arc
    {
        if (p1 instanceof Vector2)
            p1 = AsVector3(p1);
        if (p2 instanceof Vector2)
            p2 = AsVector3(p2);

        let ocsInv = this.OCSInv;
        p1 = p1.clone().applyMatrix4(ocsInv);
        p2 = p2.clone().applyMatrix4(ocsInv);

        //弦向量
        let chordV = p2.clone().sub(p1);
        //弦角度
        let chordAn = angle(chordV);
        //弦长度/2
        let chordLengthHalf = chordV.length() / 2;

        let allAngle = Math.atan(bul) * 4;
        let HalfAngle = allAngle * 0.5;
        //半径
        this._Radius = chordLengthHalf / Math.sin(HalfAngle);

        //指向圆心的角度
        let toCenterAn = chordAn + Math.PI * 0.5;//弦角度转90

        //圆心
        let center = midPoint(p1, p2);
        polar(center, toCenterAn, this._Radius - (bul * chordLengthHalf));
        this.Center = center.clone().applyMatrix4(this.OCS);

        this._Radius = Math.abs(this._Radius);

        this._StartAngle = angle(p1.clone().sub(center));
        this._EndAngle = angle(p2.clone().sub(center));

        this._Clockwise = bul < 0;

        return this;
    }

[FishOrBear]

http://www.lee-mac.com/bulgeconversion.html

This explanation should be more detailed

[FishOrBear]

Simplified code according to leemac

        //a (* 2 (atan b))
        let a = Math.atan(bul) * 2;
        //r (/ (distance p1 p2) 2 (sin a))
        let r = p1.distanceTo(p2) / 2 / Math.sin(a);
        //c (polar p1 (+ (- (/ pi 2) a) (angle p1 p2)) r)
        let c = polar(p1.clone(), Math.PI / 2 - a + angle(p2.clone().sub(p1)), r);

        this._Radius = Math.abs(r);

        this._StartAngle = angle(p1.sub(c));
        this._EndAngle = angle(p2.sub(c));

        this._Clockwise = bul < 0;

export function polar<T extends Vector2 | Vector3>(v: T, an: number, dis: number): T
{
    v.x += Math.cos(an) * dis;
    v.y += Math.sin(an) * dis;
    return v;
}

export function angle(v: Vector3 | Vector2): number
{
    let angle = Math.atan2(v.y, v.x);
    return angle;
}

[jbuckmccready]

Hmm, I knew about the bulge definition (the library is working with bulges!) but I assumed it was restricted to -1 to 1 to ensure that the line between the points always formed the longest chord of the circular segment.

Right now the code all assumes -1 to 1 bulge values, and that helps simplify certain geometry operations since the longest chord is always the line between the points.

I made an issue to track this specific change: https://github.com/jbuckmccready/cavalier_contours/issues/15

[jbuckmccready]

Closing this issue, issue https://github.com/jbuckmccready/cavalier_contours/issues/15 can be used to track this change.