My name is Nick Taylor - and I am an the ultimate newbie when it comes to JScad, although I did start programming in 1979, have the degree, and a couple of decades of commercial experience... which is a fancy way of saying I am a recovering web-dev.

I now do manufacturing and design etc... and am building an electric guitar which is based on a flattened egg shape.

So.... this is what i have so far, which generates the egg.... it is basically a parabola sitting upside down on top of a circle, joined then rotated into a 3D shape.

I am experiencing all sorts of weirdness to do with unexpected boolean behaviour (eg: intersect does what a union should do), and I look at this code and despair.... there has GOT to be a more concise way of doing this.

If anyone has any help or advice, I would be most eternally, tearfully grateful.

If there is a better way of presenting this code (eg: giving it a main function), let me know.

//
// egg_shape
// ---------------------------------------------------------------------------------

function egg_shape(resolution, radius, parabola_top) {

    const a = findTangentA(radius, parabola_top, resolution);
    const tangentPoints = findTangentPoints(a, parabola_top, radius, resolution);

    const circlePoints = [];
    const rSquared = radius * radius;
    const xMax = Math.sqrt(rSquared);
    const step = 0.5;
    
    // Top half of circle
    for (let x = -xMax; x <= xMax; x += step) {
        const y = Math.sqrt(rSquared - x * x);
        circlePoints.push([x, y]);
    }
    
    // Bottom half of circle (reverse direction)
    for (let x = xMax; x >= -xMax; x -= step) {
        const y = -Math.sqrt(rSquared - x * x);
        circlePoints.push([x, y]);
    }
    
    const circleGeom = polygon({ points: circlePoints });

    const { xLeft, xRight } = tangentPoints;
    const parabolaPoints = [];
 
    
    for (let x = xLeft; x <= xRight; x += step) {
        const y = -a * x * x + parabola_top;
        parabolaPoints.push([x, y]);
    }
    
    const parabolaGeom = polygon({ points: parabolaPoints });

    // intersect does what a union should do
    const eggProfile = intersect(circleGeom, parabolaGeom);

    // Create 3D egg by rotating the 2D profile
    return extrudeRotate({
        segments: resolution,
        angle: Math.PI * 2
    }, eggProfile);
}



//
// findTangentA
// ---------------------------------------------------------------------------------

function findTangentA(radius, h, resolution) {
    const R2 = radius * radius
    const stepA = 0.00001 
    const tolerance = 0.1
    const searchStep = 0.5 
    
    for (let a = 0.005; a < 0.02; a += stepA) {
        let count = 0
        for (let x = -radius; x <= radius; x += searchStep) {
            const y = -a * x * x + h
            const dist = x * x + y * y
            if (Math.abs(dist - R2) < tolerance) count++
        }
        if (count === 2) return a  
    }
    
    return 0.0095  // Fallback value
}



//
// findTangentPoints
// ---------------------------------------------------------------------------------

function findTangentPoints(a, h, radius, resolution) {
    const R2 = radius * radius
    const points = []
    const dx = 0.01 
    const tolerance = 0.001  
    
    for (let x = -radius; x <= radius; x += dx) {
        const y = -a * x * x + h
        const d = x * x + y * y
        if (Math.abs(d - R2) < tolerance) points.push(x)
    }
    
    if (points.length >= 2) {
        return { xLeft: Math.min(...points), xRight: Math.max(...points) }
    }
    return { xLeft: -radius * 0.8, xRight: radius * 0.8 }
}