Is a point inside regular hexagon

Question

I\'m looking for advice on the best way to proceed. I\'m trying to find whether a given point A:(a, b) is inside a regular hexagon, defined with center O:(x, y) and diameter

Answer 1

What you want is the code to find out whether a point is inside a convex polygon, an hexagon being a particular case of that.

Here's a good answer: https://stackoverflow.com/a/34689268/516188

I did modify that function for my use, I find my version clearer. It's typescript (you just squint and it's javascript):

function vectorX(v: Vector): number {
    return v[1].x - v[0].x;
}

function vectorY(v: Vector): number {
    return v[1].y - v[0].y;
}

function crossProduct(v1: Vector, v2: Vector): number {
    return vectorX(v1)*vectorY(v2) - vectorY(v1)*vectorX(v2);
}

function isInConvexPolygon(testPoint: Point, polygon: Polygon): boolean {
    // https://stackoverflow.com/a/34689268/516188
    if (polygon.length < 3) {
        throw "Only supporting polygons of length at least 3";
    }
    // going through all the edges around the polygon. compute the
    // vector cross-product http://allenchou.net/2013/07/cross-product-of-2d-vectors/
    // to find out for each edge on which side of the edge is the point.
    // if the point is on the same side for all the edges, it's inside
    let initCrossIsPositive = undefined;
    for (var i=0;i[curPointOnEdge, nextPointOnEdge];
        const vector2 = <[Point,Point]>[curPointOnEdge, testPoint];
        const cross = crossProduct(vector1, vector2);
        if (initCrossIsPositive === undefined) {
            initCrossIsPositive = cross > 0;
        } else {
            if (initCrossIsPositive !== (cross > 0)) {
                return false;
            }
        }
    }
    // all the cross-products have the same sign: we're inside
    return true;
}