find convex an concave corners in a polygon

Question

I am trying to detect if a corner is concave or convex in an arbitrary polygon. I made the function below that computes the angle between all edge-pairs. however one never knows if the if it is the inner or the outer corner angle that it returns. I have no idea how to go about this. Any help appreciated!!!!

function findConvexCorner (pt){
var isCornerConvex = [];
for (var i =0; i < pt.length ;i++)
{
    var lastPt = pt.length -1;
    if (i==0){
        var vec1 = vec3.createXYZ( pt[lastPt].x - pt[i].x , pt[lastPt].y - pt[i].y ,0.0);
        var vec2 = vec3.createXYZ( pt[i].x - pt[i+1].x , pt[i].y - pt[i+1].y ,0.0);
        vec3.normalize(vec1);vec3.normalize(vec2);
            isCornerConvex.push(Math.acos(vec3.dot(vec1,vec2))*180/Math.PI);}
    else if(i == lastPt){
        var vec2 = vec3.createXYZ( pt[i-1].x - pt[i].x , pt[i-1].y - pt[i].y ,0.0);
        var vec1 = vec3.createXYZ( pt[0].x - pt[i].x , pt[0].y - pt[i].y ,0.0);
        vec3.normalize(vec1);vec3.normalize(vec2);
            isCornerConvex.push(Math.acos(vec3.dot(vec1,vec2))*180/Math.PI);}
    else{
        var vec1 = vec3.createXYZ( pt[i-1].x - pt[i].x , pt[i-1].y - pt[i].y ,0.0);
        var vec2 = vec3.createXYZ( pt[i+1].x - pt[i].x , pt[i+1].y - pt[i].y ,0.0);
        vec3.normalize(vec1);vec3.normalize(vec2);
            isCornerConvex.push(Math.acos(vec3.dot(vec1,vec2))*180/Math.PI);}
}
console.log("Angle: "+ isCornerConvex);
}

Answer 1

Here's some code to work out concave vs convex corners:

// this assumes nextEdge and previousEdge are vectors pointing out of a vertex and to the next one
var angle = ((Math.atan2(nextEdge.x, nextEdge.y) - Math.atan2(previousEdge.x, previousEdge.y) + Math.PI * 2) % (Math.PI * 2)) - Math.PI;

if (angle > 0) {
   corner.type = 'convex';
} else if (angle < 0) {
    corner.type = 'concave';
} else {
    corner.type = 'straight';
}

Answer 2

An easy way to do this is by assessing vector determinants.

First, we make sure that the polygon is clockwise/anti-clockwise (using shoelace method).

Let's go with clockwise. That means all your interior angles can be considered to be drawn anti-clockwise between respective adjacent sides.

Say for a particular angle ABC between sides AB and BC, we can calculate the determinant between vectors BA and BC (ad - bc formula).

If the determinant is <= 0, you go for the concave angle (ie. 360 - angle between vectors). If det is greater than 0, we take the convex angle. Hope this helps