Efficiently find points inside a circle sector

Question

I have a set of 2d points distributed randomly. I need to perform a time intensive operation on a small subset of these points but I need to first figure out what points I n

Answer 1

@Oren Trutner answer was great so I decided to make a visual example of it and make some improvements to make it work on all angles.

no further speaking, check the example below.

$(document).on('keypress',function (e) {
        if(e.which === 13)
        {
            $("#calc").click();
        }
    });

    function areClockwise(v1, v2) {
        return -v1.x*v2.y + v1.y*v2.x > 0;
    }

    function vector(x = 0, y = 0) {
        return {x:x,y:y}
    }

    function degToRad(degree) {
        return degree * Math.PI / 180;
    }

    function isIn()
    {
        let illustration = $("#illustration");
        illustration.html("");
        let r = 250;
        let fieldOfViewAngle = 150;
        let x = Number($("#x").val());
        let y = Number($("#y").val());
        let startAngle = Number($("#startAngle").val());
        let startSectorAngle = degToRad(startAngle);
        let endSectorAngle = degToRad(startAngle+fieldOfViewAngle);

        $("#startLine").attr("x2",250 + r*Math.cos(-startSectorAngle)).attr("y2",250 + r*Math.sin(-startSectorAngle));
        $("#endLine").attr("x2",250 + r*Math.cos(-endSectorAngle)).attr("y2",250 + r*Math.sin(-endSectorAngle));
        $("#point").attr("cx",250 +x).attr("cy",250 -y);

        let sectorStartVector = vector(r * Math.cos(startSectorAngle),r * Math.sin(startSectorAngle));
        let sectorEndVector = vector(r * Math.cos(endSectorAngle),r * Math.sin(endSectorAngle));
        let relPoint = vector(x,y);

        if(!this.areClockwise(sectorStartVector, relPoint) &&
            this.areClockwise(sectorEndVector, relPoint))
            $("#result").html("Result: in");
        else{
            $("#result").html("Result: out")
        }
    }

.flixy {
            display: flex;
            flex-direction: column;
        }

        .flixy > div {
            margin-bottom: 20px;
            width:300px
        }

        .flixy > div > input {
            float: right;
        }

    

        X
        
    
    

        Y
        
    

    

        Start angle
        
    

    

        Radius
        
    

    

        Theta
        
    


calc