Closest Point on Segment from a center point of a circle

segment.vala

    public Gsl.Vector? closest_point_on_segment (
        Gsl.Vector segment_1, Gsl.Vector segment_2, Gsl.Vector circle_position
    ) {
        var segment = new Gsl.Vector(2);
        segment.set(0, segment_1.get (0) - segment_2.get (0));
        segment.set(1, segment_1.get (1) - segment_2.get (1));
        
        var point = new Gsl.Vector(2);
        point.set(0, circle_position.get (0) - segment_2.get (0));
        point.set(1, circle_position.get (1) - segment_2.get (1));
        
        // Length
        var segment_length = Math.sqrt (
            (segment.get (0) * segment.get (0))
            + 
            (segment.get (1) * segment.get (1))
        );
        
        if (segment_length <= 0) {
            /* Invalid segment length */
            return null;
        }
        
        // Divide against scalar
        var segment_unit = new Gsl.Vector(2);
        segment_unit.set (0, segment.get (0) / segment_length);
        segment_unit.set (1, segment.get (1) / segment_length);
        
        // Dot Product
        double projection = 
            (point.get (0) * segment_unit.get (0)) 
            + 
            (point.get (0) * segment_unit.get (1))
        ;
        
        var result = new Gsl.Vector(2);
        if (projection <= 0) {
            result.set(0, segment_1[0]);
            result.set(1, segment_1[1]);
            return result;
        }
        
        if (projection >= segment_length) {
            result.set(0, segment_2[0]);
            result.set(1, segment_2[1]);
            return result;
        }
        
        // Multiple against scalar
        var projection_vector = new Gsl.Vector(2);
        projection_vector.set (0, segment_unit.get (0) * projection);
        projection_vector.set (1, segment_unit.get (1) * projection);
        
        // Closest
        result.set (0, projection_vector.get (0) + segment_1.get (0));
        result.set (1, projection_vector.get (1) + segment_1.get (1));
        return result;
    }