def b_poly_filleted(p_list, r_list=None, open_poly=False):
    """
    draws a 'filleted' polygon with variable radius
    dependent on roundedCorner()
    """
    if not r_list:
        r_list = [0] * len(p_list)
    assert len(p_list) == len(r_list), \
        "Number of points and radii not the same"
    strokeJoin(ROUND)
    beginShape()
    for p0, p1, p2, r in zip(p_list,
                             [p_list[-1]] + p_list[:-1],
                             [p_list[-2]] + [p_list[-1]] + p_list[:-2],
                             [r_list[-1]] + r_list[:-1]
                             ):
        m1 = (p0[0] + p1[0]) / 2, (p0[1] + p1[1]) / 2
        m2 = (p2[0] + p1[0]) / 2, (p2[1] + p1[1]) / 2
        b_roundedCorner(p1, m1, m2, r)
    endShape(CLOSE)

def b_roundedCorner(pc, p2, p1, r):
    """
    Based on Stackoverflow C# rounded corner post 
    https://stackoverflow.com/questions/24771828/algorithm-for-creating-rounded-corners-in-a-polygon
    """
    def GetProportionPoint(pt, segment, L, dx, dy):
        factor = float(segment) / L if L != 0 else segment
        return PVector((pt[0] - dx * factor), (pt[1] - dy * factor))

    # Vector 1
    dx1 = pc[0] - p1[0]
    dy1 = pc[1] - p1[1]
    # Vector 2
    dx2 = pc[0] - p2[0]
    dy2 = pc[1] - p2[1]
    # Angle between vector 1 and vector 2 divided by 2
    angle = (atan2(dy1, dx1) - atan2(dy2, dx2)) / 2
    # The length of segment between angular point and the
    # points of intersection with the circle of a given radius
    tng = abs(tan(angle))
    segment = r / tng if tng != 0 else r
    # Check the segment
    length1 = sqrt(dx1 * dx1 + dy1 * dy1)
    length2 = sqrt(dx2 * dx2 + dy2 * dy2)
    min_len = min(length1, length2)
    if segment > min_len:
        segment = min_len
        max_r = min_len * abs(tan(angle))
    else:
        max_r = r
    # Points of intersection are calculated by the proportion between
    # length of vector and the length of the segment.
    p1Cross = GetProportionPoint(pc, segment, length1, dx1, dy1)
    p2Cross = GetProportionPoint(pc, segment, length2, dx2, dy2)
    # Calculation of the coordinates of the circle
    # center by the addition of angular vectors.
    dx = pc[0] * 2 - p1Cross[0] - p2Cross[0]
    dy = pc[1] * 2 - p1Cross[1] - p2Cross[1]
    L = sqrt(dx * dx + dy * dy)
    d = sqrt(segment * segment + max_r * max_r)
    circlePoint = GetProportionPoint(pc, d, L, dx, dy)
    # StartAngle and EndAngle of arc
    startAngle = atan2(p1Cross[1] - circlePoint[1],
                       p1Cross[0] - circlePoint[0])
    endAngle = atan2(p2Cross[1] - circlePoint[1],
                     p2Cross[0] - circlePoint[0])
    # Sweep angle
    sweepAngle = endAngle - startAngle
    # Some additional checks
    A, B = False, False
    if sweepAngle < 0:
        A = True
        startAngle, endAngle = endAngle, startAngle
        sweepAngle = -sweepAngle
        # ellipse(pc[0], pc[1], 15, 15) # debug
    if sweepAngle > PI:
        B = True
        startAngle, endAngle = endAngle, startAngle
        sweepAngle = TWO_PI - sweepAngle
        # ellipse(pc[0], pc[1], 25, 25) # debug
    if (A and not B) or (B and not A):
        startAngle, endAngle = endAngle, startAngle
        sweepAngle = -sweepAngle
        # ellipse(pc[0], pc[1], 5, 5) # debug
    b_arc(circlePoint[0], circlePoint[1], 2 * max_r, 2 * max_r,
          startAngle, startAngle + sweepAngle, arc_type=2)


def b_arc(cx, cy, w, h, startAngle, endAngle, arc_type=0):
    """
    A bezier approximation of an arc
    using the same signature as the original Processing arc()
    arc_type: 0 "normal" arc, using beginShape() and endShape()
              1 "middle" used in recursive call of smaller arcs
              2 "naked" like normal, but without beginShape() and endShape()
                 for use inside a larger PShape
    """
    theta = endAngle - startAngle
    # Compute raw Bezier coordinates.
    if arc_type != 1 or theta < HALF_PI:
        x0 = cos(theta / 2.0)
        y0 = sin(theta / 2.0)
        x3 = x0
        y3 = 0 - y0
        x1 = (4.0 - x0) / 3.0
        if y0 != 0:
            y1 = ((1.0 - x0) * (3.0 - x0)) / (3.0 * y0)  # y0 != 0...
        else:
            y1 = 0
        x2 = x1
        y2 = 0 - y1
        # Compute rotationally-offset Bezier coordinates, using:
        # x' = cos(angle) * x - sin(angle) * y
        # y' = sin(angle) * x + cos(angle) * y
        bezAng = startAngle + theta / 2.0
        cBezAng = cos(bezAng)
        sBezAng = sin(bezAng)
        rx0 = cBezAng * x0 - sBezAng * y0
        ry0 = sBezAng * x0 + cBezAng * y0
        rx1 = cBezAng * x1 - sBezAng * y1
        ry1 = sBezAng * x1 + cBezAng * y1
        rx2 = cBezAng * x2 - sBezAng * y2
        ry2 = sBezAng * x2 + cBezAng * y2
        rx3 = cBezAng * x3 - sBezAng * y3
        ry3 = sBezAng * x3 + cBezAng * y3
        # Compute scaled and translated Bezier coordinates.
        rx, ry = w / 2.0, h / 2.0
        px0 = cx + rx * rx0
        py0 = cy + ry * ry0
        px1 = cx + rx * rx1
        py1 = cy + ry * ry1
        px2 = cx + rx * rx2
        py2 = cy + ry * ry2
        px3 = cx + rx * rx3
        py3 = cy + ry * ry3
        # Debug points... comment this out!
        # stroke(0)
        # ellipse(px3, py3, 15, 15)
        # ellipse(px0, py0, 5, 5)
    # Drawing
    if arc_type == 0: # 'normal' arc (not 'middle' nor 'naked')
        beginShape()
    if arc_type != 1: # if not 'middle'
        vertex(px3, py3)
    if theta < HALF_PI:
        bezierVertex(px2, py2, px1, py1, px0, py0)
    else:
        # to avoid distortion, break into 2 smaller arcs
        b_arc(cx, cy, w, h, startAngle, endAngle - theta / 2.0, arc_type=1)
        b_arc(cx, cy, w, h, startAngle + theta / 2.0, endAngle, arc_type=1)
    if arc_type == 0: # end of a 'normal' arc
        endShape()