sketch-a-day/2019/sketch_190313a/arcs.py

# -*- coding: utf-8 -*-

ROTATION = {0: 0,
            BOTTOM: 0,
            DOWN: 0,
            1: HALF_PI,
            LEFT: HALF_PI,
            2: PI,
            TOP: PI,
            UP: PI,
            3: PI + HALF_PI,
            RIGHT: PI + HALF_PI,
            BOTTOM + RIGHT: 0,
            DOWN + RIGHT: 0,
            DOWN + LEFT: HALF_PI,
            BOTTOM + LEFT: HALF_PI,
            TOP + LEFT: PI,
            UP + LEFT: PI,
            TOP + RIGHT: PI + HALF_PI,
            UP + RIGHT: PI + HALF_PI,
            }

def quarter_circle(x, y, radius, quadrant):
    circle_arc(x, y, radius, ROTATION[quadrant], HALF_PI)

def half_circle(x, y, radius, quadrant):
    circle_arc(x, y, radius, ROTATION[quadrant], PI)

def circle_arc(x, y, radius, start_ang, sweep_ang):
    arc(x, y, radius * 2, radius * 2, start_ang, start_ang + sweep_ang)

def poly_arc(x, y, radius, start_ang, sweep_ang, num_points=2):
    angle = sweep_ang / int(num_points)
    a = start_ang
    with beginShape():
        while a <= start_ang + sweep_ang:
            sx = x + cos(a) * radius
            sy = y + sin(a) * radius
            vertex(sx, sy)
            a += angle

def arc_poly(x, y, d, _, start_ang, end_ang, num_points=5):
    sweep_ang = end_ang - start_ang
    angle = sweep_ang / int(num_points)
    a = start_ang
    with beginShape():
        while a <= end_ang:
            sx = x + cos(a) * d / 2
            sy = y + sin(a) * d / 2
            vertex(sx, sy)
            a += angle

def poly_rounded2(p_list, r_list):
    """
    draws a 'filleted' polygon with variable radius
    dependent on roundedCorner()
    """
    with pushStyle():
        noStroke()
        beginShape()
        for p0, p1 in zip(p_list, [p_list[-1]] + p_list[:-1]):
            m = (PVector(p0.x, p0.y) + PVector(p1.x, p1.y)) / 2
            vertex(m.x, m.y)
        endShape(CLOSE)
    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 = (PVector(p0.x, p0.y) + PVector(p1.x, p1.y)) / 2
        m2 = (PVector(p2.x, p2.y) + PVector(p1.x, p1.y)) / 2
        roundedCorner(p1, m1, m2, r)


def roundedCorner(pc, p1, p2, r):
    """
    Based on Stackoverflow C# rounded corner post 
    https://stackoverflow.com/questions/24771828/algorithm-for-creating-rounded-corners-in-a-polygon
    """
    # Vector 1
    dx1 = pc.x - p1.x
    dy1 = pc.y - p1.y

    # Vector 2
    dx2 = pc.x - p2.x
    dy2 = pc.y - p2.y

    # 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 = GetLength(dx1, dy1)
    length2 = GetLength(dx2, 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
    # the coordinates of the vector, 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.x * 2 - p1Cross.x - p2Cross.x
    dy = pc.y * 2 - p1Cross.y - p2Cross.y

    L = GetLength(dx, dy)
    d = GetLength(segment, max_r)

    circlePoint = GetProportionPoint(pc, d, L, dx, dy)

    # StartAngle and EndAngle of arc
    startAngle = atan2(p1Cross.y - circlePoint.y, p1Cross.x - circlePoint.x)
    endAngle = atan2(p2Cross.y - circlePoint.y, p2Cross.x - circlePoint.x)

    # Sweep angle
    sweepAngle = endAngle - startAngle

    # Some additional checks
    if sweepAngle < 0:
        startAngle, endAngle = endAngle, startAngle
        sweepAngle = -sweepAngle

    if sweepAngle > PI:
        startAngle, endAngle = endAngle, startAngle
        sweepAngle = TWO_PI - sweepAngle

    # Draw result using graphics
    # noStroke()
    with pushStyle():
        noStroke()
        beginShape()
        vertex(p1.x, p1.y)
        vertex(p1Cross.x, p1Cross.y)
        vertex(p2Cross.x, p2Cross.y)
        vertex(p2.x, p2.y)
        endShape(CLOSE)

    line(p1.x, p1.y, p1Cross.x, p1Cross.y)
    line(p2.x, p2.y, p2Cross.x, p2Cross.y)
    arc(circlePoint.x, circlePoint.y, 2 * max_r, 2 * max_r,
        startAngle, startAngle + sweepAngle, OPEN)

def GetLength(dx, dy):
    return sqrt(dx * dx + dy * dy)

def GetProportionPoint(pt, segment, L, dx, dy):
    # factor = segment / L if L != 0 else 0
    factor = float(segment) / L if L != 0 else segment
    return PVector(
        (pt.x - dx * factor),

        (pt.y - dy * factor))