2020-02-17 15:45:43 +00:00
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from line_geometry import intersecting
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def b_poly_arc_augmented(op_list, or_list=None, check_intersection=False, b=True):
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if not op_list: return
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if or_list == None:
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r2_list = [0] * len(op_list)
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else:
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r2_list = or_list[:]
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assert len(op_list) == len(r2_list), \
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"Number of points and radii not the same"
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if check_intersection:
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b = False
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global pontos_, my_vertex
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pontos_ = []
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def append_point(x, y):
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pontos_.append((x, y))
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my_vertex = append_point
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else:
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my_vertex = vertex
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# remove overlapping adjacent points
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p_list, r_list = [], []
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for i1, p1 in enumerate(op_list):
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i2 = (i1 - 1)
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p2, r2, r1 = op_list[i2], r2_list[i2], r2_list[i1]
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if dist(p1[0], p1[1], p2[0], p2[1]) > 1: # or p1 != p2:
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p_list.append(p1)
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r_list.append(r1)
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else:
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r2_list[i2] = min(r1, r2)
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# invert radius
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for i1, p1 in enumerate(p_list):
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i0 = (i1 - 1)
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p0 = p_list[i0]
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i2 = (i1 + 1) % len(p_list)
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p2 = p_list[i2]
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a = area(p0, p1, p2) / 1000.
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if or_list == None:
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r_list[i1] = a
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else:
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# if abs(a) < 1:
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# r_list[i1] = r_list[i1] * abs(a)
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if a < 0:
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r_list[i1] = -r_list[i1]
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# reduce radius that won't fit
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for i1, p1 in enumerate(p_list):
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i2 = (i1 + 1) % len(p_list)
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p2, r2, r1 = p_list[i2], r_list[i2], r_list[i1]
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r_list[i1], r_list[i2] = reduce_radius(p1, p2, r1, r2)
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# calculate the tangents
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a_list = []
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for i1, p1 in enumerate(p_list):
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i2 = (i1 + 1) % len(p_list)
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p2, r2, r1 = p_list[i2], r_list[i2], r_list[i1]
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cct = circ_circ_tangent(p1, p2, r1, r2)
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a_list.append(cct)
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# check intersection
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if check_intersection:
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pontos = []
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for ang, p1, p2 in a_list:
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pontos.append(p1)
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pontos.append(p2)
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if intersecting(pontos):
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return True
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# else:
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# return False
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# draw
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beginShape()
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for i1, ia in enumerate(a_list):
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i2 = (i1 + 1) % len(a_list)
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p1, p2, r1, r2 = p_list[i1], p_list[i2], r_list[i1], r_list[i2]
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a1, p11, p12 = ia
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a2, p21, p22 = a_list[i2]
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# circle(p1[0], p1[1], 10)
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if a1 != None and a2 != None:
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start = a1 if a1 < a2 else a1 - TWO_PI
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if r2 <= 0:
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a2 = a2 - TWO_PI
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2020-03-02 01:35:55 +00:00
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abs_angle = abs(a2 - start)
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if abs_angle > TWO_PI:
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2020-02-17 15:45:43 +00:00
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if a2 < 0:
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a2 += TWO_PI # a2 = a2 + TWO_PI
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else:
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a2 -= TWO_PI # a2 = a2 - TWO_PI
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if abs(a2 - start) != TWO_PI:
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if b:
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b_arc(p2[0], p2[1], r2 * 2, r2 * 2, start, a2, mode=2)
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else:
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p_arc(p2[0], p2[1], r2 * 2, r2 * 2, start, a2, mode=2, num_points=4)
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# textSize(32)
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# text(str(int(degrees(start - a2))), p2[0], p2[1])
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else:
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# when the the segment is smaller than the diference between
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# radius, circ_circ_tangent won't renturn the angle
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# ellipse(p2[0], p2[1], r2 * 2, r2 * 2) # debug
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if a1:
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my_vertex(p12[0], p12[1])
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if a2:
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my_vertex(p21[0], p21[1])
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endShape(CLOSE)
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if check_intersection:
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if intersecting(pontos_):
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return True
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else:
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return False
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def reduce_radius(p1, p2, r1, r2):
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d = dist(p1[0], p1[1], p2[0], p2[1])
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ri = abs(r1 - r2)
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if d - ri <= 0:
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if abs(r1) > abs(r2):
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r1 = map(d, ri + 1, 0, r1, r2)
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else:
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r2 = map(d, ri + 1, 0, r2, r1)
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return(r1, r2)
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def circ_circ_tangent(p1, p2, r1, r2):
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d = dist(p1[0], p1[1], p2[0], p2[1])
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ri = r1 - r2
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line_angle = atan2(p1[0] - p2[0], p2[1] - p1[1])
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if d - abs(ri) >= 0:
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theta = asin(ri / float(d))
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x1 = -cos(line_angle + theta) * r1
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y1 = -sin(line_angle + theta) * r1
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x2 = -cos(line_angle + theta) * r2
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y2 = -sin(line_angle + theta) * r2
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return (line_angle + theta,
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(p1[0] - x1, p1[1] - y1),
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(p2[0] - x2, p2[1] - y2))
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else:
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return (None,
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(p1[0], p1[1]),
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(p2[0], p2[1]))
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def b_arc(cx, cy, w, h, start_angle, end_angle, mode=0):
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"""
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A bezier approximation of an arc
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using the same signature as the original Processing arc()
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mode: 0 "normal" arc, using beginShape() and endShape()
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1 "middle" used in recursive call of smaller arcs
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2 "naked" like normal, but without beginShape() and endShape()
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for use inside a larger PShape
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"""
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theta = end_angle - start_angle
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# Compute raw Bezier coordinates.
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if mode != 1 or abs(theta) < HALF_PI:
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x0 = cos(theta / 2.0)
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y0 = sin(theta / 2.0)
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x3 = x0
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y3 = 0 - y0
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x1 = (4.0 - x0) / 3.0
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if y0 != 0:
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y1 = ((1.0 - x0) * (3.0 - x0)) / (3.0 * y0) # y0 != 0...
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else:
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y1 = 0
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x2 = x1
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y2 = 0 - y1
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# Compute rotationally-offset Bezier coordinates, using:
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# x' = cos(angle) * x - sin(angle) * y
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# y' = sin(angle) * x + cos(angle) * y
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bezAng = start_angle + theta / 2.0
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cBezAng = cos(bezAng)
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sBezAng = sin(bezAng)
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rx0 = cBezAng * x0 - sBezAng * y0
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ry0 = sBezAng * x0 + cBezAng * y0
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rx1 = cBezAng * x1 - sBezAng * y1
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ry1 = sBezAng * x1 + cBezAng * y1
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rx2 = cBezAng * x2 - sBezAng * y2
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ry2 = sBezAng * x2 + cBezAng * y2
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rx3 = cBezAng * x3 - sBezAng * y3
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ry3 = sBezAng * x3 + cBezAng * y3
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# Compute scaled and translated Bezier coordinates.
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rx, ry = w / 2.0, h / 2.0
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px0 = cx + rx * rx0
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py0 = cy + ry * ry0
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px1 = cx + rx * rx1
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py1 = cy + ry * ry1
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px2 = cx + rx * rx2
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py2 = cy + ry * ry2
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px3 = cx + rx * rx3
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py3 = cy + ry * ry3
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# Debug points... comment this out!
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# stroke(0)
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# ellipse(px3, py3, 15, 15)
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# ellipse(px0, py0, 5, 5)
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# Drawing
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if mode == 0: # 'normal' arc (not 'middle' nor 'naked')
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beginShape()
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if mode != 1: # if not 'middle'
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my_vertex(px3, py3)
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if abs(theta) < HALF_PI:
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bezierVertex(px2, py2, px1, py1, px0, py0)
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else:
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# to avoid distortion, break into 2 smaller arcs
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b_arc(cx, cy, w, h, start_angle, end_angle - theta / 2.0, mode=1)
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b_arc(cx, cy, w, h, start_angle + theta / 2.0, end_angle, mode=1)
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if mode == 0: # end of a 'normal' arc
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endShape()
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def area(p0, p1, p2):
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a = (p1[0] * (p2[1] - p0[1]) +
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p2[0] * (p0[1] - p1[1]) +
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p0[0] * (p1[1] - p2[1]))
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return a
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def p_arc(cx, cy, w, h, start_angle, end_angle, mode=0, num_points=None):
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"""
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A poly approximation of an arc
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using the same signature as the original Processing arc()
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mode: 0 "normal" arc, using beginShape() and endShape()
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2 "naked" like normal, but without beginShape() and endShape()
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for use inside a larger PShape
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"""
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if not num_points:
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num_points = 24
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# start_angle = start_angle if start_angle < end_angle else start_angle - TWO_PI
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sweep_angle = end_angle - start_angle
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if mode == 0:
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beginShape()
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if sweep_angle < 0:
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start_angle, end_angle = end_angle, start_angle
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sweep_angle = -sweep_angle
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angle = sweep_angle / int(num_points)
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a = end_angle
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while a >= start_angle:
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sx = cx + cos(a) * w / 2.
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sy = cy + sin(a) * h / 2.
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my_vertex(sx, sy)
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a -= angle
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elif sweep_angle > 0:
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angle = sweep_angle / int(num_points)
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a = start_angle
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while a <= end_angle:
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sx = cx + cos(a) * w / 2.
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sy = cy + sin(a) * h / 2.
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my_vertex(sx, sy)
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a += angle
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else:
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sx = cx + cos(start_angle) * w / 2.
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sy = cy + sin(start_angle) * h / 2.
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my_vertex(sx, sy)
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if mode == 0:
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endShape()
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