""""
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Module related to bezier curve
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"""
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def make_cubic_bezier(control_points: [(float, float)], n: int = 10) -> [(float, float)]:
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r""""
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Interpolate a Bezier-curve by split it into segments of lines (=polyline).
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A Bezier-Curve is defined by
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\[
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B(P_0, P_1, P_2, P_3:t) = (1-t)^3*P_0 + 3(1-t)^2*t*P_1 + 3(1-t)*t^2*P_2 + t^3*P_3
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\]
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for $t \in \[0, 1\]$
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:param control_points
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:param n number of segments
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:return a list of points on the Bezier-Curve.
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"""
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p0x = control_points[0][0]
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p0y = control_points[0][1]
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p1x = control_points[1][0]
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p1y = control_points[1][1]
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p2x = control_points[2][0]
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p2y = control_points[2][1]
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p3x = control_points[3][0]
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p3y = control_points[3][1]
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points = [(p0x, p0y)]
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for i in range(1, n):
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t = i / n
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u = 1 - t
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x = p0x * u**3 + 3 * p1x * t* u**2 + 3 * p2x * t**2 * u + p3x * t**3
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y = p0y * u**3 + 3 * p1y * t* u**2 + 3 * p2y * t**2 * u + p3y * t**3
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points.append( (x,y) )
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points.append((p3x, p3y))
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return points
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def make_svg_polyline(points) -> str:
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line = map(lambda p: f"{p[0]},{p[1]}", points)
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svg = f'<polyline points="{" ".join(line)}" fill="none" stroke="gray" stroke-width="3" />'
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return svg
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