在Julia中无需使用递归绘制Koch曲线。

huangapple
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英文:

Drawing Koch's curve without recursion in Julia

问题

I want to draw a Koch curve in Julia without recursion. My strategy is to divide the given line into three segments using the segPoints function:

  1. function seg_points(startPoint, endPoint, n=3)
  2.     mids = []
  3.     for i in 1:n-1
  4.         push!(mids, i/n * [startPoint[1]+endPoint[1], startPoint[2]+endPoint[2]])
  5.     end
  6.     return mids
  7. end

Then, the function polygon is used to find the top third point:

  1. function polygon(p1, p2, n=3)
  2.     x = p2[1]-p1[1]
  3.     y = p2[2]-p1[2]
  4.     P3 = p1 + [x * cos(pi/3) - y * sin(pi/3), x * sin(pi/3) + y * cos(pi/3)]
  5.     return P3
  6. end

Finally, the function koch_curve is used to draw the fractal:

  1. function koch_curve(order::Int, startPoint = [0.0,0.0], endPoint = [1.0,0.0])
  2.     pts=[startPoint, endPoint]
  3.     for i in 1:order
  4.         order_points =[]
  5.         for j in 2:length(pts)
  6.             a = pts[j-1]
  7.             b = pts[j]
  8.             c, d = seg_points(a, b)
  9.             e = polygon(c, d)
  10.             push!(order_points, c, d, e)
  11.         end
  12.         for pt in order_points
  13.             push!(pts, pt)
  14.         end
  15.     end
  16.     return pts
  17. end

But it doesn't work. The output plot is this with order=5:
在Julia中无需使用递归绘制Koch曲线。

英文:

I want to draw a Koch curve in Julia without recursion. My strategy is to divide the given line into three segments using the segPoints function:

  1. function seg_points(startPoint, endPoint, n=3)
  2. 		mids = []
  3. 		for i in 1:n-1
  4. 			push!(mids, i/n * [startPoint[1]+endPoint[1], startPoint[2]+endPoint[2]])
  5. 		end
  6. 		return mids
  7. 	end

Then, the function polygon is used to find the top third point.

  1. function polygon(p1, p2, n=3)
  2. 	x = p2[1]-p1[1]
  3. 	y = p2[2]-p1[2]
  4. 	P3 = p1 + [x * cos(pi/3) - y * sin(pi/3), x * sin(pi/3) + y * cos(pi/3)]
  5. 	return P3
  6. end

Finally in the function koch_curve is to draw the fractal:

  1. function koch_curve(order::Int, startPoint = [0.0,0.0], endPoint = [1.0,0.0])
  2. 	pts=[startPoint, endPoint]
  3. 	for i in 1:order
  4. 		order_points =[]
  5. 		for j in 2:length(pts)
  6. 			a = pts[j-1]
  7. 			b = pts[j]
  8. 			c, d = seg_points(a, b)
  9. 			e = polygon(c, d)
  10. 			push!(order_points, c, d, e)
  11. 		end
  12. 		for pt in order_points
  13. 			push!(pts, pt)
  14. 		end
  15. 	end
  16. 	return pts
  17. end

But it doesn't work. The output plot is this with order=5:
在Julia中无需使用递归绘制Koch曲线。

答案1

得分: 2

以下是代码的翻译：

首先，中点没有被正确计算。如果您想找到等分线段的点，应该使用加权平均值：

  1. function seg_points(startPoint, endPoint, n=3)
  2.     mids = []
  3.     for i in 1:n-1
  4.         push!(mids, (1 - i/n) * startPoint + i/n * endPoint)
  5.     end
  6.     return mids
  7. end

然后，您需要按正确的顺序将这些点添加，因为线段由相邻的点定义：

  1. function koch_curve(order::Int, startPoint = [0.0,0.0], endPoint = [1.0,0.0])
  2.     pts=[startPoint, endPoint]
  3.     for i in 1:order
  4.         order_points =[]
  5.         for j in 2:length(pts)
  6.             a = pts[j-1]
  7.             b = pts[j]
  8.             c, d = seg_points(a, b)
  9.             e = polygon(c, d)
  10.             # 不要推入b，因为这个b等于下一次循环的a：
  11.             push!(order_points, a, c, e, d)
  12.         end
  13.         push!(order_points, pts[end]) # 最后的b
  14.         pts = order_points
  15.     end
  16.     return pts
  17. end
英文:

First thing is the midpoints aren't being computed correctly. A weighted average should be used if you want to find the points that equally divide a segment:

  1. function seg_points(startPoint, endPoint, n=3)
  2.     mids = []
  3.     for i in 1:n-1
  4.         push!(mids, (1 - i/n) * startPoint + i/n * endPoint)
  5.     end
  6.     return mids
  7. end

Then you need to push the points in the correct order, since lines are defined by adjacent points:

  1. function koch_curve(order::Int, startPoint = [0.0,0.0], endPoint = [1.0,0.0])
  2.     pts=[startPoint, endPoint]
  3.     for i in 1:order
  4.         order_points =[]
  5.         for j in 2:length(pts)
  6.             a = pts[j-1]
  7.             b = pts[j]
  8.             c, d = seg_points(a, b)
  9.             e = polygon(c, d)
  10.             # don't push b, since this b = the next loop iter's a:
  11.             push!(order_points, a, c, e, d)
  12.         end
  13.         push!(order_points, pts[end]) # the last b
  14.         pts = order_points
  15.     end
  16.     return pts
  17. end

huangapple
  • 本文由 发表于 2023年5月21日 00:44:44
  • 转载请务必保留本文链接：https://go.coder-hub.com/76296310.html
  • fractals
  • julia
  • plot
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