Koch Star

T-Spine visualization of Koch curve structure
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def k1 (p:var[]..[])
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{
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	v1 = Vector.ByTwoPoints(p[0],p[1]).Normalized();
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	d1 = p[0].DistanceTo(p[1]);
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	p1 = p[0].Translate(v1,d1/3);
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	v2 = v1.Rotate(Vector.ZAxis(),60);
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	p2 = p1.Translate(v2,d1/3);
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	p3 = p1.Translate(v1,d1/3);
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	return [p[0],p1,p2,p3,p[1]];
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};
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With Loops
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​
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def k2 (pts:var[]..[])
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{
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	p1 = List.DropItems(List.Sublists(pts,0..1,1),-1);
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	p2 = k1(p1<1>);
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	p3 = Point.PruneDuplicates(List.Flatten(p2,-1),0.1);
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	return List.AddItemToEnd(p3[0],p3);
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};
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​
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def k3 (pt:var[]..[],it:int)
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{
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	a = [Imperative]
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	{
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		c = 0;
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		b = [];
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		while (c < it)
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		{
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			b = k2(pt);
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			pt = b;
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			c = c + 1;
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		}
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		return b;
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	}
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	return a;
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};
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With Recursion
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​
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def k2(pts:var[]..[],n:int[]..[])
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{
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	a = [Imperative]
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	{
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		if (List.Count(pts)>=Math.Pow(5,n))
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			return pts;
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		else
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		{
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			b = [Associative]
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			{
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				p1 = List.DropItems(List.Sublists(pts,0..1,1),-1);
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				p2 = k1(p1<1>);
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				p3 = List.Flatten(p2,-1);
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				return p3;
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			}
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			return Point.PruneDuplicates(k2(b,n),0.1);
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		}
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	}
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	b = List.Clean(List.Flatten(a,-1),false);
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	return List.AddItemToEnd(List.FirstItem(b),b);
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};
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Visualization with T-Splines
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// T Spline Visualization
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p001 = List.Transpose(Circle.ByCenterPointRadius(Point.Origin(),
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[50,35,25,5])<1>.PointAtParameter((1..0..#4)<2>));
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p002 = k2(p001<1>,2).Translate(Vector.ZAxis(),[0,10,15,60]);
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pc01 = PolyCurve.ByPoints(List.Transpose(p002));
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pc02 = PolyCurve.ByPoints(pc01.PointAtParameter((0..1..#10)<1>));
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ts01 = TSplineSurface.BuildPipes(List.Flatten(pc01.Explode(),-1),
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1.5,0.1,3,true,false,0,0,1,0.3,1,1,true);
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ts02 = TSplineSurface.BuildPipes(pc02.Explode(),2..0.2..#10,
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2..0.2..#10,3,true,false,0,0,1,0.3,1,1,true);
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ts03 = TSplineSurface.ByCombinedTSplineSurfaces
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(List.Flatten([ts01,ts02],-1)).Translate(150,0,0);
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koch.stl
98MB
Binary
STL file
​

Last modified 2mo ago

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