NURBS curve based on Control points,Weights & Knots - Grasshopper2024-03-29T04:35:56Zhttps://www.grasshopper3d.com/forum/topics/nurbs-curve-based-on-control-points-weights-knots?commentId=2985220%3AComment%3A1367839&feed=yes&xn_auth=noYou are the man :) wow :) i n…tag:www.grasshopper3d.com,2017-02-16:2985220:Comment:16925782017-02-16T06:12:26.794ZParivardhan Dangihttps://www.grasshopper3d.com/profile/ParivardhanDangi
<p>You are the man :) wow :) i never thought i'd see this ! where did you find it ! wonderful !</p>
<p>You are the man :) wow :) i never thought i'd see this ! where did you find it ! wonderful !</p> Your right David. Because of…tag:www.grasshopper3d.com,2015-09-29:2985220:Comment:13705802015-09-29T20:00:22.906ZParametric Househttps://www.grasshopper3d.com/profile/parametric
<p>Your right David. Because of the rapid changes in the equations, Galapagos can't reach the answer. The only solution I'm thinking of is making a database of equations with constants and then feeding them to Galapagos.</p>
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<p>Your right David. Because of the rapid changes in the equations, Galapagos can't reach the answer. The only solution I'm thinking of is making a database of equations with constants and then feeding them to Galapagos.</p>
<p></p> I'm not sure it will work, th…tag:www.grasshopper3d.com,2015-09-27:2985220:Comment:13691932015-09-27T18:13:49.701ZDavid Ruttenhttps://www.grasshopper3d.com/profile/DavidRutten
<p>I'm not sure it will work, the problem with making an equation tree like that is that it is very discontinuous. Sure, just changing numbers into other (nearby) numbers will yield small changes in outcome, but replacing division with addition or with a Sin will change the outcome of the equation drastically. Galapagos can only work when small changes to variables result in small changes in results, it can handle a certain amount of suddenness, but this may well be pushing it.</p>
<p>I'm not sure it will work, the problem with making an equation tree like that is that it is very discontinuous. Sure, just changing numbers into other (nearby) numbers will yield small changes in outcome, but replacing division with addition or with a Sin will change the outcome of the equation drastically. Galapagos can only work when small changes to variables result in small changes in results, it can handle a certain amount of suddenness, but this may well be pushing it.</p> For example look at this:
Sin…tag:www.grasshopper3d.com,2015-09-24:2985220:Comment:13677612015-09-24T12:08:29.470ZParametric Househttps://www.grasshopper3d.com/profile/parametric
<p>For example look at this:</p>
<p>Single equation for the graph of a marijuana leaf</p>
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<p><a href="http://storage.ning.com/topology/rest/1.0/file/get/2769040128?profile=original" target="_self"><img class="align-full" src="http://storage.ning.com/topology/rest/1.0/file/get/2769040128?profile=original" width="496"></img></a></p>
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<p><a href="http://storage.ning.com/topology/rest/1.0/file/get/2769040213?profile=original" target="_self"><img class="align-full" src="http://storage.ning.com/topology/rest/1.0/file/get/2769040213?profile=original" width="394"></img></a></p>
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<p>Going for polar coordinates is another…</p>
<p>For example look at this:</p>
<p>Single equation for the graph of a marijuana leaf</p>
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<p><a href="http://storage.ning.com/topology/rest/1.0/file/get/2769040128?profile=original" target="_self"><img src="http://storage.ning.com/topology/rest/1.0/file/get/2769040128?profile=original" width="496" class="align-full"/></a></p>
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<p><a href="http://storage.ning.com/topology/rest/1.0/file/get/2769040213?profile=original" target="_self"><img src="http://storage.ning.com/topology/rest/1.0/file/get/2769040213?profile=original" width="394" class="align-full"/></a></p>
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<p>Going for polar coordinates is another option!</p> For example, we have a kind o…tag:www.grasshopper3d.com,2015-09-24:2985220:Comment:13678392015-09-24T12:03:01.482ZParametric Househttps://www.grasshopper3d.com/profile/parametric
<p>For example, we have a kind of arch called elliptical 6-5 in ancient Persian architecture.</p>
<p>The arch has been shown bellow</p>
<p><a href="http://storage.ning.com/topology/rest/1.0/file/get/2769039333?profile=original" target="_self"><img class="align-full" src="http://storage.ning.com/topology/rest/1.0/file/get/2769039333?profile=original" width="640"></img></a></p>
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<p>I'm trying to use Galapagos to write my equation by using the Genetic Programming Method. The parameters will be symbols and variables which I will further feed into my evaluate function. …</p>
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<p>For example, we have a kind of arch called elliptical 6-5 in ancient Persian architecture.</p>
<p>The arch has been shown bellow</p>
<p><a href="http://storage.ning.com/topology/rest/1.0/file/get/2769039333?profile=original" target="_self"><img src="http://storage.ning.com/topology/rest/1.0/file/get/2769039333?profile=original" width="640" class="align-full"/></a></p>
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<p>I'm trying to use Galapagos to write my equation by using the Genetic Programming Method. The parameters will be symbols and variables which I will further feed into my evaluate function. </p>
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<p><a href="https://en.wikipedia.org/wiki/Genetic_programming" target="_blank">https://en.wikipedia.org/wiki/Genetic_programming</a></p>
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<p><a href="http://storage.ning.com/topology/rest/1.0/file/get/2769039521?profile=original" target="_self"><img src="http://storage.ning.com/topology/rest/1.0/file/get/2769039521?profile=original" width="298" class="align-full"/></a></p>
<p>I then divide my arch to points and check if the x and y components fit in the ∑|f(x)-y|=0 equation. I mean the goal for Galapagos will be to minimum the ∑! I can also go for a parametric equation like f(u,v) = x and g(u,v)= y. I'm in the early stages, deciding which way to go!</p>
<p><a href="https://en.wikipedia.org/wiki/Genetic_programming" target="_blank">https://en.wikipedia.org/wiki/Genetic_programming</a></p> Oh yes, different pieces of t…tag:www.grasshopper3d.com,2015-09-24:2985220:Comment:13677462015-09-24T11:38:53.992ZDavid Ruttenhttps://www.grasshopper3d.com/profile/DavidRutten
<p>Oh yes, different pieces of the curve are governed by different equations.</p>
<p>What sort shape/equation are you looking to get, and how will you know when you get it? </p>
<p>Oh yes, different pieces of the curve are governed by different equations.</p>
<p>What sort shape/equation are you looking to get, and how will you know when you get it? </p> Thanks David
So there is a pa…tag:www.grasshopper3d.com,2015-09-24:2985220:Comment:13676552015-09-24T10:11:49.942ZParametric Househttps://www.grasshopper3d.com/profile/parametric
<p>Thanks David</p>
<p>So there is a parametric equation for each span!? Unfortunately, I'm looking for a single equation for a specific arch so I guess going for Nurbs is not a good choice. Perhaps Genetic programming is the best solution for finding the equation.</p>
<p>Thanks David</p>
<p>So there is a parametric equation for each span!? Unfortunately, I'm looking for a single equation for a specific arch so I guess going for Nurbs is not a good choice. Perhaps Genetic programming is the best solution for finding the equation.</p> Sort of, nurbs curves are pol…tag:www.grasshopper3d.com,2015-09-24:2985220:Comment:13677242015-09-24T09:56:52.025ZDavid Ruttenhttps://www.grasshopper3d.com/profile/DavidRutten
<p>Sort of, nurbs curves are polynomial piece-wise curves. So (as I understand) the shape of the span between two knots is governed by three polynomial equations {f(t)=x, f(t)=y, f(t)=z}, where t is the curve parameter.</p>
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<p>The exact formulation of the functions depends on the control-points positions, the weights and the degree.</p>
<p>Sort of, nurbs curves are polynomial piece-wise curves. So (as I understand) the shape of the span between two knots is governed by three polynomial equations {f(t)=x, f(t)=y, f(t)=z}, where t is the curve parameter.</p>
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<p>The exact formulation of the functions depends on the control-points positions, the weights and the degree.</p>