<![CDATA[How to determine whether a point is inside a closed region?]]>
https://help.geogebra.org/topic/how-to-determine-whether-a-point-is-inside-a-closed-region-
Mon, 22 Jun 2015 20:05:02 +0000Tue, 02 Jun 2015 11:54:45 +0000Zend_Feed<![CDATA[ 1. how to fill the closed region by the curve with solid color? the normal operation failed as indicated in the figure; I think you first have to find the coordinates of the five intersection points of the curve. So it will be necessary to resolve x(t1)=x(t2) & y(t1) = y(t2). Maybe with some trigonometric formulas. I don't know if GeoGebra can bring some approximations.]]>
https://help.geogebra.org/topic/how-to-determine-whether-a-point-is-inside-a-closed-region-#comment-175325
Wed, 17 Jun 2015 06:41:05 +0000<![CDATA[Hi, 2. Is there Geogebra built-in functions which can help determine whether an arbitrarily given point is inside the closed pentacle region or not since it is not a convex region? with B=PointPlusProche[a, A] b = Distance[(0, 0), A] ≤ Distance[(0, 0), B] = IsInRegion[A, a] https://ggbm.at/1389267]]>
https://help.geogebra.org/topic/how-to-determine-whether-a-point-is-inside-a-closed-region-#comment-175327
Wed, 17 Jun 2015 12:08:01 +0000<![CDATA[1. how to fill the closed region by the curve with solid color? the normal operation failed as indicated in the figure; with 2 curves... https://ggbm.at/1389269]]>
https://help.geogebra.org/topic/how-to-determine-whether-a-point-is-inside-a-closed-region-#comment-175329
Wed, 17 Jun 2015 12:13:59 +0000<![CDATA[ with B=PointPlusProche[a, A] b = Distance[(0, 0), A] ≤ Distance[(0, 0), B] = IsInRegion[A, a] This method bring a false answer if B is inside one of the 5 branchs and more near the central pentagon than the exterior curve of this branch. See IsinRegionfalse figure. We can also fill the central almost pentagon by calculate the coordinates of the intersection points. By zooming it's easy to approximate those coordinates. I find t1 =3.680316 and t2 = 3.859508 Then i draw the curve between t1 and t2, and rotate it 72°, 4 times. You can see that the curve is a little bit inside the exact regular pentagon, so just draw it and fill it. https://ggbm.at/1389275 https://ggbm.at/1389277]]>
https://help.geogebra.org/topic/how-to-determine-whether-a-point-is-inside-a-closed-region-#comment-175331
Wed, 17 Jun 2015 13:37:11 +0000<![CDATA[In fact it's not necessary to solve an equation to find coordinates of the intersection points : A(0,-5) it's one of those points ! But this solution is not really one because the regular pentagon is more large than the central region of the curve. https://ggbm.at/1389281]]>
https://help.geogebra.org/topic/how-to-determine-whether-a-point-is-inside-a-closed-region-#comment-175333
Wed, 17 Jun 2015 15:25:26 +0000<![CDATA[:smiley_cat: Curve[9sin(2t) + 5sin(3t), 9cos(2t) - 5cos(3t), t, 0, 6.28319] Can i ask you where do you find this equation ? Cuz i think we can approach the exact regular pentagon as close as we want by changing integers 9,5, 2 and 3. It will be a funny way to construct the regular pentagon]]>
https://help.geogebra.org/topic/how-to-determine-whether-a-point-is-inside-a-closed-region-#comment-175335
Wed, 17 Jun 2015 15:30:28 +0000<![CDATA[Hi, This method bring a false answer if B is inside one of the 5 branchs and more near the central pentagon than the exterior curve of this branch. :flushed: Yes , you right ! An other way, with intersect... https://ggbm.at/1389285]]>
https://help.geogebra.org/topic/how-to-determine-whether-a-point-is-inside-a-closed-region-#comment-175337
Wed, 17 Jun 2015 16:24:01 +0000<![CDATA[Yes beautiful]]>
https://help.geogebra.org/topic/how-to-determine-whether-a-point-is-inside-a-closed-region-#comment-175339
Wed, 17 Jun 2015 21:26:10 +0000<![CDATA[hello but the problem continues in axis of symmetry near the inside pentagon why is the intersection of curve and ray undefined? there is a bug? saludos]]>
https://help.geogebra.org/topic/how-to-determine-whether-a-point-is-inside-a-closed-region-#comment-175341
Wed, 17 Jun 2015 23:02:17 +0000<![CDATA[The exact region of curved pentagon is too hard to be defined in a parametric curve, so the problem may be solved by assuming linear the pentagon sides, i.e. y(M)= y(F)= 2, instead of 2.02254. Cheers https://ggbm.at/1389301 https://ggbm.at/1389301]]>
https://help.geogebra.org/topic/how-to-determine-whether-a-point-is-inside-a-closed-region-#comment-175343
Thu, 18 Jun 2015 09:26:38 +0000<![CDATA[hello but the problem continues in axis of symmetry near the inside pentagon why is the intersection of curve and ray undefined? there is a bug? saludos Oh my god ! Incredible I don't find any reason of this problem. A bug ?]]>
https://help.geogebra.org/topic/how-to-determine-whether-a-point-is-inside-a-closed-region-#comment-175345
Thu, 18 Jun 2015 11:06:41 +0000<![CDATA[How GeoGebra calculate the intersection of two curves ? Because the problem clearly happened when the line is orthogonal to the tangent of the curve at the intersection point. I try with the regular trifolium, same.]]>
https://help.geogebra.org/topic/how-to-determine-whether-a-point-is-inside-a-closed-region-#comment-175347
Thu, 18 Jun 2015 12:07:26 +0000<![CDATA[How GeoGebra calculate the intersection of two curves ? This this case numerically (as the curve is not a polynomial) so it can't guarantee to get all the intersection points]]>
https://help.geogebra.org/topic/how-to-determine-whether-a-point-is-inside-a-closed-region-#comment-175349
Thu, 18 Jun 2015 15:43:07 +0000<![CDATA[I found part of the solution : there's no intersection between the line and the curve because O=(0,0) is on the line. But i don't know why this belonging cause that. See figure AsurAxe : intersection sometimes doesn't exist (i reduce T interval for problem simplification and cause elimination) On figure AsurAxe+décentré : intersection is here https://ggbm.at/1389315 https://ggbm.at/1389315 https://ggbm.at/1389317]]>
https://help.geogebra.org/topic/how-to-determine-whether-a-point-is-inside-a-closed-region-#comment-175351
Thu, 18 Jun 2015 19:21:26 +0000<![CDATA[in fact ther'es no intersection because O is on the half-line which cut the curve. the intersection between the entire line (name e on figure AsurAxe) and the curve exist on figure AsurAxe]]>
https://help.geogebra.org/topic/how-to-determine-whether-a-point-is-inside-a-closed-region-#comment-175353
Thu, 18 Jun 2015 20:42:38 +0000<![CDATA[J’ai ramené le problème à ce qui suit : Sur la figure suivante, la courbe a est un cercle de centre (0,c) tracée de façon paramétrique. B est un point quelconque du plan, C le point de a le plus proche de B. Si c est différent de 0, l’autre intersection (E) de (DB) avec le cercle existe, quand on déplace B, la moitié du temps uniquement (pour un demi-cercle. Vous pouvez construire l’intersection avec l’autre demi-cercle sans problème. En fait tout se passe comme si il y avait non pas 1 courbe, mais 2). Si c = 0 (c’est à dire quand la droite passe par (0,0)), cette intersection n’existe pas, pour la plupart des positions de B. Mais des fois elle apparaît furtivement. Il n’y a pas ce problème avec un cercle tracé avec la commande Cercle. https://ggbm.at/1389323]]>
https://help.geogebra.org/topic/how-to-determine-whether-a-point-is-inside-a-closed-region-#comment-175355
Thu, 18 Jun 2015 21:34:03 +0000<![CDATA[hello to model the inside command for a point with an aprox polygon is easy I did an applet in June of 2009 for a course of INTE (instituto nacional de tecnologias educativas del ministerio de educacion en España) the course was absurdly eliminated off menu of INTE's courses but you can acces to material in http://www.ite.educacion.es/formacion/materiales/123/cd/06/otros.html and another pages my applet is at bottom of the page. you can translate the text with google. then I wanted a similar method for parametric curve the calculus is slow in my machine but it works well and it is amazing (I think so) test it please (points in special positions are interesting) saludos WARNING: the PC may freeze and CPU can be heated https://ggbm.at/1389325 https://ggbm.at/1389327]]>
https://help.geogebra.org/topic/how-to-determine-whether-a-point-is-inside-a-closed-region-#comment-175357
Fri, 19 Jun 2015 02:01:46 +0000<![CDATA[I can't open your figure in the site /ite.educacion.es/ Does here in GeoGebraTube ? You use a topology method ant the result is really great ! Thanks. Is you definition of "degree" (integral of ((f(x) - x(A)) dg(x) - (g(x) - y(A)) df(x)) / ((f(x) - x(A))² + (g(x) - y(A))²) between 0 and 2pi) means something else first in topology ? Maybe it's also possible to calculate some others topologic indicators curve, as genre for example ? In figure foro1, i see when A is (0,2)? Does exist a additional way to conclude that A is inside ? Have a good day]]>
https://help.geogebra.org/topic/how-to-determine-whether-a-point-is-inside-a-closed-region-#comment-175359
Fri, 19 Jun 2015 07:22:41 +0000<![CDATA[I can't open your figure in the site /ite.educacion.es/ Does here in GeoGebraTube ? because in 2009 we worked with java. can you open another applets changing the security options in JAVA? then you can do it also saludos PD: lo he bajado y te lo subo note than the version in 2009 is very old https://ggbm.at/1389329]]>
https://help.geogebra.org/topic/how-to-determine-whether-a-point-is-inside-a-closed-region-#comment-175361
Fri, 19 Jun 2015 09:22:35 +0000<![CDATA[I can't open your figure in the site /ite.educacion.es/ Does here in GeoGebraTube ? You use a topology method ant the result is really great ! Thanks. Is you definition of "degree" (integral of ((f(x) - x(A)) dg(x) - (g(x) - y(A)) df(x)) / ((f(x) - x(A))² + (g(x) - y(A))²) between 0 and 2pi) means something else first in topology ? Maybe it's also possible to calculate some others topologic indicators curve, as genre for example ? In figure foro1, i see when A is (0,2)? Does exist a additional way to conclude that A is inside ? Have a good day what "A is inside" means? is not possible a path joining the point with a remote point or there is a sub_curve around the point? is the point in a laberynth inside or outside? both cases seems to me not possible actually for GG Ah! integral of ((f(x) - x(A)) dg(x) - (g(x) - y(A)) df(x)) / ((f(x) - x(A))² + (g(x) - y(A))² is the sum of infinity signed angles from curve to point saludos]]>
https://help.geogebra.org/topic/how-to-determine-whether-a-point-is-inside-a-closed-region-#comment-175363
Fri, 19 Jun 2015 14:59:01 +0000<![CDATA[hello a completely new method. integral is eliminated by another angular calculus and the calculus is faster simpler the degree of curve is more clear. the points on curve is not supported but if you want it no problem new example change f and g for older examples please test it saludos PD: if you like the course of inte you can donwload the applet changing html in link by ggb. example you want see http://www.ite.educacion.es/formacion/materiales/123/cd/html/circ_p.html and java avoids you then download http://www.ite.educacion.es/formacion/materiales/123/cd/ggb/circ_p.ggb podriamos enviar peticiones al [size=150]INTE [/size]para que recuperen los [size=150]cursos [/size]de [size=200]GeoGebra[/size] saludos https://ggbm.at/1389333]]>
https://help.geogebra.org/topic/how-to-determine-whether-a-point-is-inside-a-closed-region-#comment-175365
Fri, 19 Jun 2015 16:46:45 +0000<![CDATA[hello a completely new method. integral is eliminated by another angular calculus and the calculus is faster simpler the degree of curve is more clear. the points on curve is not supported but if you want it no problem new example change f and g for older examples please test it saludos I test it and other too and it's really great. Calculus faster simpler for this one ? Maybe not if you don't know the formula use in code : sgn((u - A) ⊗ v), u, a(raices), v, da(raices) where raices are Racines[p] and p = atan2(g(x) - y(A),f(x) - x(A))... Beautiful that it's possible to replace a integral by a finite sum extended to some roots. (it's always possible?) For that moment i translate the text of your first area polygon figure (thanks for the upload!) because Google traduction is not very good.. If GeoGebra give a false polygone area, does exist a way to have the true ? (maybe by changing weighted coefficient of the sum ?) It's too bad that Patrick's method for the pentagram curve to decide even if or not a point is inside fail, because it should work! GeoGebra programs for computate roots must be more effective. In that point of view, the figure in my last post reveal how large is the problem :cry:]]>
https://help.geogebra.org/topic/how-to-determine-whether-a-point-is-inside-a-closed-region-#comment-175367
Fri, 19 Jun 2015 20:37:37 +0000<![CDATA[Hello, @ mathmagic : very interesting! Bravo and thank you.]]>
https://help.geogebra.org/topic/how-to-determine-whether-a-point-is-inside-a-closed-region-#comment-175369
Fri, 19 Jun 2015 22:23:18 +0000<![CDATA[hello a completely new method. integral is eliminated by another angular calculus and the calculus is faster simpler the degree of curve is more clear. the points on curve is not supported but if you want it no problem new example change f and g for older examples please test it saludos I test it and other too and it's really great. Calculus faster simpler for this one ? Maybe not if you don't know the formula use in code : sgn((u - A) ⊗ v), u, a(raices), v, da(raices) where raices are Racines[p] and p = atan2(g(x) - y(A),f(x) - x(A))... Beautiful that it's possible to replace a integral by a finite sum extended to some roots. (it's always possible?) For that moment i translate the text of your first area polygon figure (thanks for the upload!) because Google traduction is not very good.. If GeoGebra give a false polygone area, does exist a way to have the true ? (maybe by changing weighted coefficient of the sum ?) It's too bad that Patrick's method for the pentagram curve to decide even if or not a point is inside fail, because it should work! GeoGebra programs for computate roots must be more effective. In that point of view, the figure in my last post reveal how large is the problem :cry: si tu quieres puedo darte el proceso mental seguido para el calculo inicial y el cambio producido en el proceso basicamente es que la integral inicial era la integral de una derivada pero la explicacion te la puedo dar en español mi ingles no llega a tanto saludos]]>
https://help.geogebra.org/topic/how-to-determine-whether-a-point-is-inside-a-closed-region-#comment-175371
Sat, 20 Jun 2015 00:53:40 +0000<![CDATA[ si tu quieres puedo darte el proceso mental seguido para el calculo inicial y el cambio producido en el proceso basicamente es que la integral inicial era la integral de una derivada pero la explicacion te la puedo dar en español mi ingles no llega a tanto Your explanation isnt too long (less than two pages) ? If yes, i want it. I have a solution for Patrick’s method. Let a : x = f(t) & y = g(t) the curve. We first find the roots of : df(t) (x(A) - f(t)) + dg(t) (y(A) - g(t)) = 0. Those solutions T correspond to the points a(T) of the curve where the normal passes through the point A. Then it’s easy to have the point of the curve which is the closest to A (name B). After, by solving an other classic equation, you can have all the intersection of the curve with the normal at B (*). For finish, some of those points M must be eliminate : when B is on [AM] (with for example a geometric logic code). (*) those two equations must be simplified before being input, otherwise GeoGebra partially solved them. Maybe that’s why some other figures fails. https://ggbm.at/1389335]]>
https://help.geogebra.org/topic/how-to-determine-whether-a-point-is-inside-a-closed-region-#comment-175373
Sat, 20 Jun 2015 20:43:21 +0000<![CDATA[Interesting approach, the above one. As shown below, I've tried to replicate it in a generalized form and have no idea why list3 produces only one output and min-value is undefined. Please, Patrick/Rousseau (co-authors of the sheet), could you amend mine appropriately? Thx&Cheers https://ggbm.at/1389351]]>
https://help.geogebra.org/topic/how-to-determine-whether-a-point-is-inside-a-closed-region-#comment-175375
Mon, 22 Jun 2015 10:31:55 +0000<![CDATA[Hi, why list3 produces only one output and min-value is undefined. because Sequence get a list, no use {....} in {Sequence[...]} same problem with Zip[...] ... https://ggbm.at/1389353]]>
https://help.geogebra.org/topic/how-to-determine-whether-a-point-is-inside-a-closed-region-#comment-175377
Mon, 22 Jun 2015 10:53:23 +0000<![CDATA[So precious drift, Patrick! Now I can proceed to complete the sheet, Thank you very much and cheers]]>
https://help.geogebra.org/topic/how-to-determine-whether-a-point-is-inside-a-closed-region-#comment-175379
Mon, 22 Jun 2015 11:22:07 +0000<![CDATA[I still need help. The definition of p(x) seems in accordance with the original sheet, nevertheless errors erupt, as show. Thx in advance https://ggbm.at/1389357]]>
https://help.geogebra.org/topic/how-to-determine-whether-a-point-is-inside-a-closed-region-#comment-175381
Mon, 22 Jun 2015 17:11:05 +0000<![CDATA[I'm afraid it's impossible to generalize. Look graphs function of h and p. When you move A, GeoGebra can't find all roots of those functions. I don't know if is the reason of your last figure error, but it's certain that this failure prevent to finish. If you want to complete the figure you need to simplified the expression of h and p before input them in GeoGebra. It's possible with the formula sin(a + b) = sin(a)cos(b) + sin(b)cos(a).]]>
https://help.geogebra.org/topic/how-to-determine-whether-a-point-is-inside-a-closed-region-#comment-175383
Mon, 22 Jun 2015 17:51:36 +0000<![CDATA[Yes, Rousseau, the att'd screenshot of comparison confirms the different behaviour of both sheets: yours and mine. Unfortunately the loss of generalization strongly reduces the superb method of investigation: point inside/outside the given contour of a parametric curve. Thanks a lot for your cooperation]]>
https://help.geogebra.org/topic/how-to-determine-whether-a-point-is-inside-a-closed-region-#comment-175385
Mon, 22 Jun 2015 20:05:02 +0000