<![CDATA[How to color a spherical triangle?]]>
https://help.geogebra.org/topic/how-to-color-a-spherical-triangle
Wed, 02 Jun 2021 01:25:32 +0000Wed, 26 May 2021 06:27:56 +0000Zend_Feed<![CDATA[https://www.geogebra.org/m/kQKduVEY]]>
https://help.geogebra.org/topic/how-to-color-a-spherical-triangle#comment-305210
Wed, 26 May 2021 09:56:20 +0000<![CDATA[What a complex expression. Thank you very much.]]>
https://help.geogebra.org/topic/how-to-color-a-spherical-triangle#comment-305220
Wed, 26 May 2021 14:13:12 +0000<![CDATA[expresion is simple (1-u) (1-v) A+(1-u) v B+u (1-v) C +u v D with 0<=u<=1 0<=v<=1 is surface with A,B,C,D vertexes when C=D is a triangle the expression divided by its modulus is a spheric triangle sums and differences of the center selects the adequate position]]>
https://help.geogebra.org/topic/how-to-color-a-spherical-triangle#comment-305228
Wed, 26 May 2021 14:46:10 +0000<![CDATA[I've since come to understand what it means. Add two questions. 1. I think it might be possible to use the UnitVector command, but didn't work. Can you please explain why? Surface(A + R UnitVector((1 - u) (1 - v) (G - A) + (1 - u) v (C - A) + (1 - v) u (D - A) + v u (E - A)), u, 0, 1, v, 0, 1) 2. The result is related to the relative positions of the four points. I've tried convexhull command but it returns a locus, I can't get and sort the four points. Is there a way? Thank you very much.]]>
https://help.geogebra.org/topic/how-to-color-a-spherical-triangle#comment-305246
Thu, 27 May 2021 02:58:47 +0000<![CDATA[unitvector is a command not a function. Surface admits only functions. ie: max(f(x),g(x)) does not work, use (f+g+abs(f-g))/2 instead. Similar unitvector does not work use vector/abs(vector) instead reordering the four points you can get good quadrilateral like in R2. move G to the left of C,D use 1.01R for better view]]>
https://help.geogebra.org/topic/how-to-color-a-spherical-triangle#comment-305260
Thu, 27 May 2021 10:02:02 +0000<![CDATA[As for the UnitVector approach, I guess the problem is that UnitVector returns a vector object instead of a point object. It seems like there should be a simple way to convert a vector to a point, but I don't know how. Maybe then it would work. That said, I am even somewhat surprised that the Surface command accepts a point as the first argument. The manual only states Surface(<Expression>, <Expression>, <Expression>, ...) but not Surface(<Point>, ...), so maybe there is some automatic conversion. As for your ConvexHull problem, you can get the ordered list of points via First(<Locus>, Length(<Locus>)-1), but there is a general problem with this approach. ConvexHull seems to return only a 2D locus, the convex hull of the projection of the points into the x-y-plane. Which means that not only would you have to match those points to the 3D version again (which would be doable though) but the result would often not be the one you want as you wouldn't necessarily get the "spherical convex hull" this way. Btw, I assuming that you actually want a "spherical convex hull", i.e., it would become a triangle if one point lies within that "spherical convex hull". (Otherwise it'd not be quite clear which of the possible quadrangles would be the "correct" one.)]]>
https://help.geogebra.org/topic/how-to-color-a-spherical-triangle#comment-305262
Thu, 27 May 2021 09:50:41 +0000<![CDATA[https://help.geogebra.org/t...]]>
https://help.geogebra.org/topic/how-to-color-a-spherical-triangle#comment-305264
Thu, 27 May 2021 10:09:07 +0000<![CDATA[artydent, Thanks.]]>
https://help.geogebra.org/topic/how-to-color-a-spherical-triangle#comment-305268
Thu, 27 May 2021 11:15:28 +0000<![CDATA[newer, shorter, nicer method in attached for surprising even more to Artydent]]>
https://help.geogebra.org/topic/how-to-color-a-spherical-triangle#comment-305272
Thu, 27 May 2021 11:31:01 +0000<![CDATA[This vector method is beyond my comprehension. But amazing. Thanks.]]>
https://help.geogebra.org/topic/how-to-color-a-spherical-triangle#comment-305310
Fri, 28 May 2021 04:46:19 +0000<![CDATA[@ artydent I did not follow the full plot, but multiply a vector by indentity makes a point - as long as it lasts]]>
https://help.geogebra.org/topic/how-to-color-a-spherical-triangle#comment-305318
Fri, 28 May 2021 10:45:35 +0000<![CDATA[Very nice. It's a base transformation (matrix m1), transforming the unit vectors onto the vectors AC, AD, AE, which means that the spherical triangle is the (shifted to center A) transformation of the octant of the unit sphere (surface b) which can be expressed nicely with spherical coordinates.]]>
https://help.geogebra.org/topic/how-to-color-a-spherical-triangle#comment-305330
Fri, 28 May 2021 15:56:48 +0000<![CDATA[Good to know, thanks. I am still somewhat confused sometimes about how points/vectors/matrices work in GeoGebra and when there is some automatic conversion and when not. In this particular case it was a different problem though why it didn't work.]]>
https://help.geogebra.org/topic/how-to-color-a-spherical-triangle#comment-305332
Fri, 28 May 2021 16:11:03 +0000<![CDATA[Hi, mathmagic, Is it feasible to generate a spherical pentagon(5 points) with an expression similar to this one? (1-u) (1-v) A+(1-u) v B+u (1-v) C +u v D with 0<=u<=1 0<=v<=1]]>
https://help.geogebra.org/topic/how-to-color-a-spherical-triangle#comment-305376
Sun, 30 May 2021 10:40:37 +0000<![CDATA[Demasiado lento por exceso en la cantidad de cálculos posible es, pero no es realmente útil]]>
https://help.geogebra.org/topic/how-to-color-a-spherical-triangle#comment-305392
Sun, 30 May 2021 20:33:50 +0000<![CDATA[Maybe my computer's configuration is too low to display properly. But it's much smoother after I set surface d to invisible. I never thought it would be possible to express this surface in terms of parametric equations, This is really amazing. Thank you for showing me the beauty of mathematics and GGB.]]>
https://help.geogebra.org/topic/how-to-color-a-spherical-triangle#comment-305398
Mon, 31 May 2021 03:40:37 +0000<![CDATA[creo que ahora funciona mucho mejor https://www.geogebra.org/m/nzds5za5]]>
https://help.geogebra.org/topic/how-to-color-a-spherical-triangle#comment-305406
Mon, 31 May 2021 10:24:29 +0000<![CDATA[now it seems easy ]]>
https://help.geogebra.org/topic/how-to-color-a-spherical-triangle#comment-305412
Mon, 31 May 2021 16:40:31 +0000<![CDATA[Definitely the best one. Thanks.]]>
https://help.geogebra.org/topic/how-to-color-a-spherical-triangle#comment-305424
Tue, 01 Jun 2021 01:29:22 +0000<![CDATA[After a few hours of study, I finally understood your work. It's beautiful. Thanks.]]>
https://help.geogebra.org/topic/how-to-color-a-spherical-triangle#comment-305428
Tue, 01 Jun 2021 09:50:14 +0000<![CDATA[I used your method to make a similar one, but with a gap. ]]>
https://help.geogebra.org/topic/how-to-color-a-spherical-triangle#comment-305430
Tue, 01 Jun 2021 10:57:27 +0000<![CDATA[GG crea una reticula de puntos en funcion de los parametros u y v algunas veces la retícula va desde 0 hasta 0.99 ie. Esto significa que se ve una fina línea porque no se alcanza el recorrido al 100% esto se remedia poniendo un valor del parámetro ligeramente superior al teórico. ie: b = Surface(1.01(A + u ((f(v), g(v), h(v)) - A)) / abs(A + u ((f(v), g(v), h(v)) - A)), u, 0, 1, v, 0, 1.01)]]>
https://help.geogebra.org/topic/how-to-color-a-spherical-triangle#comment-305434
Tue, 01 Jun 2021 13:21:34 +0000<![CDATA[Got it. Thank you!]]>
https://help.geogebra.org/topic/how-to-color-a-spherical-triangle#comment-305448
Wed, 02 Jun 2021 01:25:32 +0000