Re: plotting plane & a triangle

*To*: mathgroup at smc.vnet.net*Subject*: [mg91347] Re: plotting plane & a triangle*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Sun, 17 Aug 2008 06:38:52 -0400 (EDT)*Organization*: The Open University, Milton Keynes, UK*References*: <g8685g$hse$1@smc.vnet.net>

skunkwerk wrote: > i'm working on developing some 3d software and I was hoping to use > mathematica to test the results of some of my code. Specifically, I'm > trying to visualize a plane and a triangle, to see if they intersect, > and if not, which side of the plane the triangle's points are on (I'm > calculating this using algebra, and need to check the results) > > so far I've done: > (the triangle) > pl1 = Graphics3D[{Polygon[{{-80.2576, -594.271, 224.043}, {-120.608, > -588.635, 221.101}, {1.32756, -598.31,261.244}}]}] > > (the plane) > pl2 = Plot3D[0.402395*x - 0.899308*y + 0.171241*z + 274.122 = 0,{x, -------------------------------------------------------------!!!!! *Syntax error*: must be double equal sign (==) to check for equality. Single equal sign (=) denotes the assignment operator (set a value to something). > -10000, 10000}, {y, -10000, 10000}] > > then: > Show[pl1, pl2] > > questions: > 1) the Polygon is displayed fine on its own, but the plane looks > completely flat along z=0 and is axis-aligned, so I'm not sure what's > wrong... <snip> You should write the equation of the plane as a function of two variables x and y rather than as an equation of three variables x, y, and z. Plot3D[5.83972 (-274.122 - 0.402395 x + 0.899308 y), {x, -1000, 1000}, {y, -10000, 10000}] Since, Solve[0.402395*x - 0.899308*y + 0.171241*z + 274.122 == 0, z] {{z -> 5.83972 (-274.122 - 0.402395 x + 0.899308 y)}} z /. %[[1]] 5.83972 (-274.122 - 0.402395 x + 0.899308 y) Regards, -- Jean-Marc