Signed area demo using hatching

*To*: mathgroup at smc.vnet.net*Subject*: [mg124374] Signed area demo using hatching*From*: Chris Young <cy56 at comcast.net>*Date*: Tue, 17 Jan 2012 06:00:19 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

Finally got the hatching demo working. Thank you, John, for pointing out that the problem was that only one Locator control specification is allowed in a Manipulate, although you can actually have as many locators as you want. Unfortunately, that means you have to divide up the list of locators, instead of just creating locators with the names you want. On Jan 16, 2012, at 6:04 PM, John Fultz wrote: Manipulate only supports one Locator control at a time, but your Manipulate has two. You need to reformulate it so that all four Locator points are in a single Locator control. The reason for this is because Manipulate doesn't actually use Locator, but LocatorPane, and overlapping LocatorPanes makes no sense. In an ideal world, Manipulate might attempt to combine the controls into a single LocatorPane, but there would still be limitations (for example, adding and deleting locators would make much less sense). Here's a demo of signed area using hatchlines. Wherever the red and green hatchlines cancel out, the net area is zero. This illustrates the "Surveyor's formula" for area, http://en.wikipedia.org/wiki/Surveyor%27s_formula#Area_and_centroid . Should rewrite the routine with options and defaults, but it's pretty fast, especially with PlotPoints at 30. http://home.comcast.net/~cy56/Mma/SignedArea.nb http://home.comcast.net/~cy56/Mma/SignedAreaPic1.png http://home.comcast.net/~cy56/Mma/SignedAreaPic2.png http://home.comcast.net/~cy56/Mma/SignedAreaPic3.png \[HorizontalLine]TriHatch[A_, B_, C_, mesh_, light_, plotPts_, opts___] := Module[ { orient, (* orientation of the triangles *) interior, (* inequalities for interior of triangle *) Q (* projection of first vertex onto opposite side *) }, orient = Sign[Det[{B - A, C - A}]]; interior[P_] := And @@ (If[orient > 0, # > 0, # < 0] & /@ {Det[{B - A, P - A}], Det[{C - B, P - B}], Det[{A - C, P - C}] }); Q = Projection[A - B, C - B] + B; RegionPlot[ interior[{x, y}], {x, -2, 2}, {y, -2, 2}, PlotStyle -> Opacity[0], ColorFunction -> (White &), Mesh -> Round[ mesh Max[Norm[C - B], Norm[Q - B], Norm[Q - C]], 1 ], MeshStyle -> Directive[ Opacity[0.5], If[orient > 0, Lighter[Green, light], Lighter[Red, light]] ], MeshFunctions -> {{x, y} \[Function] Det[{Q - A, {x, y} - A}]}, PlotPoints -> plotPts, BoundaryStyle -> None, Evaluate[opts] ] ]