https://community.wolfram.com RSS Feed for Wolfram Community showing questions tagged with Architecture sorted by active. https://community.wolfram.com/groups/-/m/t/2294199 Hi everyone!! So for a project in uni I have to code a floor plan in Mathematica. It's been going great, but now I have a big problem I've been trying to solve for the last two days, but failed miserably. As you can see in the screenshot below there is a wall in room three, that is not there anymore when the walls are extruded, Plus there is this dent in the other wall... And I don't know how to fix it. I really need your help, thank you so much! (I've gone ahead and attached the whole file as well as the screenshot below.) ![Wall in Room 3 is gone when extruding walls][1] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Bildschirmfoto2021-06-20um12.38.23.jpg&userId=2294185 Florian Weinke 2021-06-20T10:49:28Z https://community.wolfram.com/groups/-/m/t/1799002 Hi all, I'm looking for an equation that can produce a series of lines of equal lengths that are perpendicular from their midpoint to point "x", by dividing curve "a" a number of times. I haven't yet been able to come up with a solution that isn't recursive or that subdivides the curve exactly. Would really appreciate being pointed in the right direction as I'm at a little bit of a loss. Thanks, Laurens ![Tangent problem][1] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=tangent_problem07.jpg&userId=1798769 Laurens Jacobs 2019-10-01T17:14:49Z https://community.wolfram.com/groups/-/m/t/1632078 Last month, a TV program "[Chico Will Scold You][1]" of Japan public broadcasting picked up the Tokyo subway. The TV show introduced the 3 D model of Tokyo subway, "[Tokyo Arteria][2]" which created by Takatsugu KURIYAMA. I was influenced by the beauty, so I tried to make something similar with Mathematica. Because I create it using Mathematica's Tube function, I named it "Tokyo Tube". ![enter image description here][3] There are 13 subways in Tokyo. I gathered the information of latitude, longitude and depth (from the ground) of all stations (287 stations) from web and book. I will explain on the Hanzomon line as an example. The figure on the left shows connecting stations by the shortest straight line. However, the actual route is a more complicated. The figure on the right is the result of Google Map route search. ![enter image description here][4] The TV program explained why Tokyo's subway is so complicated. The answer is there is the law that if you buy land, you will have the right of both the ground and the underground. So it is necessary to pay the land fee to all of them to get through a subway. In order to avoid this, a subway runs under the roads owned by the state or municipality because their underground can be used free of charge for public interest purposes. In addition, the roads in Tokyo are not straight because the roads are made by filling roads and waterways that were made in a radial shape based on the Edo Castle during the Edo period. - From the result of Google Map route search, I search the route position using PixelValuePositions function. ![enter image description here][5] ![enter image description here][6] - I sort the points by y - axis, latitude. So the first point is the starting station, the Shibuya Station and the last point is the terminal station, Oshiage Station. However, just connecting the sorted points does not follow the route (left figure). So, I use FindShortestTour function to rearrange according to the route, and select about 100 points from them for the Graphics3D (right figure). p2 = Sort[p, #1[[2]] < #2[[2]] &]; s = FindShortestTour[p2, 1, Length[p2]]; p3 = Append[ Take [p2[[Last[s]]], {1, m = Length@Last[s], Round[m/100]}], p2[[-1]]]; {ListLinePlot[p2], ListLinePlot[p3]} ![enter image description here][7] These points are converted into 3 D display based on the information of latitude, longitude and depth of all stations above. The actual map obtained by GeoGraphics function is pasted on the top surface. ![enter image description here][8] The following is the result of carrying out this work for 13 lines. ![enter image description here][9] The figure below shows the Ginza Line, the oldest in business, and the Oedo Line, the newest. The subway created later is deeper. And the Roppongi Station on the Oedo Line is at the deepest position 42.3 meters underground. ![enter image description here][10] In addition, the Fukutoshin Line, which is the most recently full-opened, was created between the Marunouchi Line and the Shinjuku Line. The distance between the lines is about 11 cm at the shortest distance. Now, the law that it can be used free of charge at a place deeper than 40 meters if it is the public interest purpose was made. The Linear Chuo Shinkansen, which digs underground straight in the urban area, will aim to open in 2027. I have attached a notebook of Graphics3D "Tokyo Tube", so please rotate it. [1]: http://www4.nhk.or.jp/chikochan/ [2]: https://www.youtube.com/watch?v=eW59JgzyH70 [3]: https://community.wolfram.com//c/portal/getImageAttachment?filename=1040801.jpg&userId=1013863 [4]: https://community.wolfram.com//c/portal/getImageAttachment?filename=287302.jpg&userId=1013863 [5]: https://community.wolfram.com//c/portal/getImageAttachment?filename=796108.jpg&userId=1013863 [6]: https://community.wolfram.com//c/portal/getImageAttachment?filename=103603.jpg&userId=1013863 [7]: https://community.wolfram.com//c/portal/getImageAttachment?filename=1044204.jpg&userId=1013863 [8]: https://community.wolfram.com//c/portal/getImageAttachment?filename=895805.jpg&userId=1013863 [9]: https://community.wolfram.com//c/portal/getImageAttachment?filename=892206.jpg&userId=1013863 [10]: https://community.wolfram.com//c/portal/getImageAttachment?filename=101107.jpg&userId=1013863 Kotaro Okazaki 2019-03-14T13:29:19Z https://community.wolfram.com/groups/-/m/t/1037946 What do you think of the idea of automatically judging if a piece of data was beautiful? This could mean the data in an image (ImageData) or maybe the result of a computation (e.g. CellularAutomaton), or anything, although I am thinking of a list or an array of numbers primarily. My first thought was that there are many filters for image processing, but I don't know which might be useful. The next thing I think of is mathematical transforms. For example, taking the Fourier or Hadamard transform you expect the coefficients to decay, and if they don't then that would not be nice. This code deletes the constant term and does some measure of the variance, using Mean as a shortcut to counting the 0's and 1's, those closer to the min than the max respectively without knowing the length or dimension. (Note Fourier does not assume the size is a power of 2 but Hadamard does.) FourierBeauty[list_] := Mean[1. - Round[Rescale[Abs[Rest[Flatten[Fourier[list]]]]]]] Maybe for an image this might not be bad. Here is what it picks out of the ExampleData test images: Grid[{#, ExampleData[#]} & /@ MaximalBy[ExampleData["TestImage"], FourierBeauty[ ImageData[ Binarize[ ImageResize[ ColorConvert[ExampleData[#], "Grayscale"], {64, 64}]]]] &], Frame -> All] ![enter image description here][1] but here are the CAs it likes the most. MaximalBy[Range[0, 255], Sum[FourierBeauty[ CellularAutomaton[#, RandomInteger[1, 2^8], {{0, 2^8 - 1}}]], 100] &]->{1, 3, 5, 17, 57, 87, 119, 127} [1]: http://community.wolfram.com//c/portal/getImageAttachment?filename=fourier-beauty-image.jpg&userId=23275 Todd Rowland 2017-03-23T02:46:11Z https://community.wolfram.com/groups/-/m/t/796356 Hello to all, I would like to share with you the following video ([Building unimaginable shapes][1] ) to me has left impressed by the results that are obtained, the question I have is, there are tools in Mathematica to do what is explained in the video? I mean essentially fold a cube at any point of their edges. I would like to receive feedback regarding any topic that is covered in the video say, greetings and thanks for advance. [1]: https://www.youtube.com/watch?v=dsMCVMVTdn0 Luis Ledesma 2016-02-19T03:14:06Z https://community.wolfram.com/groups/-/m/t/547218 Hello friends I hope you are well, I tell them the reason why today I write, after seeing a video where they explain some things about the [Weaire–Phelan structure][1], I wonder, can be such a structure in mathematica?, I search on wolfram alpha on the Weaire–Phelan structure, but I got nothing, maybe introduced it evil in that search engine , if someone can tell me how to make that structure in mathematica is grateful, I intend to do something further along with this structure, greetings to all. ![enter image description here][2] [1]: https://en.wikipedia.org/wiki/Weaire%E2%80%93Phelan_structure [2]: /c/portal/getImageAttachment?filename=12-14-hedral_honeycomb.png&userId=11733 Luis Ledesma 2015-08-13T18:31:26Z https://community.wolfram.com/groups/-/m/t/550930 Hi, I have drawn these two tiling the plane pattens (A & B), are these just considered variations of some of the current, or are these new? Geometrically they are appear to be different (but with similarities) to all the ones I have seen. Type A is similar to type 4, but my type A has three equal sides, and the other two make the same length as one of the equal. Type 4 has four equal sides. Type B is similar to type 8, but my type B has two 90 deg angles and the primary unit can overlap its self at each quadrant and maintain the patten. I would be interested in any opinion about these two Plane Tile Pattens. Thanks! Reece Hill 2015-08-21T11:20:42Z https://community.wolfram.com/groups/-/m/t/529314 Hello, I will wave the novice flag first and admit I am new to the use of Mathematica. I have the code of a shape I want to export as a *.dxf file , but after seeing some youtube tutorials and seeing some threads over here, i haven't managed to get it right. Manipulate[ Show[calabi[0, 0, 0, alpha, 0, clr], ViewPoint -> {-1.4, 0, 1.4}, Lighting -> If[clr, {{"Ambient", GrayLevel[.5]}, {"Directional", White, ImageScaled@{0, 0, 2}}}, {{"Ambient", GrayLevel[.25]}, {"Directional", RGBColor[0.5, .5, 1], ImageScaled@{0, 1, 0}}, {"Directional", RGBColor[1, 0.5, 0.5], ImageScaled@{1, -1, 0}}, {"Directional", RGBColor[0.5, 1, .5], ImageScaled@{-1, -1, 0}}}], PlotRange -> 1.2, Boxed -> False, Axes -> False, SphericalRegion -> True, ImageSize -> {450, 450}, ViewAngle -> \[Pi]/4.5], {{alpha, \[Pi]/4, "projection angle"}, 0, 2 Pi}, {{clr, False, "color code surface"}, {True, False}}, Initialization :> { u1[a_, b_] := .5 (E^(a + I*b) + E^(-a - I*b)); u2[a_, b_] := .5 (E^(a + I*b) - E^(-a - I*b)); z1k[a_, b_, n_, k_] := E^(k*2*Pi*I/n)*u1[a, b]^(2.0/n); z2k[a_, b_, n_, k_] := E^(k*2*Pi*I/n)*u2[a, b]^(2.0/n); n = 5; calabi[x_, y_, z_, \[Alpha]_, t_, c_] := Table[ With[{alpha = \[Alpha] - t}, ParametricPlot3D[ Evaluate@{Re[z1k[a, b, n, k1]] + x, Re[z2k[a, b, n, k2]] + y, Cos[alpha]*Im[z1k[a, b, n, k1]] + Sin[alpha]*Im[z2k[a, b, n, k2]] + z}, {a, -1, 1}, {b, 0, \[Pi]/2}, Boxed -> False, Axes -> False, PlotPoints -> 15, PlotStyle -> If[c, RGBColor@{If[k1 == 0 && k2 == 0, 0, Rescale[k1, {0, n - 1}]], If[k1 == 0 && k2 == 0, 0, Rescale[k2, {0, n - 1}]], If[k1 == 0 && k2 == 0, 1, 0]}, {RGBColor[.5, .5, 1], Specularity[White, 128]}], MaxRecursion -> 0, PerformanceGoal -> "Speed", Mesh -> None]], {k1, 0, n - 1}, {k2, 0, n - 1}]; }, SynchronousInitialization -> False] ![A screencap of the desired figure][1] [1]: /c/portal/getImageAttachment?filename=ScreenShot2015-07-11at23.53.12.png&userId=528896 I understand how ungrateful it is to use a first post asking for help but I've hit a dead end with this. Any help would be much appreciated. Best, Carlos Carlos Ortega 2015-07-12T10:30:20Z https://community.wolfram.com/groups/-/m/t/386677 Hi, I'm an architect I don't know much about mathematica but I'm trying to learn how to use it. The geometry is quite interesting for me to use in architectural forms so I need to export some demonstrations into 3ds models. Is there anybody who can help me about it? Aysu Aysoy 2014-11-10T08:15:04Z https://community.wolfram.com/groups/-/m/t/486430 Hello, I am new here not sure how to plot this > x=?2.2116*10^(?15)*y^(8)+1.3603*10^(?12)*y^(7)-3.42899*10^(?10)*y^(6)+4.56861*10^(?8)*y^(5)-3.45065*10^(?6)*y^(4)+1.39347*10^?4*y^(3)-0.00284795*y^(2)+0.0911615*y+24.5 t hen rotate it around by 360 or 2 pi to form a 3d object. May someone please help me graph this, it has a upper bound of 179.8 and lower bound of 0. This is supposed to form the famous building The Gherkin. Thanks in advance. I have tried a few times but didn't work properly. ![enter image description here][1] [1]: /c/portal/getImageAttachment?filename=1.png&userId=486415 Bob H 2015-04-26T01:45:03Z https://community.wolfram.com/groups/-/m/t/446059 Has anyone implemented weighted centroidal Voronoi tesselations? I'm hoping someone has, so I don't have to do it myself. Here's a reference for the interested: http://cs.nyu.edu/~ajsecord/npar2002/npar2002\_ajsecord\_preprint.pdf . Christopher Carlson 2015-02-21T02:05:53Z https://community.wolfram.com/groups/-/m/t/443135 Hi, I can't understand why the matrix **KKt** is not symmetric, and I can't see where I'm doing wrong. A second point is, if it's possible, to write **KKt** in a better and faster way. Thanks! Coordinate := Import["C:\\Users\\Riccardo\\Desktop\\Pannello \ Muratura\\dati\\coordinate.txt", "Data"] Coordinate = Coordinate[[1 ;; Length[Coordinate]]]; Elementi := Import["C:\\Users\\Riccardo\\Desktop\\Pannello \ Muratura\\dati\\elementi.txt", "Data"] Elementi = Elementi[[1 ;; Length[Elementi]]]; Materiali := Import["C:\\Users\\Riccardo\\Desktop\\Pannello \ Muratura\\dati\\materiali.txt", "Data"] Materiali = Materiali[[1 ;; Length[Materiali]]]; nc := 2(*Gradi di libertà*) nge := 3*nc(*gradi di libertà per elemento*) nd := Length[Coordinate] nn := nc*nd KKg := Table[0, {i, nd}, {j, nd}] ne := Length[Elementi] f := Table[0, {i, nn}] Table[{ nod1[i] = Elementi[[i, 1]]; nod2[i] = Elementi[[i, 2]]; nod3[i] = Elementi[[i, 3]]; xx1[i] = Coordinate[[nod1[i], 1]]; xx2[i] = Coordinate[[nod2[i], 1]]; xx3[i] = Coordinate[[nod3[i], 1]]; yy1[i] = Coordinate[[nod1[i], 2]]; yy2[i] = Coordinate[[nod2[i], 2]]; yy3[i] = Coordinate[[nod3[i], 2]]}, {i, 1, ne}]; triangolo[ i_] := {{xx1[i], yy1[i]}, {xx2[i], yy2[i]}, {xx3[i], yy3[i]}, {xx1[i], yy1[i]}} ListLinePlot[Table[triangolo[i], {i, 1, ne}], Frame -> True, Axes -> False, PlotStyle -> {Blue}, AspectRatio -> 1/1] EE = ReadList[StringToStream[Materiali[[1]]]][[1]] ni = ReadList[StringToStream[Materiali[[2]]]][[1]] tt = ReadList[StringToStream[Materiali[[3]]]][[1]] bx = ReadList[StringToStream[Materiali[[4]]]][[1]] by = ReadList[StringToStream[Materiali[[5]]]][[1]] CC = EE/(1 - ni^2)*{{1, ni, 0}, {ni, 1, 0}, {0, 0, (1 - ni)/2}} triangle[i_] := {{xx1[i], yy1[i], 1}, {xx2[i], yy2[i], 1}, {xx3[i], yy3[i], 1}} Table[{ A[i] = Det[triangle[i]], a1[i] = yy2[i] - yy3[i], a2[i] = yy3[i] - yy1[i], a3[i] = yy1[i] - yy2[i], b1[i] = xx3[i] - xx2[i], b2[i] = xx1[i] - xx3[i], b3[i] = xx2[i] - xx1[i], c1[i] = xx2[i]*yy3[i] - xx3[i]*yy2[i], c2[i] = xx3[i]*yy1[i] - xx1[i]*yy3[i], c3[i] = xx1[i]*yy2[i] - xx2[i]*yy1[i], B[i] = 1/(2*A[i]) {{a1[i], 0, a2[i], 0, a3[i], 0}, {0, b1[i], 0, b2[i], 0, b3[i]}, {b1[i], a1[i], b2[i], a2[i], b3[i], a3[i]}}, KKe[i] = (Transpose[B[i]].CC.B[i])*(tt*A[i]), gb1[i] = (nod1[i] - 1)*nc + 1, gb2[i] = (nod1[i] - 1)*nc + 2, gb3[i] = (nod2[i] - 1)*nc + 1, gb4[i] = (nod2[i] - 1)*nc + 2, gb5[i] = (nod3[i] - 1)*nc + 1, gb6[i] = (nod3[i] - 1)*nc + 2, ZZe[i] = SparseArray[{{1, gb1[i]}, {2, gb2[i]}, {3, gb3[i]}, {4, gb4[i]}, {5, gb5[i]}, {6, gb6[i]}} -> 1, {nge, nn}]} , {i, 1, ne}]; divisor = 100 SPart = FractionalPart[N[ne/divisor]]*divisor nparts = IntegerPart[(ne - SPart)/divisor] (*CHECK*)divisor*nparts + SPart - ne For[i = 1, i <= nparts, i++, KK[i] = Sum[ Transpose[ZZe[j]].KKe[j].ZZe[j], {j, 1 + (i - 1)*divisor, i*divisor}]]; KK[nparts + 1] = Sum[Transpose[ZZe[j]].KKe[j].ZZe[j], {j, 1 + ((nparts + 1) - 1)*divisor, ne}]; Table[MatrixPlot[KK[i]], {i, 1, nparts + 1}] KKt = Sum[KK[i], {i, 1, nparts + 1}]; MatrixPlot[KKt, PlotLabel -> {{"Symmetric Matrix -> "} {SymmetricMatrixQ[KKt]}}] Richard Dir 2015-02-16T14:22:57Z https://community.wolfram.com/groups/-/m/t/430092 My question is that: how to make a hole in a Graphics3D object? For example, there are two objects ,cub1 and cub2: cub1=Cuboid[{0,0,0},{20,2,20}]; cub2=Cuboid[{12,0,8},{17,2,17}]; Graphics3D[{cub1,cub2}] ![enter image description here][1] I want to make a window at the positon of the cub2, like under. DiscretizeRegion[RegionDifference[cub1,cub2]] ![enter image description here][2] But this object is obtained by use “DiscretizeRegion”, it is not a Graphics3D object, it is a MeshRegion object, and it make system too slow. Then, how to get a Graphics3D object? [1]: /c/portal/getImageAttachment?filename=2015-01-28_165029.jpg&userId=430077 [2]: /c/portal/getImageAttachment?filename=2015-01-28_165215.jpg&userId=430077 yang l 2015-01-28T09:00:47Z https://community.wolfram.com/groups/-/m/t/387917 ![How can I export this graphic into maya or 3ds?][1] [1]: /c/portal/getImageAttachment?filename=wcommun.JPG&userId=386657 Aysu Aysoy 2014-11-12T07:55:09Z https://community.wolfram.com/groups/-/m/t/392411 I need to use the same modal in grasshopper and manipulate it. I can only export the modal as a mesh but I need surface in rhino. I found this plug-in which helps mathematica to work with grasshopper: Mantis V 0.5 . But I don't think it is the right thing to use. Basically the question is: **Is it possible to write the code and manipulate it in grasshopper?** Here is the code: Manipulate[ Module[{\[CurlyEpsilon] = 10^-6, c1 = Tan[a1], c2 = Tan[a2], c3 = Tan[a3], c4 = Tan[a4], c5 = Tan[a5], c6 = Tan[a6]}, ContourPlot3D[ Evaluate[ c6 Sin[3 x] Sin[2 y] Sin[z] + c4 Sin[2 x] Sin[3 y] Sin[z] + c5 Sin[3 x] Sin[y] Sin[2 z] + c2 Sin[x] Sin[3 y] Sin[2 z] + c3 Sin[2 x] Sin[y] Sin[3 z] + c1 Sin[x] Sin[2 y] Sin[3 z] == 0], {x, \[CurlyEpsilon], Pi - \[CurlyEpsilon]}, {y, \[CurlyEpsilon], Pi - \[CurlyEpsilon]}, {z, \[CurlyEpsilon], Pi - \[CurlyEpsilon]}, Mesh -> False, ImageSize -> {400, 400}, Boxed -> False, Axes -> False, NormalsFunction -> "Average", PlotPoints -> ControlActive[10, 30], PerformanceGoal -> "Speed"]], {{a1, 1, "\!\(\*SubscriptBox[\(\[Alpha]\), \(1\)]\)"}, -Pi/2 - 0.01, Pi/2 + 0.01, ImageSize -> Tiny}, {{a2, 1, "\!\(\*SubscriptBox[\(\[Alpha]\), \(2\)]\)"}, -Pi/2 - 0.01, Pi/2 + 0.01, ImageSize -> Tiny}, {{a3, 1, "\!\(\*SubscriptBox[\(\[Alpha]\), \(3\)]\)"}, -Pi/2 - 0.01, Pi/2 + 0.01, ImageSize -> Tiny}, {{a4, 1, "\!\(\*SubscriptBox[\(\[Alpha]\), \(4\)]\)"}, -Pi/2 - 0.01, Pi/2 + 0.01, ImageSize -> Tiny}, {{a5, 1, "\!\(\*SubscriptBox[\(\[Alpha]\), \(5\)]\)"}, -Pi/2 - 0.01, Pi/2 + 0.01, ImageSize -> Tiny}, {{a6, 1, "\!\(\*SubscriptBox[\(\[Alpha]\), \(6\)]\)"}, -Pi/2 - 0.01, Pi/2 + 0.01, ImageSize -> Tiny}, AutorunSequencing -> {1, 3, 5}, ControlPlacement -> Left] ![enter image description here][1] [1]: /c/portal/getImageAttachment?filename=ScreenShot2014-11-18at1.19.24PM.png&userId=11733 Aysu Aysoy 2014-11-18T18:06:44Z https://community.wolfram.com/groups/-/m/t/386096 i find these operations really useful w the std. version used at work, but don't know how to do them or if they just aren't available in Online version: 1. delete all output cells in a Notebook (nb) 2. stop a computation (if it is taking too long) 3. kill the kernel, say for a runaway computation like an excessive recursion 4. copy an example from the documentation into your nb. There don't seem to be any In cell brackets in the documentation. On std versions, you an simply highlight the In cell bracket and do a copy/paste. 5. FrameLabel (a Plot fcn option) doesn't align the labels on the LHS & RHS frames. The documentation example has the frame labels properly aligned, but the exact same Plot cmd w FrameLabel option doesn't work in the nb, i.e. labels aren't correct. i've sent above to the Feedback, Cloud Dev. Team, but i thought i'd throw them out to the community. thanks! Carl Youngblut 2014-11-09T18:26:44Z https://community.wolfram.com/groups/-/m/t/289511 I'm chairman of a lighthouse non-profit. We own a brick caisson lighthouse whose form is that of a frustum 22 feet in diameter at the base and 21 feet in diameter at a height of 24 feet above the base. I'm trying to calculate the height of the resulting cone if the intersecting plane at the top were removed. Anyone have a suggestion? None of my queries, and I've tried many, produce anything that seems to be relevant. Keith Thompson 2014-07-08T14:50:42Z https://community.wolfram.com/groups/-/m/t/186965 How can I Insert this expression in mathematicaas shown in the photo? [img=float: right; width: 292px; height: 100px;]http://community.wolfram.com/c/portal/getImageAttachment?filename=dsfsdfsdfsdfds.PNG&userId=136046[/img] Ahmed Al-Ali 2014-01-18T15:01:58Z https://community.wolfram.com/groups/-/m/t/121507 [b]With 5 point-source lights in a square room, what is the optimal configuration for even lighting?[/b] To make this question concrete, say that each wall has length 1, the room has no height (i.e., two dimensional) and we have five identical lights that are pointsized and want to know the optimal placement that maximizes even lighting.  That could mean [mcode]f = 1/((x - x1)^2 + (y - y1)^2) + 1/((x - x2)^2 + (y - y2)^2) + 1/((x - x3)^2 + (y - y3)^2) + 1/((x - x4)^2 + (y - y4)^2) + 1/((x - x5)^2 + (y - y5)^2);[/mcode] a) maximizing the value of the minimal illumination [mcode]Minimize[f, {x,0,1},{y,0,1}][/mcode]or an integral measure like b) maximizing the total illumination where the brightest areas are considered as being some default value, e.g., the value of [mcode]Integrate[Min[f, f0], {x,0,1},{y,0,1}][/mcode] For an example configuration of light sources with [mcode]f = With[{n = 5}, Sum[1/((x - (.5 + .45 Cos[2 Pi i/n]))^2 + (y - (.5 + .45 Sin[2 Pi i/n]))^2), {i, 0, n - 1}]] [/mcode]and then here is the minimum illumination [mcode]NMinimize[{f, 0 <= x <= 1 && 0 <= y <= 1}, {x, y}] (*{14.349, {x -> 1., y -> 1.}}*) [/mcode]and here that point is shown on a contour plot [img=width: 360px; height: 359px;]/c/portal/getImageAttachment?filename=lights5.jpg&userId=23275[/img] For that configuration here is the integral (which I had to approximate with a Sum) [mcode]Sum[Min[1.2 (14.349), f], {x, 0.0001, 1, .01}, {y, 0.0001, 1, .01}]/10^4 (*17.2146*) [/mcode]I'd be interested in optimization approaches, but also aesthetic approaches, e.g., symmetries, angles, shadows, or patterns made by contour lines. To generalize, not only other numbers of lights, but try tacking on albedo of 50% so the wall reflect half of the light they receive. Todd Rowland 2013-09-10T16:45:23Z