Ask MetaFilter questions tagged with geometry

What is a triangular graph with axes perpendicular to the sides called?

Peter Petridish — Wed, 28 Oct 2009 10:59:52 -0800

What is the graph or plot called which: - is an equilateral triangle - has three axes - each axes is perpendicular to a side of the triangle? Here is an example, but searching for "likelihood triangle" turns up nothing. I've never heard of that term before.

A triangle plot seems similar, but the axes are at 60 degree angles. Everyone in my laboratory agrees that they are difficult to easily interpret without practice.

Bonus question: Is there an R package which would create such a graph?

Thanks!

Geometry Wars Retro Evolved Controller Config

FusiveResonance — Fri, 18 Sep 2009 23:49:00 -0800

Geometry Wars Filter: Help configure Nyko Airflo PC game controller for Geometry Wars Retro Evolved (PC) My google fu is failing me. I would like to configure my Nyko Airflo game controller such that the left analog stick controls movement and the right analog stick controls firing.

Currently it is as follows:
Left analog stick controls movement
Right analog stick does nothing
Button 5 fires Up
Button 4 fires Left
Button 2 fires Right
Button 1 fires Down

Photoshop Question: is there a way to get a count of pixels contained within any (irregularly shaped) selection/layer?

unmake — Thu, 10 Sep 2009 17:20:29 -0800

Photoshop Question: is there a way to get a count of pixels contained within any (irregularly shaped) selection/layer? For example, is there something in Photoshop which, when I select a circle with a 10 pixel radius, will tell me that the area of the selection is ~314 pixels?

If not, are there any other applications for this task?

Four of the clock it was, so I as I guesse

zvs — Wed, 05 Aug 2009 12:57:54 -0800

How can I estimate the time that a photo was taken? I'm working on a rephotography project (the link is my profile website, if you want an idea of what I'm dealing with). I've gotten the hang of many of the common problems I encounter when duplicating photos, but one thing still gets me -- time of day. I try to estimate based on the angle of a shadow, but that usually only gets me within a three hour window, and I hate sitting around waiting for the sun to move.

I'm a good enough geometer that I can usually figure out what the angle of a shadow is relative to true north using Photoshop, a street map, and a protractor. I have the date each photo was taken. I know NYC is about 15 minutes off of true noon for the time zone, and I know the angle varies seasonally. How can I do the math?

Stained Glassy Collages?

soelo — Tue, 09 Jun 2009 11:30:09 -0800

What software can I use to make a photo collage using non-rectangular photos? I'd like to make a photo collage similar in layout to the cover of Sims 3 using triangles instead of diamonds. I currently use PhotoScape and have access to but haven't used PaintShop, but I am willing to try some other software if it can do what I want.

I'd like to be able to create my own layout using triangles (or any other non-rectangular shape), select pictures to insert and be able to resize and rotate to get exactly what I want aligned in the triangle. It will look a bit like stained glass with pictures instead of a solid color between the leading.

Is there some Windows compatible software that will let me do this easily? If it's spendy but has a free trial, I'll try it. I'd be willing to do the cropping and rotating before trying to insert the pic into the layout.

3D GeometryFilter: Is there a mathematical equation that defines relative lengths of objects at different depths of field for humans?

miasma — Sat, 16 May 2009 15:07:19 -0800

Is there an equation that defines the change in apparent size as a function of distance from the viewer? Basically, if I'm looking at a set of railroad tracks head on, if one plank is like 10 ft away, it appears to be one size. The same plank 20 ft away appears smaller. What is the relative size difference? Put another way, how big does a 1ft line appear to be at 10 ft, at 20 ft, etc.? Furthermore, is there an angle of convergence? Just like the planks on a railroad track will converge to a single point, if i wanted two planks at different distances to appear to be in the same overlapping plane, where would I need to place them?

Get thee gone, my polygon

soma lkzx — Tue, 31 Mar 2009 07:40:42 -0800

I've got a polygon of n points. How can I simplify out noisy edges? I have a bunch of ordered (x,y) pairs that make nice little polygons, but there're just too much data to be manageable. It'd be nice to average out some of the rougher bits into less points.

Most of the edges look like the heaviside step function, a.k.a. someone walking city blocks. Checking (x_i+1,y_i+1) vs. (x_i-1,y_i-1) and the rest of the diagonals could work out, but I'd really be into a more elegant/general algorithmic solution.

Less importantly but possibly related, let's say I wanted to give these polygons smooth sides. Do I drop bezier curve after bezier curve? I also just met splines on wikipedia - should I just apply this natural cubic spline curve algorithm with (x₁,y₁) = (x_n,y_n)?

I'm currently working on this in Ruby, if that matters, but am open to pretty much anything.

Looking for a piece of art

doobiedoo — Thu, 05 Mar 2009 11:28:57 -0800

Hi I'm trying to find a piece of art - a series of lights attached to wooden arms whose tips trace some sort of toroidal geometry. At high speeds the armature disappears and the lights form volumes as luminous wireframes, like synchronised mechanical sparklers. It was on display at the Walsall Art gallery in Birmingham, UK sometime in 2004/5 I think. It's semi popular (no really it is!) but I can't think for the life of me what to google to get it, who made it etc.

spherical geometry!

klanawa — Wed, 04 Feb 2009 15:52:56 -0800

can you help me compute the area of a triangle on the sphere? i have this pretty much down:

the formula for the area is:

a = R^2 ((A+B+C) - pi)

where:

a is area
R is the radius of the sphere
A, B and C are the triangle's angles

where i'm stuck is finding the angles A, B and C. i'm starting from 3 geographic (lat,lon) points. i think i pretty much get the principle there (finding the normals to the planes represented by the lines between the three points, etc.). but i can't quite make the leap.

wolfram and the rest have helped with the theory somewhat, but this math retard needs a bit of step-by-step hand-holding. i've worn out google trying to find a site that doesn't make a lot of unreasonable assumptions about my competence as a mathmatician.

DIY Forced-Perspective wall-hanging art/mathematics advice sought.

jjjjjjjijjjjjjj — Fri, 09 Jan 2009 04:39:08 -0800

3-D folks, Mathematicians, and Artists: Trying to create my own Trompe-l'œil / forced perspective illusionary image to hang on my wall (e.g. the awesome parking garage signage everyone's already seen... more examples here, and here). I'm having trouble faking it with 2-D programs, and the math is puzzling me. So without going into too much detail, here are the facts:

1. Wanting to put artwork in a simple 90°/90°/90° corner where two walls meet a ceiling.
2. In theory: My ugly corner, plus this nice logo [svg d/l], equals this cool effect when viewed from the correct angle.
3. "correct angle" is pillow-height from the head of my bed... perhaps best visualized in this map/schematic/layout.

Having no proficiency of any kind in any 3-D package (which I suspect might make this quite easy), I resolved to figure it out with pencil and paper and then distort the three sections of the image accordingly by using a vector 2-D program (with which I do have "B-" proficiency). After many pitched hours of re-learning long-lost trigonometry (no sweat, really... glad for the opportunity), I have hit a brick wall that I need help breaking through. I suspect that there is a way to do this in Illustrator, but I'm at a loss for what it might be. CS2's neutered "3-D effects" were of no use to me either.

So, in summary: This is how the image is divided visually (just a sketch... not exact), and these are the wall assignments for each of the three pieces. I suspect that the final product will be distorted in ways superficially resembling this (completely speculation and not anything close to exact... visual reference only). Need to find a way -- hopefully repeatable, and ideally customizable to other viewing angles/corners -- to output this into three "distorted" vector files to be run on a plotter.

If anyone's got some advice to go on, I'd be very appreciative. If additional measurements/project files/clarifications would help, please do let me know. If I can find some easy and explainable way to pull this off, I'll throw a tutorial up on Instructables or something to help anyone who has a similar project/idea in the future. Thanks a ton.

(I know I could just do the old "Trace the projected transparency onto the wall" trick, but I was wanting to cut this out of vinyl on a plotter... and for that I'm going to need 3 vector files... one for each wall.)

creating circles from rectangles

brandnew — Sun, 17 Aug 2008 06:49:39 -0800

Math filter: How many equally sized rectangles will fit into a circle, and how should I arrange them in order to make the best-looking approximation? I want to create an approximate circle from a number of equally-sized rectangles. How do I do this for an arbitrarily sized rectangle or circle?

For example, suppose I have 100 rectangles of size 5x6 (or generally LxW). I want to create the best approximation of a circle using these rectangles. How can I calculate what the resulting radius of the circle will be, and how do I arrange the rectangles to achieve the best approximation?

The inverse question is also useful: If I want to create an approximate circle with a radius of 31, how many rectangles of size 5x6 (or LxW) do I need, and how should I arrange them?

The general formula / strategy / algorithm would be most useful. But, if you have the answer for 100 rectangles of size 5x6, that would be good too. I'm also interested in the answering the same question for 25-30 rectangles of size 11x11.

Best way to tile a sphere ?

silence — Mon, 02 Jun 2008 07:07:53 -0800

How can I tile a sphere using the minimum number of differently shaped units? I have a 3 meter diameter sphere and I need to tile it using units that are each about 400 square cm (ie like a 20 x 20cm square). The units must be flat (ie, not spherical triangles). I'm currently thinking of using a geodesic tiling, but a (for instance) a 5V geodesic tiling results in (i think) 6 different tile shapes, and also has the problem that the density of tiles isn't constant over the surface - there are obvious visual artefacts where the tiles bunch up. I need to try to minimise the number of different types of unit, and to optimise the appearance so that it's as even as possible. Are there any better ways of tiling a sphere?

I'm sick of the city.

grrlaction — Sun, 04 May 2008 18:11:47 -0800

How far would I need to travel from a tower 100 feet high before the sight of it would become obscured by the horizon? I'm wondering, also, where in America I could go and have literally no break in my line-of-sight. I'm tired of being crowded in by buildings.

Help me find this geeky kids' book!

rivenwanderer — Mon, 31 Mar 2008 23:13:54 -0800

I read a book sometime in elementary school (early/mid 90's) that I've been trying to find. It had to do with geometry and math and platonic solids and origami (I believe there were several nods to Flatland). The plot had something about evil army men toys and a boy having a fever dream. I think the cover had a picture of the boy riding a manta ray. I know this sounds like something I dreamed up, but I know it was real! Anyone recognize it? I've googled for various keywords to no avail.

It's been 24 years. I give up.

mecran01 — Sun, 06 Jan 2008 20:03:06 -0800

My geometry teacher in high school in 1984 showed us this puzzle. I was only half paying attention, but I believe the goal was to draw a line that intersected each segment only once. I was only half paying attention, but I believe the goal was to draw a line that intersected each segment only once. The line you drew could intersect itself. I have been doodling with this thing, off and on for 24 years.

Does anyone know the origin of this puzzle? I saw it in an IQ test. AFAIK, the solution, if there is one, has something to do with drawing a line that crosses the point(s) where two different segments meet, and there being some sort of indeterminacy about whether the line one drew intersected one point or another.

Anyway, I'm giving up. I need closure.

Mr. Farrer, who taught at Alta High School in Sandy, Utah: you win, and I apologize for not paying closer attention.

Synergetic Geometry. Where?

goalyeehah — Mon, 27 Aug 2007 20:18:51 -0800

Does anyone teach a course in Synergetic Geometry in Los Angeles??? In the U.S.???? I am looking to take classes relating to Buckminster Fuller's Synergetic Geometry. I doubt that any courses of this are being taught through traditional educational system. Are any classes being taught in Los Angeles, California or the rest of the country?

How many balloons would it take to fill a room?

nilihm — Tue, 17 Jul 2007 10:56:22 -0800

Packing efficiency of 9" balloons? I know how many play pen balls fill a room. I also know the cost ($8,272.6 for a small bathroom). So how about balloons?

How would one model the number of 9" balloons required to fill a given volume? What's the proper term for "balloon," anyway (the closest I've found is "prolate spheroid")? I don't expect a solution to the minimal packing problem, just a well-reasoned estimate that assumes random placement. Oh, and these balloons will be filled the old-fashioned way.

Thank you!

Two spheres colliding

RobotHero — Sun, 10 Jun 2007 14:42:06 -0800

Help me with the math of two spheres colliding I'm making a flash game, where I want two circular objects to collide in a half-way realistic fashion, like pool-balls.

As I understand it, when two equal-mass balls collide, assuming a perfectly elastic collision, then the two balls will switch momentum along an axis formed by their relative positions.

So what I have for variables is:
x1 y1 : the position of ball 1
x2 y2 : the position of ball 2
sx1 sy1 : the velocity of ball 1
sx2 sy2 : the velocity of ball 2

I want to be able to calculate what sx1 and sy1 should be after a collision. (And likewise for sx2 and sy2, but it would be the same method for both balls)

So, by subtracting x1 and y1 from x2 and y2, I get
tx ty : the position of ball 2, relative to ball 1

I need to represent sx1 and sx2 with two vectors, one parallel to [tx,ty] and one perpendicular.

sx1 = tx*A + ty*B
sy1 = ty*A - tx*B

A is the parallel and B is the perpendicular.

If I can solve for A and B, then I can replace the A from ball1 with the A from ball2, and vice-versa, and my new values would be:
sx1 = tx*A2 + ty*B1
sy1 = ty*A2 - tx*B1

Is this a good approach?

Plus it's been a few years since I've done serious math, so I don't remember all the tricks to isolate A and B. So far I've got this far:
sx1=tx*A - ty*sy1/tx + ty^2*A/tx

3D Trig question

pooya — Wed, 09 May 2007 08:19:20 -0800

3D Trig question: I have a 2D square in 3D space (a Face). I know the positions of the four corner vertices in form x,y,z. How do I calculate the rotation in degrees (Euler angles) as relative from the center of the face? I want to end up with degrees of rotations around x-axis,y-axis,z-axis. Bonus if you can write it in pseudocode.

How can I work out if a point x,y,z is contained by a cone ?

matholio — Sun, 14 Jan 2007 17:33:39 -0800

How can I work out if a point x,y,z is contained by a cone ? I'm exploring some 3d programming, but sadly geometry is not my strong point.

I can define a cone object :

P1(x,y,z) - point of cone
P2(x,y,z) - centre of the base of cone
R1 - radius of the base.

How do I test if a point P3(x,y,z) is inside the surface of the cone ?
If it is inside the cone, how do I determine the closest point on the surface of the cone to P3 ?

I'd like to write a generic function so I can reuse it in other programming languages.

I'd prefer the cone base to be an elipse, I guess I could add a second raduis and rotation around the x-axis, but I'm out of my depth already.
I've looked through wikipedia and wolfram's but the crazy notation they use are all but meaningless to me.

Thanks

rotation shmotation

NGnerd — Mon, 23 Oct 2006 16:37:00 -0800

Vector Geometry Filter: I'm working in matlab and need to transform a surface to match an arbitrary angle. I have the unit vector of the new normal (and the original normal is in the Z axis (0 0 1))...however i'm not sure how to rotate one normal to another (i know, i know, it sounds very simple really...) So the real problem is that the orders of rotation cannot be mixed around. Matlab allows you to rotate a surface using an angle of rotation and an arbitrary vector...so theoretically i could find a single axis and angle that would allow me to do the rotation in one operation (and thus get rid of the orders), but i'm finding the math is a beyond my head. I've also tried transforming the original data to a new plane but matlab isn't soo happy with that technique (and i've had a hard time tracking down a good equation for that as well). Any suggestions would be much appreciated....help me obi wan kenobe, you're my only hope.

Whatchamacallit

azul — Mon, 18 Sep 2006 10:02:55 -0800

Does anybody remember those circular templates that makes infinite radial patterns with colored ball pens? They had concentric holes for which to anchor a ballpoint against an outer axle, and then you change colors corresponding with the holes? What do you call those? Is it called anything at all?

Too lazy to take a hard-right.

Jimbob — Fri, 25 Aug 2006 04:45:21 -0800

Do the curved triangular shapes made when cars (or even pedestrians) take "shortcuts" at T-junctions (seen here near my house and here in Western Sahara, although this seems like a deliberate one) have a name? What's the mathematics behind them? The psychology?

Geometry term a TV tube's front-profile shape?

skyboy — Wed, 02 Aug 2006 11:40:39 -0800

Is there a geometric name for the "bulging rectangle" shape, most commonly found as the front-profile outline of classic (CRT-type) TV tubes? You know: that rectangular "television" shape with curved left & right sides, and slightly less-curved top & bottom sides.

This shape is now often found as an icon on computer monitor/projector menus to symbolize "pincushion control", among other things. Is there a term in math (geometry) to describe this particular shape?

SpheroidTruncatedIcosahedronFilter!

i_am_joe's_spleen — Fri, 09 Jun 2006 18:57:10 -0800

My daughter wants to decorate a sphere in a football pattern. How do we determine the correct side length for the pentagons and hexagons, given a sphere of diameter n?