Wikipedia:Reference desk/Archives/Mathematics/2012 January 30

= January 30 =

Was Galois Welsh?
The French word for Welsh is gallois. I wonder whether Évariste Galois had roots in Wales.
 * Quelle est l'origine du nom de famille d'Évariste Galois? Avait-il d'aïeux gallois?
 * PaulTanenbaum (talk) 02:03, 30 January 2012 (UTC)
 * C'est plutôt une question pour le Bureau linguistique. : ) 24.92.85.35 (talk) 02:30, 30 January 2012 (UTC)
 * No it's not. A question on the family background of a famous mathematician sits fine on the maths desk. However there's probably no answer: the time that a surname got attached to a family is almost certainly much further back than the family can trace its roots.    Sussexonian (talk) 04:12, 30 January 2012 (UTC)
 * I believe galois means someone from Gaul.  Sławomir Biały  (talk) 12:44, 30 January 2012 (UTC)
 * So perhaps Galois was Gallic? Qwfp (talk) 13:25, 30 January 2012 (UTC)

cube in perspective
So, I am trying to draw a cube with two point perspective, and it seems not to work. Somehow I have managed to do it slightly wrong every time, with the construction lines radiating out of the vanishing points and the horizontal lines joining them up, somehow the back edge of the cube is always at a slight angle. I have tried drawing it over and over with different vanishing points, different scales, putting the lines in in a different order to see if I'm working them out wrong, so far as I can tell, there must be some complex calculation as to where the two ends of the cube have to be drawn and what angle the construction lines there have to be for it to work, but I cannot seem to work out what that is. Can anyone see where I am going so wrong? http://i1067.photobucket.com/albums/u437/Kitutal/wrongcube.png

I've tried drawing the back line in straight to start with, but if I do that, then work out the rest from there, two of the lines don't quite line up with their vanishing points...

148.197.81.179 (talk) 16:10, 30 January 2012 (UTC)

Don't worry, I've fixed it now, turns out the drawing guide I was copying from didn't think to mention that if the horizon was not in the exact centre, which it wasn't on their example, three point perspective automatically comes into play, and since I wasn't compensating for that, hence why the last line drawn was slightly off. Thanks for all your help. 148.197.81.179 (talk) 16:27, 30 January 2012 (UTC)

But one thing it doesn't tell me, anyone have any idea how to work out where the vanishing points should go, to avoid getting squashed and distorted looking shapes? 148.197.81.179 (talk) 16:41, 30 January 2012 (UTC)


 * Not really. Since "squashed and distorted" are in the eye of the beholder, it's all a judgement call. StuRat (talk) 01:34, 31 January 2012 (UTC)


 * The correct vanishing point for a family of parallel lines is the intersection of the parallel line through the viewer's eye with the paper. If the drawing is viewed from any other location, the perspective will be wrong. -- BenRG (talk) 03:18, 1 February 2012 (UTC)


 * No three-point perspective gets involved here. Once you've drawn two 'vertical' edges of the cube parallel, and perpendicular to the horizon line, the third and fourth one must be parallel to them, too. In the 3D projection, each set of parallel lines from 3D space projects either
 * to a set of parallel lines in 2D, if and only if the lines are parallel to the drawing plane, or
 * to a set of lines meeting all in one point (concurrent lines).
 * In the latter case the point is called a vanishing point.
 * For every direction of parallel lines in 3D there exists either a unique direction of their parallel images on the plane or a unique vanishing point.
 * If you draw a city block of buildings, say File:McMasterUMedical.jpg, almost all their non-vertical edges belong to two directions, so we say you have two-point perspectve, just because there are two most important vanishing points in the picture. However, if those buildings were built at different angles, then you would have four or dozen vanishing points (see e.g. File:Carlb-fogo-newfoundland-2002.jpg or File:Masouleh.jpg). But it is still the same perspective, so there's essentially no such thing as 'one point', 'two point' or 'three point' perspective—there's always that many vanishing points, as you have parallel lines families, which you want do depict.
 * If you draw a room with a regular tiling on the floor, there will be one vanishing point for each tile edge direction: two vanishing points for square tiling (see File:Evensong in York Minster.jpg for example), three v.p. for hexagonal tiling (File:Graphene xyz.jpg), six fo snub square tiling etc.
 * All vanishing points for lines parallel to a given plane in 3D form a single perspective line in 2D. This is a vanishing line of all planes parallel to the given one, and if the plane is considered horizontal, then the line is called a horizon.
 * Having said all of that, we know your image has no third vanishing point. All vertical edges of the cube must be vertical on the drawing. If they are not, there must be some graphical error. What error is it? It is wrong position of the upper green line. Its right end is one pixel too high. Due to a small angle between the green and yellow line this tiny offset of the endpoint caused relatively large shift of the crossing point, which results in a significant slope of the rear cube's edge.
 * CiaPan (talk) 07:36, 1 February 2012 (UTC)
 * You're imagining that the cube has perpendicular edges and the canvas is perpendicular like buildings are commonly done. If for instance the canvas is at an angle to the perpendicular and they are looking down at the cube from an angle it will have three perspective vanishing points. You get the same effect with a building looking at a corner if you point a camera upwards rather than straight on. Dmcq (talk) 10:06, 1 February 2012 (UTC)


 * I'm not sure what you mean by 'perpendicular'. If is is 'orthogonal to each other' then OF COURSE YES, I assume that, because otherwise the 3D figure would not be called a cube. If it is 'vertical' it the sense 'orthogonal to a horizontal plane', then also OF COURSE YES, I assume that, because otherwise the perspective line would not be called a horizon. And OF COURSE I assume the projection plane is 'vertical' i.e. parallel to four of the cube's edges, because
 * OP starts his/her story with 'I am trying to draw a cube with two point perspective ',
 * OP has drawn three edges parallel to each other and perpendicular to the horizon line,
 * OP complains about the fourth edge in the construcion not being parallel to the three
 * and everybody knows (or can read above) that parallel lines (cube's edges) will project in such perspective as parallel IF AND ONLY IF they are parallel to the projection plane (canvas). --CiaPan (talk) 11:09, 1 February 2012 (UTC)
 * Well the straightforward reason the OP's back line in the diagram they supplied is not perpendicular is because they can't join up points properly. The top green line from the left perspective point goes slightly above the point where the right hand perpendicular side and the top ray from the right perspective meet, added to that the bottom of that back green line should have been slightly to the left so of course the back green line slopes. If they tried with a vector drawing package instead or simply drew the line vertical knowing that's how it should be they'd do better. Dmcq (talk) 12:02, 1 February 2012 (UTC)