[sage-support] Re: Using sage to find point on a line a given distance from circle in 3D
Thanks so much for characterizing the problem properly in this manner - that's exactly right. I just did a search for torus-line intersections and found some solutions: http://tog.acm.org/GraphicsGems/gemsii/intersect/inttor.c On Sep 26, 9:11 pm, "David Joyner" <[EMAIL PROTECTED]> wrote: > Maybe I don't understand the question exactly. > > Consider the circle x^2+y^2=1, z=0, and the set S of all points > at a small distance d, say d near 1/100, from this circle. I think > that is a torus, isn't it? > You want a symbolic equation (ie, a function of d) for the points in > the intersection > of this torus with a line? > > Just guessing, I would imagine this could depend on d in a complicated way, > as when d is small you could have 0, 1, 2, 3, or 4 solutions, but when d is > large, it seems to me you could have 0, 1 or 2 solutions. > Maybe it's not so simple? > > On Fri, Sep 26, 2008 at 11:46 PM, Eugene Jhong <[EMAIL PROTECTED]> wrote: > > > Newbie to sage - trying to find a point on a line in 3D that is a > > specified distance from a circle (the line is not coplanar with the > > circle). Here's what I've inputed into sage: > > > var("line_dir_x line_dir_y line_dir_z line_p_x line_p_y line_p_z > > cent_x cent_y cent_z norm_x norm_y norm_z u radius length") > > line_dir = vector([line_dir_x, line_dir_y, line_dir_z]) # direction > > of line > > line_p = vector([line_p_x, line_p_y, line_p_z]) # point on > > the line > > cent = vector([cent_x, cent_y, cent_z]) # center > > of circle > > norm = vector([norm_x, norm_y, norm_z]) # normal to > > plane of circle > > p = line_p + u * line_dir > > diff0 = p - cent > > dist = diff0.dot_product(norm) > > diff1 = diff0 - dist * norm > > sqr_len = diff1.dot_product(diff1) > > closest_point1 = cent + (radius/sqrt(sqr_len))*diff1 > > diff2 = p - closest_point1 > > eq = length**Integer(2) == diff2.dot_product(diff2) > > solve([eq], u) > > > Here's what eq looks like: > > > rleg_len^2 == (-radius*(-norm_z*(norm_z*(line_dir_z*u + line_p_z - > > cent_z) + norm_y*(line_dir_y*u + line_p_y - cent_y) + > > norm_x*(line_dir_x*u + line_p_x - cent_x)) + line_dir_z*u + line_p_z - > > cent_z)/sqrt((-norm_z*(norm_z*(line_dir_z*u + line_p_z - cent_z) + > > norm_y*(line_dir_y*u + line_p_y - cent_y) + norm_x*(line_dir_x*u + > > line_p_x - cent_x)) + line_dir_z*u + line_p_z - cent_z)^2 + (- > > norm_y*(norm_z*(line_dir_z*u + line_p_z - cent_z) + > > norm_y*(line_dir_y*u + line_p_y - cent_y) + norm_x*(line_dir_x*u + > > line_p_x - cent_x)) + line_dir_y*u + line_p_y - cent_y)^2 + (- > > norm_x*(norm_z*(line_dir_z*u + line_p_z - cent_z) + > > norm_y*(line_dir_y*u + line_p_y - cent_y) + norm_x*(line_dir_x*u + > > line_p_x - cent_x)) + line_dir_x*u + line_p_x - cent_x)^2) + > > line_dir_z*u + line_p_z - cent_z)^2 + (-radius*(- > > norm_y*(norm_z*(line_dir_z*u + line_p_z - cent_z) + > > norm_y*(line_dir_y*u + line_p_y - cent_y) + norm_x*(line_dir_x*u + > > line_p_x - cent_x)) + line_dir_y*u + line_p_y - cent_y)/sqrt((- > > norm_z*(norm_z*(line_dir_z*u + line_p_z - cent_z) + > > norm_y*(line_dir_y*u + line_p_y - cent_y) + norm_x*(line_dir_x*u + > > line_p_x - cent_x)) + line_dir_z*u + line_p_z - cent_z)^2 + (- > > norm_y*(norm_z*(line_dir_z*u + line_p_z - cent_z) + > > norm_y*(line_dir_y*u + line_p_y - cent_y) + norm_x*(line_dir_x*u + > > line_p_x - cent_x)) + line_dir_y*u + line_p_y - cent_y)^2 + (- > > norm_x*(norm_z*(line_dir_z*u + line_p_z - cent_z) + > > norm_y*(line_dir_y*u + line_p_y - cent_y) + norm_x*(line_dir_x*u + > > line_p_x - cent_x)) + line_dir_x*u + line_p_x - cent_x)^2) + > > line_dir_y*u + line_p_y - cent_y)^2 + (-radius*(- > > norm_x*(norm_z*(line_dir_z*u + line_p_z - cent_z) + > > norm_y*(line_dir_y*u + line_p_y - cent_y) + norm_x*(line_dir_x*u + > > line_p_x - cent_x)) + line_dir_x*u + line_p_x - cent_x)/sqrt((- > > norm_z*(norm_z*(line_dir_z*u + line_p_z - cent_z) + > > norm_y*(line_dir_y*u + line_p_y - cent_y) + norm_x*(line_dir_x*u + > > line_p_x - cent_x)) + line_dir_z*u + line_p_z - cent_z)^2 + (- > > norm_y*(norm_z*(line_dir_z*u + line_p_z - cent_z) + > > norm_y*(line_dir_y*u + line_p_y - cent_y) + norm_x*(line_dir_x*u + > > line_p_x - cent_x)) + line_dir_y*u + line_p_y - cent_y)^2 + (- > > norm_x*(norm_z*(line_dir_z*u + line_p_z - cent_z) + > > norm_y*(line_dir_y*u + line_p_y - cent_y) + norm_x*(line_dir_x*u + > > line_p_x - cent_x)) + line_dir_x*u + line_p_x - cent_x)^2) + > > line_dir_x*u + line_p_x - cent_x)^2 > > > I try to do the solve but it doesn't seem to terminate after several > > hours. Just looking for any pointers about finding an analytical > > solution to this seemingly simple problem. --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~---
[sage-support] sageplot axis numbering
Hey I'm writing a paper about the trigonometric functions, using LaTeX and sagetex. And would therefore like to chance the the default numbering on the x-axis to a pi scale. Thanks, Munthe --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] a sage interact to contribute
Dear sage-support, I'm learning SAGE interact and wrote one to illustrate the limit of sin(t)/t \to 1 as t \to 0. I did not see a similar one on the Caculus interact page and thought it can be a little contribution that I put in for the community. Can I post mine there? If the answer is "yes", how can I do that. Thanks Pong --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: a sage interact to contribute
On Saturday 27 September 2008, Wai Yan Pong wrote: > Dear sage-support, > > I'm learning SAGE interact and wrote one to illustrate the limit of > sin(t)/t \to 1 as t \to 0. I did not see a similar one on the Caculus > interact page and thought it can be a little contribution that I put in for > the community. Can I post mine there? If the answer is "yes", how can I do > that. Hi there, you are talking about this wiki page, right? http://wiki.sagemath.org/interact/calculus If so, just sign up and in and start editing. No need to ask for permission, the concept of a wiki is that anyone can edit it. Cheers, Martin -- name: Martin Albrecht _pgp: http://pgp.mit.edu:11371/pks/lookup?op=get&search=0x8EF0DC99 _www: http://www.informatik.uni-bremen.de/~malb _jab: [EMAIL PROTECTED] --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] problem with animate on OS X 10.5, Sage 3.1.2
Can anyone else reproduce this? sage: a = animate([sin(x + float(k)) for k in srange(0,2*pi,0.3)], xmin=0, xmax=2*pi, figsize=[2,1]) sage: a Animation with 21 frames sage: a.show() dyld: Symbol not found: __cg_png_create_info_struct Referenced from: /System/Library/Frameworks/ApplicationServices.framework/Versions/A/ Fram\ eworks/ImageIO.framework/Versions/A/ImageIO Expected in: /Applications/sage/local/lib//libPng.dylib sh: line 1: 75999 Trace/BPT trap convert -delay 20 -loop 0 *.png "/Users/palmieri/.sage/sage_notebook/worksheets/admin/46/cells/37/ sage0.\ gif" --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: problem with animate on OS X 10.5, Sage 3.1.2
On Sep 27, 5:41 pm, John H Palmieri <[EMAIL PROTECTED]> wrote: > Can anyone else reproduce this? I can't since I do not have convert on a Mac, but the problem is that we switched to a dynamic libpng. The solution is: * create a convert script in $SAGE_LOCAL/bin * set DYLD_LIBRARY_PATH to SAGE_ORIG_DYLD_LIBRARY_PATH * call convert with an absolute path (use "which convert" from outside Sage) and pass on all parameters (i.e. /use/local/foo/convert "$@") We should probably do that automatically on OSX for convert, emacs and the other usual suspects. The problem boils down to Apple renaming some of the symbols in libpng and creating libPng.dylib in the process. Cheers, Michael --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] problem with wiki.sagemath.org
I apologize in advance that if this is not a right place to ask this question. I have some problem in using wiki.sagemath.org. I created an account but when I tried to re-login sometime later it compliant that my password is wrong. (I'm pretty sure I remember my password correctly).When I tried to create an account again using the same name, wiki compliant that the username has already been taken (so obviously it remember something). Now the only explanation that I could think of is that I choose "not to remember something" (sorry I forgot what the something is) by unchecking a box at some point. Could it be the reason? PS. I also tried to recover my password by providing wiki my email however it complaint that no info associate with my email address (again I'm pretty sure the email that I gave was correct, it simply my gmail account) Please help. --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: problem with wiki.sagemath.org
Hi Michael, Thank you for your reply. And shame on the spammer. However, as I said wiki compliant about the fact that my username is used by someone. Could you remove mine? I will send you my username off the list. Pong On Sep 27, 9:06 pm, mabshoff <[EMAIL PROTECTED] dortmund.de> wrote: > On Sep 27, 9:03 pm, pong <[EMAIL PROTECTED]> wrote: > > Hi Pong, > > > > > I apologize in advance that if this is not a right place to ask this > > question. > > > I have some problem in using wiki.sagemath.org. I created an account > > but when I tried to re-login sometime later it compliant that my > > password is wrong. (I'm pretty sure I remember my password > > correctly).When I tried to create an account again using the same > > name, wiki compliant that the username has already been taken (so > > obviously it remember something). > > > Now the only explanation that I could think of is that I choose "not > > to remember something" (sorry I forgot what the something is) by > > unchecking a box at some point. Could it be the reason? > > > PS. I also tried to recover my password by providing wiki my email > > however it complaint that no info associate with my email address > > (again I'm pretty sure the email that I gave was correct, it simply my > > gmail account) > > Please recreate your account, I did some spammer cleanup and might > have inadvertently delete it :( > > > Please help. > > Cheers, > > Michael --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---