graphics - Intersection between line and sphere -


i need find intersection between line , sphere defined following equations

line: p = p0 + tv, p0 eye of camera , v direction of ray.

sphere: (p - pc)^t (p - pc) = r^2, pc center of sphere , r radius

how solve t?

i assume v normalized.

the point of closest approach of line center of sphere occurs @ t1:

v . (p0 + t1 v - pc) = 0 v . (pc - p0) = t1

at t1 distance line center of sphere is

h = sqrt((pc - p0)^2 - t1^2)

the intersection surface of sphere occur (if occurs @ all) @ t1 +/- td, where

td^2 + h^2 = r^2 td^2 = r^2 - h^2      = r^2 - (pc - p0)^2 + t1^2      = r^2 - (pc - p0)^2 + (v . (pc - p0))^2

Comments

Post a Comment

Popular posts from this blog

cakephp - simple blog with croogo -

i not problem, made simple blog in croogo, problem is not adding or modifying or delete, because arabic language ?? function add in controller `public function admin_add() { $this->set('title_for_layout', __('add part')); if (!empty($this->request->data)) { $this->part->create(); if ($this->part->save($this->request->data)) { $this->session->setflash(__('the part has been saved'), 'default', array('class' => 'success')); $this->redirect(array('action' => 'index'));//, $this->part->id)); } else { $this->session->setflash(__('the part not saved. please, try again.'), 'default', array('class' => 'error')); } } }` => model `class part extends appmodel { public $name = 'part'; var $belongst...
Read more

How to group boxplot outliers in gnuplot -

i have large set of data points. try plot them boxplot, of outliers exact same value , represented on line beside each other. found how set horizontal distance between outliers in gnuplot boxplot , doesn't much, apparently not possible. is possible group outliers together, print 1 point , print number in brackets beside indicate how many points there are? think make more readable in graph. for information, have 3 boxplots 1 x value , times 6 in 1 graph. using gnuplot 5 , played around pointsize, doesn't reduce distance anymore. hope can help! edit: set terminal pdf set output 'dat.pdf' file0 = 'dat1.dat' file1 = 'dat2.dat' file2 = 'dat3.dat' set pointsize 0.2 set notitle set xlabel 'x' set ylabel 'y' header = system('head -1 '.file0); n = words(header) set xtics ('' 1) set [i=1:n] xtics add (word(header, i) i) set style data boxplot plot file0 using (1-0.25):1:(0.2) boxplot lw 2 lc rgb '#8b0000...
Read more

bash - Performing variable substitution in a string -

i have string contains use of variable, , i'd substitute variable's value string. right best have is #!/bin/bash foo='$name; echo bar' name="the name" expanded="$(eval echo "$foo")" echo "$expanded" which has obvious defects: prints the name bar while i'd print the name; echo bar instead of eval can bash's regex matching bash's string replacement: foo='$name; echo bar' name="the name" [[ "$foo" =~ \$([[:alnum:]]+) ]] && s="${!bash_rematch[1]}" && expanded="${foo/\$${bash_rematch[1]}/$s}" echo "$expanded" name; echo bar
Read more