Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

suppose i want to model a 3D plane intersections when they make a corner. that is three or more than three planes will be intersected at some corners of cubes or other volumetric objects. i can find this corner point by considering as a plane intersection problem. also, i can do this by considering as line intersections problem. here, lines can be found by intrersecting two planes at a time.so, i would like to know this plane intersection and line intersection is given almost same result or two different results. suppose, i fitted planes by least square and found the best planes from the given set of points. now, i am confused and think these two method would be given 2 results. any comment please.

share|improve this question
add comment

1 Answer 1

up vote 2 down vote accepted

Here is what I have done in a similar situation. Call your three planes $A$, $B$, $C$, and their lines of intersection $ab$, $bc$, $ca$. Each pair of lines should intersect in a point, but likely they slightly miss. A good candidate is the midpoint of the shortest segment connecting the pair of lines. So, you could write a routine to compute that shortest segment (you can find the computation in many locations on the web, e.g., this StackOverflow question); let's call it $m(L_1,L_2)$ for two lines $L_1$ and $L_2$. Then average the three points:
$$\frac{1}{3} \left[ m( ab, bc ) + m( bc, ca ) + m(ca, ab) \right] \;.$$ This is a bit of a hack, but it is computationally easy and recognizes the numerical realities.

share|improve this answer
    
could you please tell me what is 'm' in here. –  niro Sep 1 '11 at 12:12
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.