Intersection of line and surface

  • Thread starter mathman
  • Start date
  • #1
mathman
Science Advisor
8,022
526
A straight line in 3 space can be described as A + Bt, where A is a position, B a direction, and t a scalar parameter. CAD surfaces can be represented in terms of polynomial functions of two variables (u and v) with the highest degree term being [itex]u^nv^n[/itex]. The intersections can then be obtained as roots of a polynomial in t. I have seen proofs that for n = 2 or n = 3, the polynomial in t is of 8th or 18th degree respectively [itex](2n^2)[/itex].

Question: Does this relationship [itex](2n^2)[/itex] hold for n > 3?
 

Answers and Replies

  • #2
35,805
12,530
I do not have a proof but it looks like the general formula.

It also works for n=1.
 

Related Threads on Intersection of line and surface

Replies
1
Views
1K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
2
Views
7K
  • Last Post
Replies
2
Views
5K
  • Last Post
Replies
9
Views
2K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
2
Views
8K
Replies
4
Views
5K
  • Last Post
Replies
3
Views
2K
Top