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Find if line crosses a sphere

Trying to create a very simple boolean function that will find if a line crosses a sphere.

This does not look like what I want, although the question was similar: The intersection of a line and a sphere?

I also tried the algorithms listed at:

http://www.docstoc.com/docs/7747820/Intersection-of-a-Line-and-a-Sphere

and

http://www.ccs.neu.edu/home/fell/CSU540/programs/RayTracingFormulas.htm

without real luck.

My last code (in Haskell) looks like this:

data Point = Point { x :: Float, y :: Float, z :: Float} deriving (Eq, Show, Read)
data Sphere = Sphere { center :: Point, radius :: Float } deriving (Eq, Show, Read)

inView :: Point -> Point -> Sphere -> Bool
inView (Point x1 y1 z1) (Point x2 y2 z2) (Sphere (Point x3 y3 z3) r)
  | result > 0 && result < r = False
  | otherwise                = True
  where result = top/bot
        top = (x3 - x1) * (x2 - x1) + (y3 - y1) * (y2 - y1) + (z3 - z1) * (z2 - z1)
        bot = (x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1) + (z2 - z1) * (z2 - z1)

If it returns true, if 2 points have a straight line to the site. This works for some simple cases, but is not suitable for others that should work, for example:

inView (Point {x = 43.64, y = -183.20, z = 187.37}) (Point {x = 42.04, y = -183.58, z = 187.37}) (Sphere (Point 0 0 0) 5)

Any help would be appreciated.

+5
4

. ​​ :

p1 + u (p2 - p1)

( u - ), top/bot u, .

, :

where u = top/bot
      nearestPoint = {- p1 + u (p2 - p1) -}
      result = {- distance between nearestPoint and p3 -}

, . result.

, , , , Data.VectorSpace. :

import Data.VectorSpace

type Point = (Double, Double, Double)
inView :: Point -> Point -> Sphere -> Bool
inView p1 p2 (Sphere p3 r) = result < r
    where u = top/bot
          top = ...
          bot = ...
          nearestPoint = p1 ^+^ u *^ (p2 ^-^ p1)
          result = magnitude (p3 ^-^ nearestPoint)
+2

, -, :

, .

: ?

+1

, : http://www.devmaster.net/wiki/Ray-sphere_intersection

, googling , , .

, , , , : ,

0

,

inView :: Point -> Point -> Sphere -> Bool
inView (Point x1 y1 z1) (Point x2 y2 z2) (Sphere (Point x3 y3 z3) r)
  | result > 0 && result < r^2 = False // is this correct? I know nothing about Haskell, but seems like this should be True
  | otherwise                  = True
  where result = -t1^2/t2 + t3
        t1 = (x3 - x1) * (x2 - x1) + (y3 - y1) * (y2 - y1) + (z3 - z1) * (z2 - z1)
        t2 = (x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1) + (z2 - z1) * (z2 - z1)
        t3 = (x3 - x1) * (x3 - x1) + (y3 - y1) * (y3 - y1) + (z3 - z1) * (z3 - z1)

NB. , Haskell , ^2 .

e: working here here

0

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