Further doc improvements for Line_.closestPointToRay() based on

comments in http://codereview.chromium.org/251097 .

Review URL: http://codereview.chromium.org/243111

git-svn-id: svn://svn.chromium.org/chrome/trunk/src@28181 0039d316-1c4b-4281-b951-d872f2087c98

1 files changed, 10 insertions, 11 deletions

diff --git a/o3d/samples/o3djs/manipulators.js b/o3d/samples/o3djs/manipulators.js
index d84cea0..e1ddce6 100644
--- a/o3d/samples/o3djs/manipulators.js
+++ b/o3d/samples/o3djs/manipulators.js
@@ -152,7 +152,7 @@ o3djs.manipulators.Line_.prototype.setPoint = function(point) {
   this.point_ = o3djs.math.copyVector(point);

   this.recalc_();

 }

-  

+

 /**

  * Gets one point through which this line travels.

  * @private

@@ -208,26 +208,25 @@ o3djs.manipulators.Line_.prototype.closestPointToRay = function(startPoint,
   // the ray are closest together, the line segment between cp1 and

   // cp2 is perpendicular to both of the lines.

   //

-  // We can therefore write the following equations ("**" is the "dot"

-  // operator):

+  // We can therefore write the following equations:

   //

-  //   dir  ** (cp2 - cp1) = 0

-  // raydir ** (cp2 - cp1) = 0

+  //   dot(   dir, (cp2 - cp1)) = 0

+  //   dot(raydir, (cp2 - cp1)) = 0

   //

   // Define t' and u' as the parameter values for cp1 and cp2,

   // respectively. Expanding, these equations become

   //

-  //    dir ** ((raystart + u' * raydir) - (point + t' * dir)) = 0

-  // raydir ** ((raystart + u' * raydir) - (point + t' * dir)) = 0

+  //   dot(   dir, ((raystart + u' * raydir) - (point + t' * dir))) = 0

+  //   dot(raydir, ((raystart + u' * raydir) - (point + t' * dir))) = 0

   //

   // With some reshuffling, these can be expressed in vector/matrix

   // form:

   //

-  //   [    dir ** raystart -    dir ** point ]

-  //   [ raydir ** raystart - raydir ** point ] *  (continued)

+  //   [ dot(   dir, raystart) - dot(   dir, point) ]

+  //   [ dot(raydir, raystart) - dot(raydir, point) ] +  (continued)

   //

-  //       [ -(   dir ** dir)     dir ** raydir ] [ t' ]   [0]

-  //       [ -(raydir ** dir)  raydir ** raydir ] [ u' ] = [0]

+  //       [ -dot(   dir, dir)   dot(   dir, raydir) ]   [ t' ]   [0]

+  //       [ -dot(raydir, dir)   dot(raydir, raydir) ] * [ u' ] = [0]

   //

   // u' is the parameter for the world space ray being cast into the

   // screen. We can deduce whether the starting point of the ray is