POV-Ray : Newsgroups : povray.binaries.images : Hesse normal form for lines - distance formula. Server Time25 Jan 2022 14:44:25 EST (-0500)
 Hesse normal form for lines - distance formula. (Message 1 to 1 of 1)
 From: William F Pokorny Subject: Hesse normal form for lines - distance formula. Date: 4 Dec 2020 10:36:52 Message: <5fca5794\$1@news.povray.org>
```
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"headline": "Hesse normal form for lines - distance formula.",
"dateCreated": "2020-12-04T15:36:52+00:00",
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The Hesse or Hessian normal form is often used to define planes. There
is a similar encoding for lines; in an old book I stumbled across a
distance formula used as a part the line encoding which makes for a nice
method to specify planes by rotation and offset relative to the y axis.

It naturally divides regions into positive and negative values with good

// Set up for left handed rotation about y. 0 angle aligns with x.
#declare FnHessianDist = function (x,y,z,Theta,Offset) {
}

It's useful. I'll be creating an inbuilt version called f_hessian_dist
for povr. The SDL written function above can be used in any version of
POV-Ray supporting functions.

Attached in an isosurface doodle making multiple uses of it all bound by
a sphere. You can do octagonal columns and such too. Suppose other ways
to do the same things, but being able to specify just angle and offset
makes it easier.

Bill P.
```

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