## Simple geometric formulae.

### Simple geometric formulae.

Quote:>I'm looking for some simple geometric formulae such as
>    distance from a point to a line segment
>    distance from a point to a bezier
>    distance from a point to an ellipse
>    how to determine whether a point is inside an ellipse
>    how to determine whether a point is inside a polygon
>    etc.

I am also interested in any references to this information, as well as
intersection of a line and a plane
intersection of a line and a sphere
I would appreciate it if someone could forward any pointers  to
such info.  Thanks much in advance.

Alex Brown
steinmetz!unioncs!brownh

### Simple geometric formulae.

Quote:>I'm looking for some simple geometric formulae such as
>    distance from a point to a line segment
>    distance from a point to a bezier
>    distance from a point to an ellipse
>    how to determine whether a point is inside an ellipse
>    how to determine whether a point is inside a polygon
>    etc.

2 books that you may consider,

%A M.E. Mortenson
%T Geometric Modeling
%I J. Wiley
%C New York
%D 1985

%A I.D. Faux
%A M.J. Pratt
%T Computational Geometry for Design and Manufacture
%I Ellis Horwood
%C Chichester
%D 1979

Also, any text on computer graphics or analytic geometry should be useful.

Patrick Van Hove

### Simple geometric formulae.

>>I'm looking for some simple geometric formulae such as
>>        distance from a point to a line segment
>>        distance from a point to a bezier
>>        distance from a point to an ellipse
>>        how to determine whether a point is inside an ellipse
>>        how to determine whether a point is inside a polygon
>>        etc.

>I am also interested in any references to this information, as well as
>    intersection of a line and a plane
>    intersection of a line and a sphere
>I would appreciate it if someone could forward any pointers  to
>such info.  Thanks much in advance.

>Alex Brown

Alex,
I recently posted a long, long note on the fastest test for a point
inside a polygon.  Line/plane, line/sphere, and line/quadric intersections
are covered in lots of places:  SIGGRAPH 87 "Intro to Ray Tracing" Course
Notes has them all, Kay & Kajiya's "Ray Tracing Complex Scenes" in SIGGRAPH
'86 Proceedings is about the newest in a long line of sources for ray/plane
intersection, sphere & other quadrics are in Kajiya's SIGGRAPH 83 "Tutorial
on Ray Tracing" in the "State of the Art in Image Synthesis" Course Notes.

I just received some recommendations on good books on geometry for use in
computer graphics, and will list these below (haven't checked them all out
yet, though).

"A Programmer's Geometry", A. Bowyer, J. Woodwark, Butterworths Press, 1983?
- heard about from some people at Cornell's computer graphics lab as being

A bunch of recommendations came from Jeff Goldsmith at JPL:

Computational Geometry for Design and Manufacture
Faux & Pratt
--an early CAD text.  It has lots of good stuff
on splines and 3D math.

Differential Geometry of Curves and Surfaces
DoCarmo
--A super text on classical differential geometry.
(Not quite the same as analytic geometry.)

CRC Standard Math Tables
--This has an awesome section on analytic geometry.
Calculus, too.  Can't live without it.  It is not
the same as the first part of the Chemistry and
Physics one.

Analytic Geometry
S* and Ballou
--Once was the standard college text on the subject.
That was a long time ago, but it is very easy to
read and it covers the fundamentals.

That's all, folks,

Eric Haines

### Simple geometric formulae.

>>I'm looking for some simple geometric formulae such as
>>        distance from a point to a line segment
>>        distance from a point to a bezier
>>        distance from a point to an ellipse
>>        how to determine whether a point is inside an ellipse
>>        how to determine whether a point is inside a polygon
>>        etc.

>I am also interested in any references to this information, as well as
>    intersection of a line and a plane
>    intersection of a line and a sphere
>I would appreciate it if someone could forward any pointers  to
>such info.  Thanks much in advance.

>Alex Brown
>steinmetz!unioncs!brownh

I have a book that consists of formulae and optomized code fragments
for lots of problems like these mentioned:

"A Programmer's Geometry",
by Adran Bowyer and John Woodwark
1983

Butterworth Publishers
80 Montvale Avenue
Stoneham, MA  02180
(617)438-8464

- Philip Schneider

P.S. For the intersection of a line and a sphere, look at the code in
just about every ray-tracing program ever written . . . :-)

I am also interested in any references to this information, as well as
intersection of a line and a plane
intersection of a line and a sphere
I would appreciate it if someone could forward any pointers  to
such info.  Thanks much in advance.

Alex Brown
steinmetz!unioncs!brownh