Simple geometric formulae.

Simple geometric formulae.

Post by H. Bro » Tue, 02 Jan 1990 20:33:00




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.

Post by Patrick Van Ho » Tue, 02 Jan 1990 02:54:00



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.

Post by John Sapona » Tue, 02 Jan 1990 16:48:00




>>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
fairly helpful.

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.

Post by Philip J. Schneid » Tue, 02 Jan 1990 18:26:00




>>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 . . . :-)

 
 
 

1. Simple geometric formulae


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

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