brownh@unioncs.UUCP (H. Brown) (01/21/88)
In article <554@acornrc.UUCP> you write: >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
vanhove@XN.LL.MIT.EDU (Patrick Van Hove) (01/21/88)
In article <554@acornrc.UUCP> you write: >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
saponara@batcomputer.tn.cornell.edu (John Saponara) (01/21/88)
In article <515@unioncs.UUCP> brownh@unioncs.UUCP (H. Brown) writes: >In article <554@acornrc.UUCP> you write: >>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 Steen 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
pjs@granite.dec.com (Philip J. Schneider) (01/22/88)
In article <515@unioncs.UUCP> brownh@unioncs.UUCP (H. Brown) writes: > > >In article <554@acornrc.UUCP> you write: >>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 . . . :-)