Need some algorithm references for 2d geometry

Need some algorithm references for 2d geometry

Post by Michael Lee Finne » Sun, 08 Oct 2000 04:00:00

I live out in the middle of nowhere and am going to
DC tomorrow. I expect to visit Border's and/or Barnes
and Noble. I need suggestions for some good
references (books currently in print, but online
certainly appreciated as well) that would cover the
following topics. Yes, I know I can order online from
any of these bookstores, but I really like to see the
book before I buy it. Especially when there are
multiple books from which to choose.

I have a set of shapes where each shape is defined by
a set of first and second order Bezier curves (lines
and quadratics) due to the method by which the shapes
are generated. I need algorithms for...

   1. Representation of the shapes (representation of
the Beziers is reasonably obvious, although some
representations may be better than others for this

   2. Combining the shapes via union, intersection
and differencing (not necessarily trivial as the
complement of a shape may not be reasonable to
represent or manipulate).

   3. Finding the intersection of two Beziers (since
they are always first or second order, closed form
solutions are always possible -- but very tedious
(and I don't have Maple or Mathematica, nor can I
reasonably expect to get them) -- however, iterative
solutions are probably just as good.

I'm sure that there are many other issues in 2D
modelling like this that I need to know, but those
are the major unknowns for me at the present.

Further, references on topics such as constructing
pleasing curves given a set of knots and optional
constraints, where the curves must be modelled by
first and second order Beziers. Knuth references some
work done by John Douglas Hobby which use third order
Beziers, but I haven't found anything on that via

Thanks for whatever suggestions you can provide.


1. 3D geometry references needed (In n)

I would appreciate English references for the following concepts/algorithms
for 3D geometric modeling.

        Line equations in 3D space
        Area and normal vector of concave polygons
        Equation of a plane
        Interior point algorithms for concave polygons
        Surface area of polyhedrons
        Interior point algorithms for polyhedrons
        Spatial reasoning about 3D objects (Are these polygons perpendicular?)

Janelle Jurek


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