HELP: Intersection of B-Spline Surfaces

HELP: Intersection of B-Spline Surfaces

Post by Dinesh Shikha » Thu, 15 Sep 1994 15:24:12

Dear all,

  We are working on a Surface modeller project and we
  deal with B-spline surfaces. The following problem
  is to be solved and we do not have many good references
  to concrete work done in this area.

  Problem: Intersection of two B-spline surfaces
    Given two B-spline surfaces (BSS), we want to find
    the curve formed by the intersection of the two surfaces.
    The representations of the resultant curve may be
    piecewise linear curve or composite Bezier curve.

    The issues we are struggling with are
    i.   Algorithm for performing surface X surface intersection
    ii.  Tolerance measure for distance
    iii. Special cases where the boundary of one surface
         touches other surface. The word "touches" has some
         distance tolerance associated with it.

   We are looking for some references to survey papers,
   specific work done.

   and I'll post a summary of replies.

   Thank you.

Dinesh Shikhare

National Centre for Software Technology (NCST)
Graphics and CAD Division,
Juhu, Bombay 400049,
INDIA.                      Phone: +91 (22) 620 1606
                            Fax  : +91 (22) 621 0139



1. Help, conic/conic, conic/spline, spline/spline, intersections?


My math is a bit (quite a bit?) rusty. I need to calculate the  
intersections of two conics, in 2D, of the general form:

        ax^2 + 2bxy + cy^2 + dx +ey +f = 0

If it makes it easier one of the conics can be in the form:

        x^2/b^2 + y^2/a^2 = 1

I would just adjust the one conic so its position remains the same  
relative to the other. I am primarily interested in ellipses if this  
makes the problem easier.

Also, does anyone know of any reference material on intersecting  
conics, B-splines, and nth degree Bezier curves with one another?

Any help would be greatly appreciated. Thanks
Ditek International Inc.

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