Using multivariate resultants to find the intersection of three quadric surfaces
ACM Transactions on Graphics (TOG)
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
OBBTree: a hierarchical structure for rapid interference detection
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Algebraic loop detection and evaluation algorithms for curve and surface interrogations
GI '96 Proceedings of the conference on Graphics interface '96
A parametric algorithm for drawing pictures of solid objects composed of quadric surfaces
Communications of the ACM
3D game engine design: a practical approach to real-time computer graphics
3D game engine design: a practical approach to real-time computer graphics
Polynomial root finding using iterated Eigenvalue computation
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Journal of Symbolic Computation
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The design-for-assembly technique requires realistic physicallybased simulation algorithms and in particular efficientgeometric collision detection routines. Instead of approximatingmechanical parts by large polygonal models, we work with the muchsmaller original CAD-data directly, thus avoiding precision andtolerance problems. We present a generic algorithm, which candecide whether two solids intersect or not. We identify classes ofobjects for which this algorithm can be efficientlyspecialized, and describe in detail how this specialization isdone. These classes are objects that are bounded by quadric surfacepatches and conic arcs, objects that are bounded by natural quadricpatches, torus patches, line segments and circular arcs, andobjects that are bounded by quadric surface patches, segments ofquadric intersection curves and segments of cubic spline curves. Weshow that all necessary geometric predicates can be evaluated byfinding the roots of univariate polynomials of degree at most4 for the first two classes, and at most 8 for the thirdclass. In order to speed up the intersection tests we use boundingvolume hierarchies. With the help of numerical optimizationtechniques we succeed in calculating smallest enclosing spheres andbounding boxes for a given set of surface patches fulfillingthe properties mentioned above.