Ray tracing of spline surfaces: Bézier clipping, Chebyshev boxing, and bounding volume hierarchy – a critical comparison with new results

Ray tracing is a well-known rendering technique for producing high-quality and photorealistic pictures. Spline surfaces are also well known and widely used. Thus, there is the need for fast and robust methods for computing the intersections of rays with these surfaces. In this paper, we discuss and compare three recent geometric algorithms for solving the raypatch intersection problem and present new results that are helpful in dealing with this problem.

[1]  Josef Hoschek,et al.  Fundamentals of computer aided geometric design , 1996 .

[2]  Falai Chen,et al.  Implicitization using moving curves and surfaces , 1995, SIGGRAPH.

[3]  Hans-Peter Seidel,et al.  Vision - An Architecture for Global Illumination Calculations , 1995, IEEE Trans. Vis. Comput. Graph..

[4]  Alain Fournier,et al.  Chebyshev Polynomials for Boxing and Intersections of Parametric Curves and Surfaces , 1994, Comput. Graph. Forum.

[5]  Andrew Woo,et al.  Fast ray-box intersection , 1990 .

[6]  Joe Warren.  Curves and surfaces in computer vision and graphics III : 16-18 November 1992, Boston, Massachusetts , 1992 .

[7]  Gerald Farin,et al.  Curves and surfaces for computer aided geometric design , 1990 .

[8]  T. J. Rivlin.  The Chebyshev polynomials , 1974 .

[9]  G. Farin.  NURB curves and surfaces: from projective geometry to practical use , 1995 .

[10]  Nicholas M. Patrikalakis,et al.  Computation of the solutions of nonlinear polynomial systems , 1993, Comput. Aided Geom. Des..

[11]  Emo Welzl,et al.  Smallest enclosing disks (balls and ellipsoids) , 1991, New Results and New Trends in Computer Science.

[12]  Tony DeRose,et al.  Computing values and derivatives of Bézier and B-spline tensor products , 1995, Comput. Aided Geom. Des..

[13]  Philipp Slusallek,et al.  Object-oriented framework for curves and surfaces , 1992, Other Conferences.

[14]  Eric Haines.  FAST RAY – CONVEX POLYHEDRON INTERSECTION , 1991 .

[15]  Leonard A. Ferrari,et al.  Curves and Surfaces in Computer Vision and Graphics , 1990 .

[16]  James F. Blinn,et al.  Scan line methods for displaying parametrically defined surfaces , 1988, CACM.

[17]  Tomoyuki Nishita,et al.  Ray tracing trimmed rational surface patches , 1990, SIGGRAPH.

[18]  Steven K. Feiner,et al.  Computer graphics: principles and practice (2nd ed.) , 1990 .

[19]  Steve D. Upstill,et al.  The renderman companion - a programmer's guide to realistic computer graphics , 1990 .

[20]  Andrew S. Glassner,et al.  An introduction to ray tracing , 1989 .

[21]  Jon G. Rokne.  AN EASY BOUNDING CIRCLE , 1991 .

[22]  D. R. Forsey,et al.  An adaptive subdivision algorithm for crack prevention in the display of parametric surfaces , 1990 .

[23]  Rida T. Farouki,et al.  On the numerical condition of polynomials in Bernstein form , 1987, Comput. Aided Geom. Des..

[24]  Marc Daniel,et al.  The numerical problem of using Bézier curves and surfaces in the power basis , 1989, Comput. Aided Geom. Des..

[25]  James T. Kajiya,et al.  Ray tracing parametric patches , 1982, SIGGRAPH.

[26]  Mark H. Overmars,et al.  Teaching computational geometry , 1995, COMG.

[27]  Thomas W. Sederberg,et al.  Point and tangent computation of tensor product rational Bézier surfaces , 1995, Computer Aided Geometric Design.

[28]  John Neil Spackman.  Scene decompositions for accelerated ray tracing , 1989 .

[29]  C. Woodward,et al.  Ray tracing parametric surfaces by subdivision in viewing plane , 1989 .

[30]  Jack Ritter,et al.  An efficient bounding sphere , 1990 .

[31]  Richard H. Bartels,et al.  Ray Tracing Free-Form B-Spline Surfaces , 1986, IEEE Computer Graphics and Applications.

[32]  Xiaolin Wu.  A linear-Time Simple Bounding Volume Algorithm , 1992, Graphics Gems III.

[33]  Hermann A. Maurer,et al.  New Results and New Trends in Computer Science , 1991, Lecture Notes in Computer Science.

[34]  Thomas W. Sederberg,et al.  Faster Ray Tracing Using Adaptive Grids , 1997, IEEE Computer Graphics and Applications.

[35]  Wilhelm Barth,et al.  Efficient ray tracing for Bezier and B-spline surfaces , 1993, Comput. Graph..

[36]  C. Yang.  On speeding up ray tracing of B-spline surfaces , 1987 .

[37]  Melvin R. Spencer.  Polynomial real root finding in Bernstein form , 1994 .

[38]  Dinesh Manocha,et al.  OBBTree: a hierarchical structure for rapid interference detection , 1996, SIGGRAPH.

[39]  Daniel L. Toth,et al.  On ray tracing parametric surfaces , 1985, SIGGRAPH.

[40]  T. Sederberg,et al.  Comparison of three curve intersection algorithms , 1986 .

[41]  Tomoyuki Nishita,et al.  Curve intersection using Bézier clipping , 1990, Comput. Aided Des..

[42]  Turner Whitted,et al.  A 3-dimensional representation for fast rendering of complex scenes , 1980, SIGGRAPH '80.

[43]  Turner Whitted,et al.  An improved illumination model for shaded display , 1979, CACM.