Segment Tracing Using Local Lipschitz Bounds

We introduce Segment Tracing, a new algorithm that accelerates the classical Sphere Tracing method for computing the intersection between a ray and an implicit surface. Our approach consists in computing the Lipschitz bound locally over a segment to improve the marching step computation and accelerate the overall process. We describe the computation of the Lipschitz bound for different operators and primitives. We demonstrate that our algorithm significantly reduces the number of field function queries compared to previous methods, without the need for additional accelerating data‐structures. Our method can be applied to a vast variety of implicit models ranging from hierarchical procedural objects built from complex primitives, to simulation‐generated implicit surfaces created from many particles.

[1]  P. J. Narayanan,et al.  Real-Time Ray Tracing of Implicit Surfaces on the GPU , 2010, IEEE Transactions on Visualization and Computer Graphics.

[2]  D. P. Mitchell.  Robust ray intersection with interval arithmetic , 1990 .

[3]  Tomoyuki Nishita,et al.  GPU‐based Fast Ray Casting for a Large Number of Metaballs , 2008, Comput. Graph. Forum.

[4]  Tim Reiner,et al.  Interactive modeling of implicit surfaces using a direct visualization approach with signed distance functions , 2011, Comput. Graph..

[5]  Brian Wyvill,et al.  Introduction to Implicit Surfaces , 1997 .

[6]  Alexei Sourin,et al.  Function representation in geometric modeling: concepts, implementation and applications , 1995, The Visual Computer.

[7]  H BarrAlan.  Global and local deformations of solid primitives , 1984 .

[8]  Charles T. Loop,et al.  Real-time GPU rendering of piecewise algebraic surfaces , 2006, ACM Trans. Graph..

[9]  James F. Blinn,et al.  Real-time GPU rendering of piecewise algebraic surfaces , 2006, SIGGRAPH 2006.

[10]  John C. Hart,et al.  Ray tracing deterministic 3-D fractals , 1989, SIGGRAPH.

[11]  HanrahanPat.  Ray tracing algebraic surfaces , 1983 .

[12]  Tomoyuki Nishita,et al.  A Method for Displaying Metaballs by using Bézier Clipping , 1994, Comput. Graph. Forum.

[13]  Eric Galin,et al.  Fast Distance Computation Between a Point and Cylinders, Cones, Line-Swept Spheres and Cone-Spheres , 2004, J. Graphics, GPU, & Game Tools.

[14]  Steve C. Maddock,et al.  Ray casting implicit fractal surfaces with reduced affine arithmetic , 2007, The Visual Computer.

[15]  John C. Hart,et al.  Sphere tracing: a geometric method for the antialiased ray tracing of implicit surfaces , 1996, The Visual Computer.

[16]  Devendra Kalra,et al.  Guaranteed ray intersections with implicit surfaces , 1989, SIGGRAPH.

[17]  Hans Hagen,et al.  Fast Ray Tracing of Arbitrary Implicit Surfaces with Interval and Affine Arithmetic , 2009, Comput. Graph. Forum.

[18]  Derek Nowrouzezahrai,et al.  Non-linear sphere tracing for rendering deformed signed distance fields , 2019, ACM Trans. Graph..

[19]  Pat Hanrahan,et al.  Ray tracing algebraic surfaces , 1983, SIGGRAPH.

[20]  G. Wyvill,et al.  Ray-tracing soft objects , 1990 .

[21]  Bedrich Benes,et al.  Terrain Modeling from Feature Primitives , 2015 .

[22]  Brian Wyvill,et al.  A Survey on Implicit Surface Polygonization , 2015, ACM Comput. Surv..

[23]  Alan H. Barr,et al.  Global and local deformations of solid primitives , 1984, SIGGRAPH.

[24]  Bedrich Benes,et al.  Terrain Modelling from Feature Primitives , 2015, Comput. Graph. Forum.

[25]  Nancy Argüelles,et al.  Author ' s , 2008 .

[26]  Brian Wyvill,et al.  Extending the CSG Tree. Warping, Blending and Boolean Operations in an Implicit Surface Modeling System , 1999, Comput. Graph. Forum.

[27]  Steve Marschner,et al.  Fundamentals of Computer Graphics (3. ed.) , 2009 .

[28]  Benjamin Keinert,et al.  Enhanced Sphere Tracing , 2014, STAG.

[29]  Pierre Poulin,et al.  Fitted BVH for Fast Raytracing of Metaballs , 2010, Comput. Graph. Forum.

[30]  Andrei Sherstyuk.  Fast Ray Tracing of Implicit Surfaces , 1999, Comput. Graph. Forum.

[31]  Jarke J. van Wijk,et al.  Ray tracing objects defined by sweeping a sphere , 1984, Comput. Graph..