Locally restricted blending of Blobtrees

Blobtrees are volume representations particularly useful for models which require smooth blending. When blending is applied to two or more Blobtree models, extra volume will be created in between the two surfaces to form a smooth connection. Although it is easy to apply blending, it is hard to accurately control the resulting shape. More complications arise when the blended objects have large size differences. In this case the influence of the larger objects can overwhelm the influence of the smaller objects. As a result, the shape of the smaller objects can change drastically and the connection between surfaces can appear sharp instead of smooth. This paper presents a locally restricted blend method that solves the blending problem described above. The locally restricted blend locally changes the blending influence of each of the surfaces in order to control blending with the other surfaces. Unlike previous methods, this blend method works with multiple Blobtree surfaces and offers intuitive control over the resulting shape.

[1]  A. Ricci,et al.  A Constructive Geometry for Computer Graphics , 1973, Computer/law journal.

[2]  Brian Wyvill,et al.  Shrinkwrap: An efficient adaptive algorithm for triangulating an iso-surface , 2004, The Visual Computer.

[3]  Alexander A. Pasko,et al.  Constructive Hypervolume Modeling , 2001, Graph. Model..

[4]  Jules Bloomenthal,et al.  Bulge Elimination in Convolution Surfaces , 1997, Comput. Graph. Forum.

[5]  Marie-Paule Cani,et al.  Implicit Modelling with Skeleton Curves: Controlled Blending in Contact Situation , 2002, Shape Modeling International.

[6]  Thomas Ertl,et al.  Computer Graphics - Principles and Practice, 3rd Edition , 2014 .

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

[8]  Brian Wyvill,et al.  CONTROLLED BLENDING OF PROCEDURAL IMPLICIT SURFACES , 1990 .

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

[10]  Tosiyasu L. Kunii,et al.  Bounded blending for function-based shape modeling , 2005, IEEE Computer Graphics and Applications.

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

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

[13]  P.-C. Hsu,et al.  The Scale Method for Blending Operations in Functionally‐Based Constructive Geometry , 2003, Comput. Graph. Forum.

[14]  M. Carter.  Computer graphics: Principles and practice , 1997 .

[15]  P.-C. Hsu,et al.  Field Functions for Blending Range Controls on Soft Objects , 2003, Comput. Graph. Forum.

[16]  Steve Maddock,et al.  Implicit Surfaces: Appearance, Blending and Consistency , 2005 .

[17]  Roman Kuchkuda,et al.  An introduction to ray tracing , 1993, Comput. Graph..

[18]  James F. Blinn,et al.  A Generalization of Algebraic Surface Drawing , 1982, TOGS.

[19]  René Caubet,et al.  Combining implicit surfaces with soft blending in a CSG tree , 2007 .

[20]  Q. Li.  Smooth Piecewise Polynomial Blending Operations for Implicit Shapes , 2007, Comput. Graph. Forum.

[21]  Jules Bloomenthal,et al.  Implicit surfaces '98 , 1998, COMG.

[22]  Brian Wyvill,et al.  Controlled Blending for Implicit Surfaces using a Graph , 1999 .

[23]  Brian Wyvill,et al.  Controllable Binary Csg Operators for "soft Objects" , 2004, Int. J. Shape Model..

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

[25]  Alyn P. Rockwood,et al.  The displacement method for implicit blending surfaces in solid models , 1989, TOGS.

[26]  Cornelius W. A. M. van Overveld,et al.  Combining CSG modeling with soft blending using Lipschitz-based implicit surfaces , 2002, The Visual Computer.

[27]  Samuel Hornus,et al.  Subdivision-curve primitives: a new solution for interactive implicit modeling , 2001, Proceedings International Conference on Shape Modeling and Applications.

[28]  Jules Bloomenthal,et al.  Convolution surfaces , 1991, SIGGRAPH.