Field Functions for Blending Range Controls on Soft Objects

Abstract

This paper proposes new field functions that have adjustable inner radius and outer radius of influence. Incorporatingthe proposed field functions with soft object modeling, soft blending, Ricci's super‐ellipsoid blends, Perlin'sset operations, and R‐functions, etc. can have blending range controls by adjusting the inner and the outer radiiof influence of given field functions. As a result, the sizes of the resulting blending surfaces on soft objects willnot be restricted by the sizes of the blended primitive soft objects and can be enlarged and shrunk freely withoutdeforming the overall shapes of blended primitive soft objects. In addition, a small soft object can have a largeblending region, and a large one can have a small blending region Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling ‐ Curve, surface, solid and object representations

A gradient-based implicit blend

“…(1) give fine control over the resulting shape, as does the superelliptic blend [Hoffmann and Hopcroft 1985;Hsu and Lee 2003]; (2) avoid the gradient discontinuities in the field function exhibited by displacement blends [Rockwood 1989]; (3) handle field functions with local support.…”

Adequate inner bound for geometric modeling with compact field functions

“…While several new composition operators [24,25,26] and composition concepts [27,28] are introduced for field functions with global support, operators for compactly supported fields received less attention until the last decade. Hsu et al [13] improved the control of the blending size using adequate transfer functions modifying the slope of the composed field functions. Barthe et al [14] defined a set of constraints for the creation of binary composition operators on compact fields, focusing on the implicit surface and the outside bound of the field functions.…”

“…A marginal exception is the work of Hsu et al [13] where an inner bound is introduced to directly control the blending size when material is removed. In this work, this bound is not related to any operator conformity property.…”

“…This mapping is symmetric, but if required, individual controls on the inner and outer widths can be achieved using, for instance, Hsu's et al step function [13]. The use of transfer functions for similar conversions is actually common.…”

“…Outside this bound, the function f uniformly equals zero. Many different operators have been developed over the years, increasing their variety and improving their effectiveness [3,12,13,14,15]. While simple max-based composition functions may be enough to define n-ary Boolean operators with sharp transitions (i.e., union, intersection and difference), the most recent and advanced operators are restricted to the composition of only two fields at once [16,17].…”