Bounded Blending for Function-Based Shape Modeling

Recent advances in implicit surface modeling now provide highly controllable blending effects. These effects rely on the field functions of R 3 → R in which the implicit surfaces are defined. In these fields, there is an outside part in which blending is defined and an inside part. The implicit surface is the interface between these two parts. As recent operators often focus on blending, most efforts have been made on the outer part of field functions and little attention has been paid on the inner part. Yet, the inner fields are important as soon as difference and intersection operators are used. This makes its quality as crucial as the quality of the outside.In this paper, we analyze these shortcomings, and deduce new constraints on field functions such that differences and intersections can be seamlessly applied without introducing discontinuities or field distortions. In particular, we show how to adapt state of the art gradient-based union and blending operators to our new constraints. Our approach enables a precise control of the shape of both the inner or outer field boundaries. We also introduce a new set of asymmetric operators tailored for the modeling of fine details while preserving the integrity of the resulting fields.

Section: Related Workmentioning

confidence: 99%

Adequate inner bound for geometric modeling with compact field functions

Canezin¹,

Guennebaud²,

Barthe³

2013

“…Since the variational technique has global influence (Figure 5a), however, we also construct a bounding field to restrict the warp to a local region. Application of the bounding field is similar to the bounded blending technique [22], however there the artist had to manually define a bounding field using primitive composition. The Warp node automatically constructs a bounding field using the stored WarpCurve as a skeleton.…”

Section: Overviewmentioning

confidence: 99%

WarpCurves: A tool for explicit manipulation of implicit surfaces

Sugihara

Wyvill

Schmidt

2010

We introduce WarpCurves, a technique for interactively manipulating an implicit surface using curve-based spatial deformations. Although implicit surfaces have several advantages in 3D modeling, current workflows are limited by the compositional nature of implicit modeling. Wide classes of surface features that are easy to create with the direct manipulation tools available for explicit surface representations are difficult to reproduce using volumetric implicit operations. We describe a novel spatial deformation that can be used to approximate direct surface manipulation. With our method an artist first draws a curve on the current surface to indicate the feature region-of-interest. Deformations applied to this handle curve are transferred to the implicit surface via an automatically-constructed C 2 continuous space mapping. Additional curves can be added in a hierarchical manner to create complex shapes. Our technique is implemented as a node in the BlobTree hierarchical implicit volume representation, and hence can be used along with other volumetric nodes (operators) such as blending and CSG. Our results show that surface deformations which would be difficult to reproduce using existing volumetric operations can be quickly constructed using warp curves, making them a valuable addition to the implicit modeling toolbox.

“…Moreover, it is easily possible to combine implicitly defined surfaces in various ways, e.g., by blending them together or by Boolean operations (CSG), see e.g. [4,15,23].…”

Section: Related Workmentioning

confidence: 99%

“…For each bisector half-plane we define two blending half-planes B l j 1 The curves are projected orthogonally in the plane with normal (∇ f )(v) through v, and then ordered clockwise. and B r j which include a user-specified small angle θ with B j and also contain the line (23).…”

Section: Implicitly Defined Verticesmentioning

confidence: 99%

Modeling and 3D object reconstruction by implicitly defined surfaces with sharp features

Song

Jüttler

2009

We propose a new method for describing sharp features (i.e., edges and vertices) of implicitly defined surfaces. We consider an initial implicitly defined surface, which is represented as the zero set of a C 1 smooth scalar field with non-vanishing gradients. In order to represent sharp edges and vertices, this surface is augmented by adding new types of implicit representations, called edge descriptors and vertex descriptors. They are defined with the help of the distance field of edge curves. In our implementation, we use circular splines to describe these edge curves, since they support a fast and non-iterative closest point computation.After adding the edge and vertex descriptors to the initial scalar field, the zero set of the augmented function contains the sharp features. We apply the new representation to surface modelling by implicitly defined surfaces with sharp features and to object reconstruction. In the latter case we describe an algorithm for detecting the sharp curves and vertices of a shape which is given by an unorganized point cloud, which are then approximated by circular splines, in order to define the edge and vertex descriptors.