Embedded Implicit Stand-ins for Animated Meshes: a Case of Hybrid Modelling

In this paper we address shape modelling problems, encountered in computer animation and computer games development that are difficult to solve just using polygonal meshes. Our approach is based on a hybrid modelling concept that combines polygonal meshes with implicit surfaces. A hybrid model consists of an animated polygonal mesh and an approximation of this mesh by a convolution surface stand-in that is embedded within it or is attached to it. The motions of both objects are synchronised using a rigging skeleton. This approach is used to model the interaction between an animated mesh object and a viscoelastic substance, normally modelled in implicit form. The adhesive behaviour of the viscous object is modelled using geometric blending operations on the corresponding implicit surfaces. Another application of this approach is the creation of metamorphosing implicit surface parts that are attached to an animated mesh. A prototype implementation of the proposed approach and several examples of modelling and animation with near real-time preview times are presented

Trimming implicit surfaces

ABSTRACT Algorithms of trimming implicit surfaces yielding surface sheets and stripes are presented. These twodimensional manifolds with boundaries result from set-theoretic operations on an implicit surface and a solid or another implicit surface. The algorithms generate adaptive polygonal approximation of the trimmed surfaces by extending our original implicit surface polygonization algorithm. The presented applications include modeling several spiral shaped surface sheets and stripes (after M. Escher's art works) and extraction of ridges on implicit surfaces. Another promising application of the presented algorithms is modeling heterogeneous objects as implicit complexes

Fast reliable interrogation of procedurally defined implicit surfaces using extended revised affine arithmetic.

Techniques based on interval and previous termaffine arithmetic next term and their modifications are shown to provide previous term reliable next term function range evaluation for the purposes of previous termsurface interrogation.next term In this paper we present a technique for the previous termreliable interrogation of implicit surfacesnext term using a modification of previous termaffine arithmeticnext term called previous term revised affine arithmetic.next term We extend the range of functions presented in previous termrevised affine arithmeticnext term by introducing previous termaffinenext term operations for arbitrary functions such as set-theoretic operations with R-functions, blending and conditional operators. The obtained previous termaffinenext term forms of arbitrary functions provide previous termfasternext term and tighter function range evaluation. Several case studies for operations using previous termaffinenext term forms are presented. The proposed techniques for previous termsurface interrogationnext term are tested using ray-previous termsurfacenext term intersection for ray-tracing and spatial cell enumeration for polygonisation. These applications with our extensions provide previous termfast and reliablenext term rendering of a wide range of arbitrary previous termprocedurally defined implicit surfacesnext term (including polynomial previous termsurfaces,next term constructive solids, pseudo-random objects, previous termprocedurally definednext term microstructures, and others). We compare the function range evaluation technique based on previous termextended revised affine arithmeticnext term with other previous termreliablenext term techniques based on interval and previous termaffine arithmeticnext term to show that our technique provides the previous termfastestnext term and tightest function range evaluation for previous termfast and reliable interrogation of procedurally defined implicit surfaces.next term Research Highlights The main contributions of this paper are as follows. ► The widening of the scope of previous termreliablenext term ray-tracing and spatial enumeration algorithms for previous termsurfacesnext term ranging from algebraic previous termsurfaces (definednext term by polynomials) to general previous termimplicit surfaces (definednext term by function evaluation procedures involving both previous termaffinenext term and non-previous termaffinenext term operations based on previous termrevised affine arithmetic)next term. ► The introduction of a technique for representing procedural models using special previous termaffinenext term forms (illustrated by case studies of previous termaffinenext term forms for set-theoretic operations in the form of R-functions, blending operations and conditional operations). ► The detailed derivation of special previous termaffinenext term forms for arbitrary operators

Shape Modeling by Sketching using Convolution Surfaces

International audienceThis paper proposes a user-friendly modeling system that interactively generates 3D organic-like shapes from user drawn sketches. A skeleton, in the form of a graph of branching polylines and polygons, is first extracted from the user's sketch. The 3D shape is then defined as a convolution surface generated by this skeleton. The skeleton's resolution is adapted according to the level of detail selected by the user. The subsequent 2D strokes are used to infer new object parts, which are combined with the existing shape using CSG operators. We propose an algorithm for computing a skeleton defined as a connected graph of polylines and polygons. To combine the primitives we propose precise CSG operators for a convolution surfaces blending hierarchy. Our new formulation has the advantage of requiring no optimization step for fitting the 3D shape to the 2D contours. This yields interactive performances and avoids any non-desired oscillation of the reconstructed surface. As our results show, our system allows nonexpert users to generate a wide variety of free form shapes with an easy to use sketch-based interface

Polygonization of Multi-Component Non-Manifold Implicit Surfaces through A Symbolic-Numerical Continuation Algorithm

In computer graphics, most algorithms for sampling implicit surfaces use a 2-points numerical method. If the surface-describing function evaluates positive at the first point and negative at the second one, we can say that the surface is located somewhere between them. Surfaces detected this way are called sign-variant implicit surfaces. However, 2-points numerical methods may fail to detect and sample the surface because the functions of many implicit surfaces evaluate either positive or negative everywhere around them. These surfaces are here called sign-invariant implicit surfaces. In this paper, instead of using a 2-points numerical method, we use a 1-point numerical method to guarantee that our algorithm detects and samples both sign-variant and sign-invariant surface components or branches correctly. This algorithm follows a continuation approach to tessellate implicit surfaces, so that it applies symbolic factorization to decompose the function expression into symbolic components, sampling then each symbolic function component separately. This ensures that our algorithm detects, samples, and triangulates most components of implicit surfaces