Oleg Fryazinov

Procedural function-based modelling of volumetric microstructures

We propose a new approach to modelling heterogeneous objects containing internal volumetric structures with size of details orders of magnitude smaller than the overall size of the object. The proposed function-based procedural representation provides compact, precise, and arbitrarily parametrized models of coherent microstructures, which can undergo blending, deformations, and other geometric operations, and can be directly rendered and fabricated without generating any auxiliary representations (such as polygonal meshes and voxel arrays). In particular, modelling of regular lattices and cellular microstructures as well as irregular porous media is discussed and illustrated. We also present a method to estimate parameters of the given model by fitting it to microstructure data obtained with magnetic resonance imaging and other measurements of natural and artificial objects. Examples of rendering and digital fabrication of microstructure models are presented.

Multi-scale space-variant FRep cellular structures

Existing mesh and voxel based modeling methods encounter difficulties when dealing with objects containing cellular structures on several scale levels and varying their parameters in space. We describe an alternative approach based on using real functions evaluated procedurally at any given point. This allows for modeling fully parameterized, nested and multi-scale cellular structures with dynamic variations in geometric and cellular properties. The geometry of a base unit cell is defined using Function Representation (FRep) based primitives and operations. The unit cell is then replicated in space using periodic space mappings such as sawtooth and triangle waves. While being replicated, the unit cell can vary its geometry and topology due to the use of dynamic parameterization. We illustrate this approach by several examples of microstructure generation within a given volume or along a given surface. We also outline some methods for direct rendering and fabrication not involving auxiliary mesh and voxel representations.

Procedural Function-Based Spatial Microstructures

We propose a new approach to modelling heterogeneous objects containing internal spatial geometric structures with size of details orders of magnitude smaller than the overall size of the object. The proposed function-based procedural representation provides compact, precise, and arbitrarily parametrized models of coherent microstructures, which can undergo blending, deformations, and other geometric operations, and can be directly rendered and fabricated without generating any auxiliary representations (such as polygonal meshes and voxel arrays). In particular, modelling of regular lattices and cellular microstructures as well as irregular porous media is discussed and illustrated. Examples of rendering and digital fabrication of microstructure models are presented.

Technical Section: Fast reliable interrogation of procedurally defined implicit surfaces using extended revised affine arithmetic

Techniques based on interval and affine arithmetic and their modifications are shown to provide reliable function range evaluation for the purposes of surface interrogation. In this paper we present a technique for the reliable interrogation of implicit surfaces using a modification of affine arithmetic called revised affine arithmetic. We extend the range of functions presented in revised affine arithmetic by introducing affine operations for arbitrary functions such as set-theoretic operations with R-functions, blending and conditional operators. The obtained affine forms of arbitrary functions provide faster and tighter function range evaluation. Several case studies for operations using affine forms are presented. The proposed techniques for surface interrogation are tested using ray-surface intersection for ray-tracing and spatial cell enumeration for polygonisation. These applications with our extensions provide fast and reliable rendering of a wide range of arbitrary procedurally defined implicit surfaces (including polynomial surfaces, constructive solids, pseudo-random objects, procedurally defined microstructures, and others). We compare the function range evaluation technique based on extended revised affine arithmetic with other reliable techniques based on interval and affine arithmetic to show that our technique provides the fastest and tightest function range evaluation for fast and reliable interrogation of procedurally defined implicit surfaces.

Surface and Volume Discretization of Functionally Based Heterogeneous Objects

The presented approach to discretization of functionally defined heterogeneous objects is oriented towards applications associated with numerical simulation procedures, for example, finite element analysis (FEA). Such applications impose specific constraints upon the resulting surface and volume meshes in terms of their topology and metric characteristics, exactness of the geometry approximation, and conformity with initial attributes. The function representation of the initial object is converted into the resulting cellular representation described by a simplicial complex. We consider in detail all phases of the discretization algorithm from initial surface polygonization to final tetrahedral mesh generation and its adaptation to special FEA needs. The initial object attributes are used at all steps both for controlling geometry and topology of the resulting object and for calculating new attributes for the resulting cellular representation.

Discretization of functionally based heterogeneous objects

The presented approach to discretization of functionally defined heterogeneous objects is oriented towards applications associated with numerical simulation procedures, for example, finite element analysis (FEA). Such applications impose specific constraints upon the resulting surface and volume meshes in terms of their topology and metric characteristics, exactness of the geometry approximation, and conformity with initial attributes. The function representation of the initial object is converted into the resulting cellular representation described by a simplicial complex. We consider in detail all phases of the discretization algorithm from initial surface polygonization to final tetrahedral mesh generation and its adaptation to special FEA needs. The initial object attributes are used at all steps both for controlling geometry and topology of the resulting object and for calculating new attributes for the resulting cellular representation.

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. We model the interaction between an animated mesh object and a viscoelastic substance, which is normally represented in an implicit form. Our approach is aimed at achieving verisimilitude rather than physically based simulation. 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.

Efficient evaluation of continuous signed distance to a polygonal mesh

An efficient representation of a polygonal mesh by a signed continuous distance field is the main focus of this work. We compare different approaches to implementing such a representation and choose the most efficient one. Several optimizations to the existing methods are presented including the new traversal technique for the BVH-based signed distance evaluation and packet queries. We also discuss details of the GPU implementation of the efficient signed distance evaluation. Several application examples are presented such as blending set operations, linear metamorphosis, space-time blending and microstructure generation for polygonal meshes.

SMI 2013: Morphological shape generation through user-controlled group metamorphosis

Morphological shape design is interpreted in this paper as a search for new shapes from a particular application domain represented by a set of selected shape instances. This paper proposes a new foundation for morphological shape design and generation. In contrast to existing generative procedures, an approach based on a user-controlled metamorphosis between functionally based shape models is presented. A formulation of the pairwise metamorphosis is proposed with a variety of functions described for the stages of deformation, morphing and offsetting. This formulation is then extended to the metamorphosis between groups of shapes with user-defined, dynamically correlated and weighted feature elements. A practical system was implemented in the form of plugin to Maya and tested by an industrial designer on a group of representative shapes from a particular domain.

BSP-fields: An exact representation of polygonal objects by differentiable scalar fields based on binary space partitioning

The problem considered in this work is to find a dimension independent algorithm for the generation of signed scalar fields exactly representing polygonal objects and satisfying the following requirements: the defining real function takes zero value exactly at the polygonal object boundary; no extra zero-value isosurfaces should be generated; C^1 continuity of the function in the entire domain. The proposed algorithms are based on the binary space partitioning (BSP) of the object by the planes passing through the polygonal faces and are independent of the object genus, the number of disjoint components, and holes in the initial polygonal mesh. Several extensions to the basic algorithm are proposed to satisfy the selected optimization criteria. The generated BSP-fields allow for applying techniques of the function-based modeling to already existing legacy objects from CAD and computer animation areas, which is illustrated by several examples.