This paper presents a novel approach to the reconstruction of geometric models and surfaces from ... more This paper presents a novel approach to the reconstruction of geometric models and surfaces from given sets of points using volume splines. It results in the representation of a solid by the inequality The volume spline is based on use of the Green's function for interpolation of scalar function values of a chosen "carrier" solid. Our algorithm is capable of generating highly concave and branching objects automatically. The particular case where the surface is reconstructed from cross-sections is discussed too. Potential applications of this algorithm are in tomography, image processing, animation and CAD f o r bodies with complex surfaces.
The issues of digital preservation of shapes and internal structures of historical and cultural o... more The issues of digital preservation of shapes and internal structures of historical and cultural objects are discussed. An overview of existing approaches to computer modeling of shapes is presented and corresponding problems are considered. We propose a digital preservation paradigm quite different from the currently popular "scan and mesh" approach yielding visible surface models. Our approach is based on constructive modeling that reflects the logical structure of modeled shapes. Constructive Solid Geometry (CSG) and Function Representation (FRep) are examined and practically applied as mathematical representations which fit the purposes of long term digital preservation. Examples of CSG based reconstruction of historical temples and FRep based modeling of traditional lacquer ware are given.
The modern world of computer graphics is mostly dominated by polygonal models. Due to their scala... more The modern world of computer graphics is mostly dominated by polygonal models. Due to their scalability and ease of rendering such models have various applications in a wide range of fields. Unfortunately some shape modelling and animation problems can hardly be ...
The presented approach to discretization of functionally defined heterogeneous objects is oriente... more 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.
In this paper we further develop a novel approach for modelling heterogeneous objects containing ... more In this paper we further develop a novel approach for modelling heterogeneous objects containing entities of various dimensions and representations within a cellular-functional framework based on the implicit complex notion. We provide a brief description for implicit complexes and describe their structure including both the geometry and topology of cells of different types. Then the paper focuses on the development of algorithms for set-theoretic operations on heterogeneous objects represented by implicit complexes. We also describe a step-by-step procedure for the construction of a hybrid model using these operations. Finally, we present a case-study showing how to construct a hybrid model integrating both boundary and function representations. Our examples also illustrate modelling with attributes and dynamic modelling.
The problem considered in this work is to find a dimension independent algorithm for the generati... more 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 zer o value exactl y at th e polygon al object boun dar y; n o extr a zer o-value isosur faces sh ould be gen er ated; C 1 con tin uity 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 th e selected optimization cr iter ia. Th e gen er a ted BSP-fields allow for applyin g tech n iques of fun ction -based modellin g to already existing legacy objects from CAD and computer animation areas, which is illustrated by several examples. Report
... together with the underlying hybrid modelling technology into existing mod-elling software an... more ... together with the underlying hybrid modelling technology into existing mod-elling software and games engines can greatly enhance the ability of artists to generate complex models and animations. References KRAVTSOV, D., FRYAZINOV, O., ADZHIEV, V., PASKO, A., AND ...
Polygonal models are widely used in computer animation. Static polygonal models are commonly anim... more Polygonal models are widely used in computer animation. Static polygonal models are commonly animated using an underlying skeleton controlling the deformation of the mesh. This technique known as skeletal animation allows the artist to produce complex animation sequences in a relatively easy way. However, performing complex transitions between arbitrary animated meshes remains a challenging problem. There is a set of
... Bounding Volumes for Implicit Intersections Galina Pasko∗ British Institute of Technology and... more ... Bounding Volumes for Implicit Intersections Galina Pasko∗ British Institute of Technology and E-commerce, UK Oleg Fryazinov Bournemouth University, UK. Turlif Vilbrandt DigitalMaterialization Group, Japan Alexander Pasko§ Bournemouth University, UK 1 Introduction ...
We propose a new approach to modelling heterogeneous objects containing internal volumetric struc... more 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 parametrised 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.
Proceedings of the 28th Spring Conference on Computer Graphics - SCCG '12, 2012
An efficient representation of a polygonal mesh by a signed continuous distance field is the main... more 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.
We present a general mathematical framework for transforming functionally defined shapes. The pro... more We present a general mathematical framework for transforming functionally defined shapes. The proposed model of extended space mappings considers transformations of a hypersurface in coordinate-function space with its projection onto geometric space. This model covers coordinate space mappings, metamorphosis, and algebraic operations on defining functions, and introduces several new types of transformations, such as function-dependent space mappings and combined mappings. The approach is illustrated by new local deformations created by means of function mappings, feature-based space mapping, offsetting along the normal, thin shell generation, 2D shape blending, and collision-free metamorphosis.
Morphological shape design is interpreted in this paper as a search for new shapes from a particu... more 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. : Results of the user-controlled group metamorphosis: the seven initial chairs (blue) with user-defined and weighted features result in the newly generated shapes (pink).
The automatic generation of volumes bounding the intersection of two implicit surfaces (isosurfac... more The automatic generation of volumes bounding the intersection of two implicit surfaces (isosurfaces of real functions of 3D point coordinates) or Feature Based Volumes (FBV) is presented. Such FBVs are defined by constructive operations, function normalization and offsetting. By applying various offset operations to the intersection of two surfaces, we can obtain variations in the shape of an FBV. The resulting volume can be used as a boundary for blending operations applied to two corresponding volumes, and also for visualisation of feature curves and the modelling of surface based structures including microstructures.
Techniques based on Interval and Affine Arithmetic and their modifications are shown to provide r... more 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 raysurface intersection for ray-tracing and spatial cell enumeration for polygonization. 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.
Enabling animators to smoothly transform between animated meshes of differing topologies is a lon... more Enabling animators to smoothly transform between animated meshes of differing topologies is a long-standing problem in geometric modelling and computer animation. In this paper, we propose a new hybrid approach built upon the advantages of scalar-field-based models (often called implicit surfaces) which can easily change their topology by changing their defining scalar field. Given two meshes, animated by their rigging-skeletons, we associate each mesh with its own approximating implicit surface. This implicit surface moves synchronously with the mesh. The shape-metamorphosis process is performed in several steps: first we collapse the two meshes to their corresponding approximating implicit surfaces, then we transform between the two implicit surfaces and finally we inverse transition from the resulting metamorphosed implicit surface to the target mesh. The examples presented in this paper demonstrating the results of the proposed technique were implemented using an in-house plug-in for Maya TM .
In this paper we address shape modelling problems, encountered in computer animation and computer... more 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.
Existing mesh-and voxel-based modeling methods encounter difficulties when dealing with objects c... more 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.
This paper presents a novel approach to the reconstruction of geometric models and surfaces from ... more This paper presents a novel approach to the reconstruction of geometric models and surfaces from given sets of points using volume splines. It results in the representation of a solid by the inequality The volume spline is based on use of the Green's function for interpolation of scalar function values of a chosen "carrier" solid. Our algorithm is capable of generating highly concave and branching objects automatically. The particular case where the surface is reconstructed from cross-sections is discussed too. Potential applications of this algorithm are in tomography, image processing, animation and CAD f o r bodies with complex surfaces.
The issues of digital preservation of shapes and internal structures of historical and cultural o... more The issues of digital preservation of shapes and internal structures of historical and cultural objects are discussed. An overview of existing approaches to computer modeling of shapes is presented and corresponding problems are considered. We propose a digital preservation paradigm quite different from the currently popular "scan and mesh" approach yielding visible surface models. Our approach is based on constructive modeling that reflects the logical structure of modeled shapes. Constructive Solid Geometry (CSG) and Function Representation (FRep) are examined and practically applied as mathematical representations which fit the purposes of long term digital preservation. Examples of CSG based reconstruction of historical temples and FRep based modeling of traditional lacquer ware are given.
The modern world of computer graphics is mostly dominated by polygonal models. Due to their scala... more The modern world of computer graphics is mostly dominated by polygonal models. Due to their scalability and ease of rendering such models have various applications in a wide range of fields. Unfortunately some shape modelling and animation problems can hardly be ...
The presented approach to discretization of functionally defined heterogeneous objects is oriente... more 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.
In this paper we further develop a novel approach for modelling heterogeneous objects containing ... more In this paper we further develop a novel approach for modelling heterogeneous objects containing entities of various dimensions and representations within a cellular-functional framework based on the implicit complex notion. We provide a brief description for implicit complexes and describe their structure including both the geometry and topology of cells of different types. Then the paper focuses on the development of algorithms for set-theoretic operations on heterogeneous objects represented by implicit complexes. We also describe a step-by-step procedure for the construction of a hybrid model using these operations. Finally, we present a case-study showing how to construct a hybrid model integrating both boundary and function representations. Our examples also illustrate modelling with attributes and dynamic modelling.
The problem considered in this work is to find a dimension independent algorithm for the generati... more 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 zer o value exactl y at th e polygon al object boun dar y; n o extr a zer o-value isosur faces sh ould be gen er ated; C 1 con tin uity 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 th e selected optimization cr iter ia. Th e gen er a ted BSP-fields allow for applyin g tech n iques of fun ction -based modellin g to already existing legacy objects from CAD and computer animation areas, which is illustrated by several examples. Report
... together with the underlying hybrid modelling technology into existing mod-elling software an... more ... together with the underlying hybrid modelling technology into existing mod-elling software and games engines can greatly enhance the ability of artists to generate complex models and animations. References KRAVTSOV, D., FRYAZINOV, O., ADZHIEV, V., PASKO, A., AND ...
Polygonal models are widely used in computer animation. Static polygonal models are commonly anim... more Polygonal models are widely used in computer animation. Static polygonal models are commonly animated using an underlying skeleton controlling the deformation of the mesh. This technique known as skeletal animation allows the artist to produce complex animation sequences in a relatively easy way. However, performing complex transitions between arbitrary animated meshes remains a challenging problem. There is a set of
... Bounding Volumes for Implicit Intersections Galina Pasko∗ British Institute of Technology and... more ... Bounding Volumes for Implicit Intersections Galina Pasko∗ British Institute of Technology and E-commerce, UK Oleg Fryazinov Bournemouth University, UK. Turlif Vilbrandt DigitalMaterialization Group, Japan Alexander Pasko§ Bournemouth University, UK 1 Introduction ...
We propose a new approach to modelling heterogeneous objects containing internal volumetric struc... more 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 parametrised 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.
Proceedings of the 28th Spring Conference on Computer Graphics - SCCG '12, 2012
An efficient representation of a polygonal mesh by a signed continuous distance field is the main... more 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.
We present a general mathematical framework for transforming functionally defined shapes. The pro... more We present a general mathematical framework for transforming functionally defined shapes. The proposed model of extended space mappings considers transformations of a hypersurface in coordinate-function space with its projection onto geometric space. This model covers coordinate space mappings, metamorphosis, and algebraic operations on defining functions, and introduces several new types of transformations, such as function-dependent space mappings and combined mappings. The approach is illustrated by new local deformations created by means of function mappings, feature-based space mapping, offsetting along the normal, thin shell generation, 2D shape blending, and collision-free metamorphosis.
Morphological shape design is interpreted in this paper as a search for new shapes from a particu... more 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. : Results of the user-controlled group metamorphosis: the seven initial chairs (blue) with user-defined and weighted features result in the newly generated shapes (pink).
The automatic generation of volumes bounding the intersection of two implicit surfaces (isosurfac... more The automatic generation of volumes bounding the intersection of two implicit surfaces (isosurfaces of real functions of 3D point coordinates) or Feature Based Volumes (FBV) is presented. Such FBVs are defined by constructive operations, function normalization and offsetting. By applying various offset operations to the intersection of two surfaces, we can obtain variations in the shape of an FBV. The resulting volume can be used as a boundary for blending operations applied to two corresponding volumes, and also for visualisation of feature curves and the modelling of surface based structures including microstructures.
Techniques based on Interval and Affine Arithmetic and their modifications are shown to provide r... more 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 raysurface intersection for ray-tracing and spatial cell enumeration for polygonization. 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.
Enabling animators to smoothly transform between animated meshes of differing topologies is a lon... more Enabling animators to smoothly transform between animated meshes of differing topologies is a long-standing problem in geometric modelling and computer animation. In this paper, we propose a new hybrid approach built upon the advantages of scalar-field-based models (often called implicit surfaces) which can easily change their topology by changing their defining scalar field. Given two meshes, animated by their rigging-skeletons, we associate each mesh with its own approximating implicit surface. This implicit surface moves synchronously with the mesh. The shape-metamorphosis process is performed in several steps: first we collapse the two meshes to their corresponding approximating implicit surfaces, then we transform between the two implicit surfaces and finally we inverse transition from the resulting metamorphosed implicit surface to the target mesh. The examples presented in this paper demonstrating the results of the proposed technique were implemented using an in-house plug-in for Maya TM .
In this paper we address shape modelling problems, encountered in computer animation and computer... more 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.
Existing mesh-and voxel-based modeling methods encounter difficulties when dealing with objects c... more 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.
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Papers by A. Pasko