The mathematical structure of raster graphics
The mathematical structure of raster graphics
On the representation and manipulation of rigid solids
On the representation and manipulation of rigid solids
Dimension-independent modeling with simplicial complexes
ACM Transactions on Graphics (TOG)
Separation for boundary to CSG conversion
ACM Transactions on Graphics (TOG)
Dimension-independent convex-cell based HPC: representation scheme and implementation issues
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
ACM Transactions on Graphics (TOG)
Interactive Boolean operations for conceptual design of 3-D solids
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Computational geometry in C (2nd ed.)
Computational geometry in C (2nd ed.)
Representations for Rigid Solids: Theory, Methods, and Systems
ACM Computing Surveys (CSUR)
C modeling with A-patches from rational trivariate functions
Computer Aided Geometric Design
Geometric modeling and representation based on sweep mathematical morphology
Information Sciences—Informatics and Computer Science: An International Journal
Graphical Models - Special issue on SMI 2004
Real-time GPU rendering of piecewise algebraic surfaces
ACM SIGGRAPH 2006 Papers
A novel framework for physically based sculpting and animation of free-form solids
The Visual Computer: International Journal of Computer Graphics
Fast and simple hardware accelerated voxelizations using simplicial coverings
The Visual Computer: International Journal of Computer Graphics
Free-Form Solid Modeling with Trimmed Surface Patches
IEEE Computer Graphics and Applications
Geometric Algebra for Computer Graphics
Geometric Algebra for Computer Graphics
Technical Section: GPU-based rendering of curved polygons using simplicial coverings
Computers and Graphics
Geometric Algebra with Applications in Engineering
Geometric Algebra with Applications in Engineering
Direct trimming of NURBS surfaces on the GPU
ACM SIGGRAPH 2009 papers
A robust segment/triangle intersection algorithm for interference tests. Efficiency study
Computational Geometry: Theory and Applications
Connected sum of digital closed surfaces
Information Sciences: an International Journal
LSM: A layer subdivision method for deformable object matching
Information Sciences: an International Journal
Heterogeneous spline surface intersections
Proceedings of the 26th Spring Conference on Computer Graphics
GPU-Accelerated Minimum Distance and Clearance Queries
IEEE Transactions on Visualization and Computer Graphics
Guide to Geometric Algebra in Practice
Guide to Geometric Algebra in Practice
Foundations of Geometric Algebra Computing
Foundations of Geometric Algebra Computing
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Formal models can be useful in computer graphics as a conceptual framework supporting representation systems. This allows to formally derive properties and algorithms and proof their correctness and validity. This paper describes a formal model based on a geometric algebra. This algebra has been used to obtain specific representation systems and study their equivalence. The representation systems derived in a natural way from this model are based on simplicial coverings and can be applied to non-manifold solids and to solids with holes. Representations have been developed for polyhedral and free-form solids. Algorithms described and proved include boolean operations and representation conversion. The paper covers the three abstraction levels: theoretical model, representations and derived algorithms. As a practical application an experimental modeller for free-form solid has been developed (ESC-MOD system: ''Extended Simplicial Chains MOdeller'').