An introduction to splines for use in computer graphics & geometric modeling
An introduction to splines for use in computer graphics & geometric modeling
Extrusion and boundary evaluation for multidimensional polyhedra
Computer-Aided Design - Beyond solid modelling
Integration of polynomials over n-dimensional polyhedra
Computer-Aided Design - Beyond solid modelling
An introduction to the programming language FL
Research topics in functional programming
Incremental topological flipping works for regular triangulations
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Dimension-independent modeling with simplicial complexes
ACM Transactions on Graphics (TOG)
Geometric programming: a programming approach to geometric design
ACM Transactions on Graphics (TOG)
The DrScheme project: an overview
ACM SIGPLAN Notices
Communications of the ACM
Geometric Programming for Computer Aided Design
Geometric Programming for Computer Aided Design
SURFACES FOR COMPUTER-AIDED DESIGN OF SPACE FORMS
SURFACES FOR COMPUTER-AIDED DESIGN OF SPACE FORMS
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We discuss the problem of geometric design of curved ducts with variable cross-section by transfinite interpolation with integro-differential constraints. This work is a contribution to a research program including numerical simulation and preliminary design of an experimental apparatus for studying fluid-dynamics of air internal combustion engines of new conception. The proposed geometric modeling approach is based on piecewise multivariate transfinite interpolation of assigned cross-sections, via combination of section-generating functions with univariate quintic Hermite's polynomials. The volume mapping produced by such transfinite interpolation is composed with a local section scaling extracted form a one-parameter family of affine transformations, where the diagonal coefficients depend on the ratio between the areas of the starting and current sections. An appropriately chosen point sampling of the duct generated by the composition of volume mapping and section scaling is employed to generate a cell decomposition of the duct volume with tetrahedral elements. Such elements are used for numerical simulation of the fluid-dynamics problem.