Geometric Modeling

Geometric Environment Modeling System

Flexible system configurations and adaptability to changing environments and environmental conditions are key concerns for autonomous systems in future applications, either in industrial production processes, building automation, or health-care scenarios. New technologies for instrumented and smart environments support the distribution and acquisition of a diversity of information, but the orga...

Geometric and Solid Modeling

Simplicial Complexes and Geometric Realization Since we de ned simplices as convex combinations of points, it is conceivable that this de nition is too narrow. That is, when constructing a simplicial complex, can we obtain more complicated structures using simplices that are only homeomorphic to convex combinations? From a topological point of view, the answer is no, and is justi ed as follows....

Splines and geometric modeling

Piecewise polynomials of some xed degree and continuously di erentiable upto some order are known as splines or nite elements. Splines are used in applications ranging from image processing, computer aided design, to the solution of partial di erential equations via nite element analysis. The spline tting problem of constructing a mesh of nite elements that interpolate or approximate multivaria...

Notes on Geometric Modeling

Chapter 4: Geometric Modeling

2 Smoothing Polyhedra 13 2.1 C1 Continuity and Compatibility Conditions . . . . . . . . . . . . . . . . . . . . . . 13 2.1.1 Necessary and Sufficiency Conditions . . . . . . . . . . . . . . . . . . . . . . . 14 2.1.2 Compatibility and Non-Singularity Constraints . . . . . . . . . . . . . . . . . 14 2.2 Polyhedra Smoothing Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2....