Free-form deformation of solid geometric models
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
Functional composition algorithms via blossoming
ACM Transactions on Graphics (TOG)
Free form surface analysis using a hybrid of symbolic and numeric computation
Free form surface analysis using a hybrid of symbolic and numeric computation
An optimal algorithm for expanding the composition of polynomials
ACM Transactions on Graphics (TOG)
Geometric constraint solver using multivariate rational spline functions
Proceedings of the sixth ACM symposium on Solid modeling and applications
Comparing Offset Curve Approximation Methods
IEEE Computer Graphics and Applications
B-Spline Free-Form Deformation of Polygonal Objects through Fast Functional Composition
GMP '00 Proceedings of the Geometric Modeling and Processing 2000
Precise Voronoi cell extraction of free-form rational planar closed curves
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Sliding windows algorithm for B-spline multiplication
Proceedings of the 2007 ACM symposium on Solid and physical modeling
ACM SIGGRAPH 2008 papers
Computation of the solutions of nonlinear polynomial systems
Computer Aided Geometric Design
Hausdorff and minimal distances between parametric freeforms in R2and R3
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Precise Hausdorff distance computation for planar freeform curves using biarcs and depth buffer
The Visual Computer: International Journal of Computer Graphics
Dual loops meshing: quality quad layouts on manifolds
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
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Functional composition can be computed efficiently, robustly, and precisely over polynomials and piecewise polynomials represented in the Bezier and B-spline forms (DeRose et al., 1993) [13], (Elber, 1992) [3], (Liu and Mann, 1997) [14]. Nevertheless, the applications of functional composition in geometric modeling have been quite limited. In this work, as a testimony to the value of functional composition, we first recall simple applications to curve-curve and curve-surface composition, and then more extensively explore the surface-surface composition (SSC) in geometric modeling. We demonstrate the great potential of functional composition using several non-trivial examples of the SSC operator, in geometric modeling applications: blending by composition, untrimming by composition, and surface distance bounds by composition.