NURBS-Diff: A Differentiable Programming Module for NURBS
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We mathematically define the derivatives of the NURBS curves or surfaces with respect to the input parameters (control points, weights, and the knot vector).
It is interesting to note that the difference in left and right derivatives of curves is due to the fact that different sets of functions are nonvanishing for ...
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It is often necessary to evaluate derivatives of NURBS along with a point. Consider a routine that evaluates all derivatives up to order q . Here is a summary ...
The operators are used to compute NURBS entities by performing algebraic operations using NURBS ... Dot and cross products, sum/difference and derivative ...
Material model based on NURBS response surfaces - ScienceDirect
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Constitutive material tensor is calculated by using the derivatives of rational surfaces. The surfaces possess two axes of strain and an axis of stress. The ...
1. Recognize special shapes and offset them precisely. · 2. Sample the offset curve or surface based on second derivatives. · 3. Interpolate these points with ...
Feb 15, 2014 · Shape optimization of axisymmetric solids of revolution using a geometry description by NURBS surfaces, with a Sequential Quadratic ...
A non-uniform rational B-splines (NURBS) based optimization ...
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Apr 7, 2024 · This work presents a systematic optimization method utilizing non-uniform rational B-splines (NURBS) to represent fibers in composites and ...
We present a method for generating a one-parameter family of curves that produce a smooth transition between a Bézier curve and its control polygon.