Truss lattices are common in a wide variety of engineering applications, due to their high ratio of strength versus relative density. They are used both as the interior support for other structures, and as structures on their own. Using 3D sphere packing, we propose a set of methods for generating truss lattices that fill the interior of B-rep models, polygonal or (trimmed) NURBS based, of arbitrary shape. Once the packing of the spheres has been established, beams between the centers of adjacent spheres are constructed, as spline based B-rep geometry. We also demonstrate additional capabilities of our methods, including connecting the truss lattice to (a shell of) the B-rep model, as well as constructing a tensor-product trivariate volumetric representation of the truss lattice — an important step towards direct compatibility for analysis.

The Construction of Conforming-to-shape Truss Lattice Structures via 3D Sphere Packing

A new method of collision free motion path planning using Non uniform rational B- Spline curves for mobile robots is addressed in this paper. Obstacles of polygonal nature are used and the navigation occurs in a dynamic environment. Mathematical Modeling with vector addition technique is used to compute the set of points which will form the final path. NURBS technique is applied on the computed set of points which results in smooth curve as the final path, giving the advantage of more efficient motion. NURBS offsets of the computed NURBS path have been defined to avoid collision. Number of obstacles is not a constraint in the model presented. Number and position of obstacles can be changed dynamically which will be encountered by the robot and the path computed will be updated accordingly ensuring the shortest path.

Robot motion planning in a dynamic environment using offset Non-Uniform Rational B-Splines (NURBS)

This is a survey paper regarding NURB(Non-Rational B spline) which will portray the very popularly used mathematical representation of 2 or 3 Dimensional objects which can be standard shapes or free form shapes. Many researchers since 1970 is been working on different fields of shape formation, path generation, feedrate adaptation, increasing machining efficiency etc to propose algorithms which can influence the properties of NURB curves and execute some problem solutions in efficient ways. Here we make a study of the finest algorithms which have been proposed and applied on specific areas of Computer Numerical Control and efficient results were obtained.

http://ieeexplore.ieee.org/iel7/7088896/7100186/07100595.pdf

On NURBS algorithms and application: A survey

• Attempted 3 approaches for generation of points: 1. Direct Interpolation Approach: Interpolating points in each triangle 2. Slicing Approach: Slicing the geometry by plane. Obtaining two intersection points for each triangle and interpolating points between them. 3. Slicing-Chain Approach Similar to Slicing Approach, but forming chains of the lines formed by intersection of plane and triangles. Interpolating the points on the chain.

/pdf/uniform-micro-patterning-of-an-arbitrary-surface-1kdyq0meqo.pdf

Uniform Micro-Patterning of an Arbitrary Surface

A new approach for computing NURBS offset curves and surfaces was proposed in this paper. First of all, the special NURBS curves and surfaces were recognized to be different with free form ones. The offsets of the special cases were precisely calculated according to their equations. The offset of free form NURBS curves and surfaces were solved using the following steps: (1) Decomposing the NURBS curve and surface into Bezier segments or surface patches; (2) Sampling Bezier segments or surface patches and removing duplicate points; (3) Interpolating the offset points and creating offset curve or surface; (4) Reducing the control points by removing all removable knots with a user defined tolerance. On the premise of keeping the shape of offset curves and surfaces, not only the degree of curve or surface could be freely controlled, but also less number of control points was needed and also duplicate knots were avoided. It was proved in practical engineering that the efficiency and precision were improved mush.

A new NURBS offset curves and surfaces algorithm based on different geometry shape

Current surface reconstruction algorithms focus on complex surfaces or irregular surfaces However, surfaces of revolution are very important in industrial applications and reconstruction of rotating surfaces is often required The most important step in surface reconstruction of revolution is to determine its axis In this paper, iteration method is utilized to compute the central axis, which solves the problem of the shape identification of slice data According to the defection difference of slice data, which will result in different shape, relative identification algorithms of circle and circular arc are proposed to recover the profiles Different types of data are tested in our prototype system for reverse engineering Experimental results show that the algorithm is practical and efficient

A new research of surfaces reconstruction of revolution in reverse engineering

In order to solve the problems that complex mesh needs a huge storage and high transmission price, and is difficult to be edited, simple algorithms are often required to obtain a series of object simulations In this paper, three different parameterization algorithms are adopted to analyze their different effects on mesh quality after remeshing Based on the parameterized mesh over a planar domain, subdivision algorithm is used to transform the mesh with arbitrary structure to a regular triangular or quadrilateral mesh The algorithm in this paper aims at remeshing not only disk-like objects without holes but also closed objects, which using the concept of virtual boundary The algorithm is proved practical and efficient in our prototype system

Li Ji-Jun

Papers

A new NURBS offset curves and surfaces algorithm based on different geometry shape

A new research of surfaces reconstruction of revolution in reverse engineering

Research on the parameterization and remeshing technique application in surface reconstruction