scholarly journals Method for the design of nonaxially symmetric optical systems using free-form surfaces (Erratum)

2021 ◽  
Vol 60 (11) ◽  
Author(s):  
Dmitry Reshidko ◽  
Jose Sasian
Keyword(s):  
Optical Systems ◽  
Free Form ◽  
Free Form Surfaces

Proposal for Machining Optical Free Form Surfaces Using Atmospheric Pressure Plasma Jet

2011 ◽  
Vol 291-294 ◽  
pp. 2995-2998
Author(s):  
Yan Fu Zhang ◽  
Bo Wang ◽  
Shen Dong
Keyword(s):  
Atmospheric Pressure ◽  
Atmospheric Pressure Plasma ◽  
Plasma Jet ◽  
Atmospheric Plasma ◽  
Optical Systems ◽  
Maximum Diameter ◽  
Free Form ◽  
Atmospheric Pressure Plasma Jet ◽  
Pressure Plasma ◽  
Free Form Surfaces

Optics with free form surface can be achieve special imaging effects and reduce component amounts in optical systems. However, it is difficulty to fabricate high accuracy, damage-free optical surface with free form surfaces by conventional method. Atmospheric plasma machining is a non-contact chemical processing method which can fabricate optics without damaged layer. Numerical controlled atmospheric pressure plasma machining (NC-APPM) method is proposed to machine optical free form surfaces. A new atmospheric pressure plasma jet generator was designed to get Gaussian rotational symmetry removal spot and the spot maximum diameter is 1.5mm. Base on dwelling time algorithm, a sinusoidal wave structure, the pitch 2mm and the amplitude 500 nm, is fabricated on a pre-polished flat silica quartz surface using three-axis numerically controlled machine made by ourselves. The result shows that the amplitude error is 59 nm compare to the expectation value surfaces using numerical controlled atmospheric plasma machining method.

scholarly journals Construction and analysis of unified 4-point interpolating nonstationary subdivision surfaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mehwish Bari ◽  
Ghulam Mustafa ◽  
Abdul Ghaffar ◽  
Kottakkaran Sooppy Nisar ◽  
Dumitru Baleanu
Keyword(s):  
Computer Graphics ◽  
Geometric Modeling ◽  
Tension Control ◽  
Free Form ◽  
Subdivision Surfaces ◽  
Smooth Curves ◽  
Practical Applications ◽  
Tension Parameter ◽  
Exact Reproduction ◽  
Free Form Surfaces

AbstractSubdivision schemes (SSs) have been the heart of computer-aided geometric design almost from its origin, and several unifications of SSs have been established. SSs are commonly used in computer graphics, and several ways were discovered to connect smooth curves/surfaces generated by SSs to applied geometry. To construct the link between nonstationary SSs and applied geometry, in this paper, we unify the interpolating nonstationary subdivision scheme (INSS) with a tension control parameter, which is considered as a generalization of 4-point binary nonstationary SSs. The proposed scheme produces a limit surface having $C^{1}$ C 1 smoothness. It generates circular images, spirals, or parts of conics, which are important requirements for practical applications in computer graphics and geometric modeling. We also establish the rules for arbitrary topology for extraordinary vertices (valence ≥3). The well-known subdivision Kobbelt scheme (Kobbelt in Comput. Graph. Forum 15(3):409–420, 1996) is a particular case. We can visualize the performance of the unified scheme by taking different values of the tension parameter. It provides an exact reproduction of parametric surfaces and is used in the processing of free-form surfaces in engineering.

Automatic Generation of Anisotropic Patterns of Geometric Features for Industrial Design

2015 ◽  
Vol 138 (2) ◽  
Author(s):  
Diego Andrade ◽  
Ved Vyas ◽  
Kenji Shimada
Keyword(s):  
Boundary Conditions ◽  
Computer Aided Design ◽  
Industrial Design ◽  
Automatic Generation ◽  
Free Form ◽  
Geometric Features ◽  
Target Domain ◽  
Metric Tensor ◽  
Target Region ◽  
Free Form Surfaces

While modern computer aided design (CAD) systems currently offer tools for generating simple patterns, such as uniformly spaced rectangular or radial patterns, these tools are limited in several ways: (1) They cannot be applied to free-form geometries used in industrial design, (2) patterning of these features happens within a single working plane and is not applicable to highly curved surfaces, and (3) created features lack anisotropy and spatial variations, such as changes in the size and orientation of geometric features within a given region. In this paper, we introduce a novel approach for creating anisotropic patterns of geometric features on free-form surfaces. Complex patterns are generated automatically, such that they conform to the boundary of any specified target region. Furthermore, user input of a small number of geometric features (called “seed features”) of desired size and orientation in preferred locations could be specified within the target domain. These geometric seed features are then transformed into tensors and used as boundary conditions to generate a Riemannian metric tensor field. A form of Laplace's heat equation is used to produce the field over the target domain, subject to specified boundary conditions. The field represents the anisotropic pattern of geometric features. This procedure is implemented as an add-on for a commercial CAD package to add geometric features to a target region of a three-dimensional model using two set operations: union and subtraction. This method facilitates the creation of a complex pattern of hundreds of geometric features in less than 5 min. All the features are accessible from the CAD system, and if required, they are manipulable individually by the user.

scholarly journals Development of Non-contact Profile Sensor for 3-D Free-form Surfaces (1st Report)

1992 ◽  
Vol 58 (11) ◽  
pp. 1886-1892
Author(s):  
Takashi MIYOSHI ◽  
Hiroshi AOKI ◽  
Katsumasa SAITO
Keyword(s):  
Free Form ◽  
Free Form Surfaces

Fully Free-Form Deformation Features (δ-F4) Incorporating Discontinuities

2004 ◽  
Author(s):  
Vincent Cheutet ◽  
Jean-Philippe Pernot ◽  
Jean-Claude Leon ◽  
Bianca Falcidieno ◽  
Franca Giannini
Keyword(s):  
Surface Deformation ◽  
Geometric Constraints ◽  
Free Form ◽  
Initial Surface ◽  
Cad Systems ◽  
Free Form Deformation ◽  
Deformation Features ◽  
Generate Surface ◽  
Prototype Software ◽  
Free Form Surfaces

To limit low-level manipulations of free-form surfaces, the concept of Fully Free Form Deformation Features (δ-F4) have been introduced. They correspond to shapes obtained by deformation of a surface area according to specified geometric constraints. In our work, we mainly focused on those features aimed at enforcing the visual effect of the so-called character lines, extensively used by designers to specify the shape of an object. Therefore, in the proposed approach, 3D lines are used to drive surface deformation over specified areas. Depending on the wished shape and reflection light effects, the insertion of character lines may generate surface tangency discontinuities. In CAD systems, such kind of discontinuities is generally created by a decomposition of the initial surface into several patches. This process can be tedious and very complex, depending on the shape of the deformation area and the desired surface continuity. Here, a method is proposed to create discontinuities on a surface, using the trimming properties of surfaces. The corresponding deformation features produce the resulting surface in a single modification step and handle simultaneously more constraints than current CAD systems. The principle of the proposed approach is based on arbitrary shaped discontinuities in the parameter domain of the surface to allow the surface exhibiting geometric discontinuities at user-prescribed points or along lines. The proposed approach is illustrated with examples obtained using our prototype software.

Mechanistic Modeling of the Ball End Milling Process for Multi-Axis Machining of Free-Form Surfaces

2000 ◽  
Vol 123 (3) ◽  
pp. 369-379 ◽  
Author(s):  
Rixin Zhu ◽  
Shiv G. Kapoor ◽  
Richard E. DeVor
Keyword(s):  
End Milling ◽  
Chip Thickness ◽  
Mechanistic Modeling ◽  
Free Form ◽  
Surface Geometry ◽  
Workpiece Surface ◽  
Ball End Milling ◽  
Modeling Approach ◽  
Free Form Surfaces ◽  
Cutting Point

A mechanistic modeling approach to predicting cutting forces is developed for multi-axis ball end milling of free-form surfaces. The workpiece surface is represented by discretized point vectors. The modeling approach employs the cutting edge profile in either analytical or measured form. The engaged cut geometry is determined by classification of the elemental cutting point positions with respect to the workpiece surface. The chip load model determines the undeformed chip thickness distribution along the cutting edges with consideration of various process faults. Given a 5-axis tool path in a cutter location file, shape driving profiles are generated and piecewise ruled surfaces are used to construct the tool swept envelope. The tool swept envelope is then used to update the workpiece surface geometry employing the Z-map method. A series of 3-axis and 5-axis surface machining tests on Ti6A14V were conducted to validate the model. The model shows good computational efficiency, and the force predictions are found in good agreement with the measured data.

Sign in / Sign up

Export Citation Format

Share Document