C 2-(C 3-) continuous interpolation spline curve and surface

1998 ◽  
Vol 13 (3) ◽  
pp. 238-245
Author(s):  
Fang Kui ◽  
Tan Jianrong ◽  
Zhu Guoqing
Keyword(s):  
Interpolation Spline ◽  
Spline Curve ◽  
Continuous Interpolation

Method of Corner Smooth Transition Based on Interpolation Spline

2013 ◽  
Vol 655-657 ◽  
pp. 1260-1266
Author(s):  
Jian Huang ◽  
Ai Ping Song ◽  
Jian Ming Tao ◽  
Dan Ping Yi
Keyword(s):  
Machine Tool ◽  
High Speed ◽  
Transition Process ◽  
Smooth Transition ◽  
Curvature Radius ◽  
Adjustment Coefficient ◽  
Interpolation Spline ◽  
Processing Efficiency ◽  
Spline Curve ◽  
The Impact

Adjustable form cubic interpolation spline curve, changing its form adjustment coefficient can adjust the curvature radius and shape. Using this spline curve can realize the high-speed smooth connecting between adjacent processing trajectory during NC movement. To internal outline corner transition, use cambered spline transfer curve; To external outline corner transition, can use cambered or toroidal spline transfer curve. During the corner transition process, keep the speed constant, adjust the curvature the curvature radius to control the value of acceleration. Corner smooth transition based on the interpolation spline, can effectively reduce the mutation of acceleration, improve processing efficiency, and weaken the impact to the machine tool.

scholarly journals Rational Cubics and Conics Representation: A Practical Approach

1970 ◽  
Vol 1 (2) ◽  
Author(s):  
M. Sarfraz ◽  
Z. Habib
Keyword(s):  
Computer Graphics ◽  
Cubic Spline ◽  
Practical Approach ◽  
Shape Parameters ◽  
Conic Sections ◽  
Interpolation Spline ◽  
Cubic Curves ◽  
Spline Curve ◽  
Special Cases

A rational cubic spline, with one family of shape parameters, has been discussed with the view to its application in Computer Graphics. It incorporates both conic sections and parametric cubic curves as special cases. The parameters (weights), in the description of the spline curve can be used to modify the shape of the curve, locally and globally, at the knot intervals. The rational cubic spline attains parametric   smoothness whereas the stitching of the conic segments preserves visually reasonable smoothness at the neighboring knots. The curve scheme is interpolatory and can plot parabolic, hyperbolic, elliptic, and circular splines independently as well as bits and pieces of a rational cubic spline.Key Words: Computer Graphics, Interpolation, Spline, Conic, Rational Cubic

C˜2 Continuous Cubic Hermite Interpolation Splines with Second-Order Elliptic Variation

2021 ◽  
Vol 7 (6) ◽  
pp. 6317-6331
Author(s):  
Jie Li ◽  
Yaoyao Tu ◽  
Shilong Fei
Keyword(s):  
Shape Control ◽  
Spline Function ◽  
Hermite Interpolation ◽  
Second Order ◽  
Basis Functions ◽  
Interpolation Spline ◽  
Selection Scheme ◽  
Spline Curve ◽  
Spline Curves ◽  
Two Parameters

In order to solve the deficiency of Hermite interpolation spline with second-order elliptic variation in shape control and continuity, c-2 continuous cubic Hermite interpolation spline with second-order elliptic variation was designed. A set of cubic Hermite basis functions with two parameters was constructed. According to this set of basis functions, the three-order Hermite interpolation spline curves were defined in segments 02, and the parameter selection scheme was discussed. The corresponding cubic Hermite interpolation spline function was studied, and the method to determine the residual term and the best interpolation function was given. The results of an example show that when the interpolation conditions remain unchanged, the cubic Hermite interpolation spline curves not only reach 02 continuity, but also can use the parameters to control the shape of the curves locally or globally. By determining the best values of the parameters, the cubic Hermite interpolation spline function can get a better interpolation effect, and the smoothness of the interpolation spline curve is the best.

Description and Smoothing of NC Motion Path Based on the Cubic Trigonometric Interpolation Spline

2013 ◽  
Vol 365-366 ◽  
pp. 515-521 ◽  
Author(s):  
Jian Ming Tao ◽  
Ai Ping Song ◽  
Dan Ping Yi
Keyword(s):  
Smooth Transition ◽  
Motion Path ◽  
Trigonometric Interpolation ◽  
Feed Speed ◽  
Control Points ◽  
Interpolation Spline ◽  
Spline Curve ◽  
Nc Machine ◽  
The Stability ◽  
The Impact

In order to better describe the complex motion path of NC machining and realize the smooth transition between path segments, a kind of cubic trigonometric interpolation spline curve was put forward based on a set of special basis function. The spline curve which with adjustable shape satisfies the C1 continuity and it can accurately describe some common engineering curves such as straight line, circular arc and free curve. According to the given information of control points, different shapes of interpolation spline curve can be gotten by changing the adjustment coefficients. Through selecting proper control points and shape adjustment coefficients near the corner, insert the spline curve can realize the smooth transition at the corner of adjacent NC motion path segments, which can ensure the stability of motion path and the continuous of feed speed. Meanwhile, it also can reduce the impact to NC machine.

Boundary Detection Using Open Spline Curve Based on Mumford-Shah Model

2009 ◽  
Vol 35 (2) ◽  
pp. 132-136 ◽  
Author(s):  
Xiao-Mao LI ◽  
Lin-Lin ZHU ◽  
Yan-Dong TANG
Keyword(s):  
Boundary Detection ◽  
Spline Curve

ACCURACY OF RIVER GEOMETRY INTERPOLATION USING CUBIC SPLINE CURVE AT ALB MISSING AREA AND INFULUENCE OF FLOW REGIME

2018 ◽  
Vol 74 (4) ◽  
pp. I_859-I_864
Author(s):  
Takayuki OKABE ◽  
Takanori YAMAZAKI ◽  
Atsumasa OZAWA ◽  
Shinichi MORITA ◽  
Shigeo HORIUCHI ◽  
...  
Keyword(s):  
Flow Regime ◽  
Cubic Spline ◽  
Spline Curve ◽  
Cubic Spline Curve

scholarly journals Graph-Based Construction of 3D Korean Giwa House Models

Buildings ◽  
2019 ◽  
Vol 9 (3) ◽  
pp. 68
Author(s):  
Mankyu Sung
Keyword(s):  
Data Structure ◽  
Computer Graphics ◽  
Real Time ◽  
Texture Image ◽  
Time Rate ◽  
Commercial Software ◽  
Spline Curve ◽  
High Level ◽  
Complicated Part ◽  
Different Parts

This paper proposes a graph-based algorithm for constructing 3D Korean traditional houses automatically using a computer graphics technique. In particular, we target designing the most popular traditional house type, a giwa house, whose roof is covered with a set of Korean traditional roof tiles called giwa. In our approach, we divided the whole design processes into two different parts. At a high level, we propose a special data structure called ‘modeling graphs’. A modeling graph consists of a set of nodes and edges. A node represents a particular component of the house and an edge represents the connection between two components with all associated parameters, including an offset vector between components. Users can easily add/ delete nodes and make them connect by an edge through a few mouse clicks. Once a modeling graph is built, then it is interpreted and rendered on a component-by-component basis by traversing nodes in a procedural way. At a low level, we came up with all the required parameters for constructing the components. Among all the components, the most beautiful but complicated part is the gently curved roof structures. In order to represent the sophisticated roof style, we introduce a spline curve-based modeling technique that is able to create curvy silhouettes of three different roof styles. In this process, rather than just applying a simple texture image onto the roof, which is widely used in commercial software, we actually laid out 3D giwa tiles on the roof seamlessly, which generated more realistic looks. Through many experiments, we verified that the proposed algorithm can model and render the giwa house at a real time rate.

Exploration on Shape of Profiles Determined by Chord Angle Control Method

2011 ◽  
Vol 314-316 ◽  
pp. 837-841
Author(s):  
Ling Ling ◽  
Yuan Sheng Zeng
Keyword(s):  
Theoretical Basis ◽  
Control Method ◽  
Angle Measurement ◽  
Mapping Method ◽  
Control Methods ◽  
Forming Process ◽  
Spline Curve ◽  
Curve Line ◽  
Line Measure

Through compassion of relative merits of the existing two control methods of straighten anti-curve line and chord line measure for cold-formed profiles, a three-pivot chord angle control method of non-endpoint measurement was proposed in this paper, and its feasibility was proved by using mathematical deduction. Using mapping method, the forming of profiles can be controlled by the only one set of orderly array chord angles and chord lines obtained by a spline curve of profiles, and meanwhile, the length of automation feedstock in forming process of profiles was explored. The present research achievements can provide a good theoretical basis for the further application on controlling profile forming with the chord angle measurement.

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