Development of Simultaneous Measurement of 3-D Shapes and Normal Vectors for Specular Objects

1999 ◽  
Vol 11 (2) ◽  
pp. 112-116
Author(s):  
Saburo Okada ◽  
◽  
Masaaki Imade ◽  
Hidekazu Miyauchi
Keyword(s):  
Optical Measurement ◽  
Maximum Error ◽  
Surface Shape ◽  
Normal Vector ◽  
Curved Surfaces ◽  
Vector Data ◽  
Optical Position ◽  
Normal Vectors ◽  
Specular Objects ◽  
Shape Data

Our research institute developed and built an experimental optical measurement system for specular objects able to simultaneously measure 3-D shapes and normal vectors of surfaces to measure shapes of objects with mirror-finished surfaces and to restore original shapes accurately by inputting measured values in CG and CAD systems. A semiconductor laser spotlight is irradiated on the measured surface vertically or obliquely. Space coordinates of rays reflected on the surface are instantaneously measured at 2 different points in space using optical position sensors rotating at a constant speed. The 3-D coordinates and normal vectors of the reflection point are obtained geometrically. A performance evaluation using a metallic semisphere with a mirror-finished surface showed that the system simultaneously measured 3-D displacement and normal vectors of specular curved surfaces of any angles up to 20 degrees, with maximum error of several degrees in normal vectors and several millimeters in surface shape. The developed system may restore higher quality curved surfaces than conventionally because it reconstitutes curved surfaces using both measured 3-D shape data and normal vector data.

Computer Aided Style Design System Based on Highlight Lines

2009 ◽  
Author(s):  
Sakiko Yano ◽  
Hideki Aoyama
Keyword(s):  
Surface Shape ◽  
Free Form ◽  
Design System ◽  
Normal Vector ◽  
High Quality ◽  
Design Work ◽  
Design Processes ◽  
Normal Vectors ◽  
Free Form Surfaces ◽  
Unit Normal

Free-form surfaces are useful for modeling the external shape of industrial products but designers are still facing difficulty in designing high-quality aesthetic surfaces because commercial CAD systems currently available lack the required performance to support their design work. This has therefore led to the increasing need for design-aiding modeling systems to enhance the efficiency of high quality surface design processes. This paper proposes a method of redesigning aesthetic surface shapes by controlling unit normal vectors on the surface and discusses a fundamental system constructed based on the proposed technique. Attempts were also made to construct the required character lines using the proposed technique. Additionally, the validity of the proposed technique was also verified. In the surface evaluation stage of existing product design processes, the highlight-check method using highlight lines on the surface of a model is the most common and popular evaluation method even though methods using curvature and isophote have been proposed. With this method, the unit normal vectors on the surface are controlled by highlight lines. A highlight line is defined as a curve which consists of points with a constant angle to the right reflective direction when a beam shines on an arbitrary point on a surface. With this highlight-check system, highlight lines are displayed on the screen and evaluated by the designer. When highlight lines are faulty or those required by the designer cannot be obtained, the designer just needs to enter the required highlight lines manually by drawing with a pen tablet on LCD interactive display to improve surface quality. Usually, the system takes input highlight line information as unit normal vector information, and constructs the required surface shape using that information.

Research and application on force control of industrial robot polishing concave curved surfaces

2018 ◽  
Vol 233 (6) ◽  
pp. 1674-1686 ◽  
Author(s):  
Yufeng Ding ◽  
Xinpu Min ◽  
Weiwei Fu ◽  
Zilong Liang
Keyword(s):  
Force Control ◽  
Industrial Robot ◽  
Cavity Surface ◽  
Normal Vector ◽  
Curved Surfaces ◽  
Integral Control ◽  
Proportional Integral ◽  
Surface Normal ◽  
Automatic Polishing ◽  
Normal Vectors

In order to improve the quality of the industrial robot automatic polishing on curved surfaces and ensure the constant polishing pressure during polishing process, a method for polishing complex concave cavity surfaces with industrial robot is proposed in this article. The method can achieve stable force control and precise position control and is easy to be realized online. In order to ensure the removal rate uniformity of surface material at different normal vectors, a method for adjusting the speed of motorized spindle in real time according to the surface normal vector is proposed. After planning the trajectory and normal vectors, combined with the feedback force signal from the sensor and the proportional–integral controller in the direction of the normal vector, the robot terminal tool corrects the trajectory in the direction of the surface normal vector, indirectly realizing force control between the tool and the surface. The robot polishing system with different polishing tools has different system stiffness. In order to ensure the polishing system with different stiffness to have a better tracking performance of the contact force, an adaptive proportional–integral control algorithm proposed in this article can be used to evaluate the stiffness of polishing system and to adjust proportional–integral parameters. The simulation and experimental results indicate that the method can realize the polishing of concave cavity surface commendably.

scholarly journals The Numerical Analysis of the Flow on the Smooth and Nonsmooth Boundaries by IBEM/DBIEM

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Gang Xu ◽  
Guangwei Zhao ◽  
Jing Chen ◽  
Shuqi Wang ◽  
Weichao Shi
Keyword(s):  
Boundary Value ◽  
Three Dimensional ◽  
Boundary Surface ◽  
Tangential Velocity ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Surface Shape ◽  
Normal Vector ◽  
Computational Domain ◽  
Nonsmooth Boundary

The value of the tangential velocity on the Boundary Value Problem (BVP) is inaccurate when comparing the results with analytical solutions by Indirect Boundary Element Method (IBEM), especially at the intersection region where the normal vector is changing rapidly (named nonsmooth boundary). In this study, the singularity of the BVP, which is directly arranged in the center of the surface of the fluid computing domain, is moved outside the computational domain by using the Desingularized Boundary Integral Equation Method (DBIEM). In order to analyze the accuracy of the IBEM/DBIEM and validate the above-mentioned problem, three-dimensional uniform flow over a sphere has been presented. The convergent study of the presented model has been investigated, including desingularized distance in the DBIEM. Then, the numerical results were compared with the analytical solution. It was found that the accuracy of velocity distribution in the flow field has been greatly improved at the intersection region, which has suddenly changed the boundary surface shape of the fluid domain. The conclusions can guide the study on the flow over nonsmooth boundaries by using boundary value method.

Extracting Geometric Edges from 3D Point Clouds Based on Normal Vector Change

2014 ◽  
Vol 571-572 ◽  
pp. 729-734
Author(s):  
Jia Li ◽  
Huan Lin ◽  
Duo Qiang Zhang ◽  
Xiao Lu Xue
Keyword(s):  
Point Clouds ◽  
Detection Algorithm ◽  
Growth Strategy ◽  
Normal Vector ◽  
Geometric Morphometric ◽  
3D Point Clouds ◽  
Real Scene ◽  
Edge Points ◽  
Normal Vectors ◽  
Change Intensity

Normal vector of 3D surface is important differential geometric property over localized neighborhood, and its abrupt change along the surface directly reflects the variation of geometric morphometric. Based on this observation, this paper presents a novel edge detection algorithm in 3D point clouds, which utilizes the change intensity and change direction of adjacent normal vectors and is composed of three steps. First, a two-dimensional grid is constructed according to the inherent data acquisition sequence so as to build up the topology of points. Second, by this topological structure preliminary edge points are retrieved, and the potential directions of edges passing through them are estimated according to the change of normal vectors between adjacent points. Finally, an edge growth strategy is designed to regain the missing edge points and connect them into complete edge lines. The results of experiment in a real scene demonstrate that the proposed algorithm can extract geometric edges from 3D point clouds robustly, and is able to reduce edge quality’s dependence on user defined parameters.

scholarly journals A special interpretation of the concept constant breadth for a space curve

2019 ◽  
Vol 23 (Suppl. 1) ◽  
pp. 371-382
Author(s):  
Tuba Agirman-Aydin
Keyword(s):  
Variable Coefficients ◽  
Space Curve ◽  
Normal Vector ◽  
Exit Point ◽  
Constant Breadth ◽  
Normal Vectors ◽  
Linear Differential ◽  
Curve Of Constant Breadth ◽  
Definition Of ◽  
Curvature And Torsion

The definition of curve of constant breadth in the literature is made by using tangent vectors, which are parallel and opposite directions, at opposite points of the curve. In this study, normal vectors of the curve, which are parallel and opposite directions are placed at the exit point of the concept of curve of constant breadth. In this study, on the concept of curve of constant breadth according to normal vector is worked. At the conclusion of the study, is obtained a system of linear differential equations with variable coefficients characterizing space curves of constant breadth according to normal vector. The coefficients of this system of equations are functions depend on the curvature and torsion of the curve. Then is obtained an approximate solution of this system by using the Taylor matrix collocation method. In summary, in this study, a different interpretation is made for the concept of space curve of constant breadth, the first time. Then this interpretation is used to obtain a characterization. As a result, this characterization we?ve obtained is solved.

A Novel Mini Calibrator for Thermochromic Liquid Crystals

2000 ◽  
Vol 123 (3) ◽  
pp. 604-607 ◽  
Author(s):  
Christopher J. Elkins ◽  
John Fessler ◽  
John K. Eaton
Keyword(s):  
Liquid Crystal ◽  
Liquid Crystals ◽  
Wide Band ◽  
Maximum Error ◽  
Curved Surfaces ◽  
Copper Block ◽  
Crystal Sample ◽  
Dark Blue ◽  
Cooling Ability

A small calibrator has been constructed to facilitate wide-band liquid crystal temperature measurements on complex, curved surfaces. The calibrator’s size, 21.3 mm by 20.3 mm by 10.0 mm thick, makes it ideal for in-situ calibrations at multiple sites on curved surfaces. Its design utilizes the heating/cooling ability of a thermoelectric cooler, and its temperature is quickly and accurately controlled by computer. To test the calibrator’s accuracy, a liquid crystal sample was calibrated. Subsequent comparisons to thermistor measurements of a uniform temperature copper block painted with liquid crystals showed the calibration to be accurate to +/−0.1°C between the red start and the approximate blue start temperatures, and the maximum error was less than +/−0.3°C in the dark blue/violet region.

Computing Offsets of NURBS Curve and Surface

2012 ◽  
Vol 542-543 ◽  
pp. 537-540
Author(s):  
Ying Yue ◽  
Jun Jia
Keyword(s):  
Curve Surface ◽  
Computational Time ◽  
Normal Vector ◽  
Unit Normal Vector ◽  
Nurbs Curve ◽  
Vector Direction ◽  
Normal Vectors ◽  
Offset Curve ◽  
Offset Error ◽  
Unit Normal

This paper presents an algorithm for the offsetting of NURBS curve/surface. First the unit normal vectors of the progenitor NURBS curve/surface is computed precisely, then the offset curve/surface can be obtained by offsetting the progenitor curve/surface in the normal vector direction with the required distance. Considerable extra computational time can be saved, especially when they are to be offset by several times. As the method successfully computes the unit normal vector of the progenitors, the offset error of this method is zero. The method can also be generalized to other degree NURBS curve/surface.

scholarly journals Second-order normal vectors to a convex epigraph

1994 ◽  
Vol 50 (1) ◽  
pp. 123-134 ◽  
Author(s):  
Alberto Seeger
Keyword(s):  
Convex Function ◽  
Mathematical Object ◽  
Second Order ◽  
Normal Vector ◽  
Subdifferential Mapping ◽  
Normal Vectors

The second–order behaviour of a nonsmooth convex function f is reflected by the so–called second–order subdifferential mapping ∂2f. This mathematical object has been intensively studied in recent years. Here we study ∂2f in connection with the geometric concept of “second-order normal vector” to the epigraph of f.

scholarly journals The Geometry of Power Systems Steady-State Equations– Part II: a Power Surface Study

2020 ◽  
pp. 47-53
Author(s):  
B. Ayuev ◽  
V. Davydov ◽  
P. Erokhin ◽  
V. Neuymin ◽  
A. Pazderin
Keyword(s):  
Steady State ◽  
Power Systems ◽  
Transmission Loss ◽  
Normal Vector ◽  
State Equations ◽  
Marginal State ◽  
Normal Vectors ◽  
System States ◽  
Steady State Solutions ◽  
System Power

Steady-state equations play an essential part in the theory of power systems and the practice of computations. These equations are directly or mediately used almost in all areas of the theory of power system states, constituting its basis. This two-part study deals with a geometrical interpretation of steady-state solutions in a power space. Part I has proposed considering the power system's steady states in terms of power surface. Part II is devoted to an analytical study of the power surface through its normal vectors. An interrelationship between the entries of the normal vector is obtained through incremental transmission loss coefficients. Analysis of the normal vector has revealed that in marginal states, its entry of the slack bus active power equals zero, and the incremental transmission loss coefficient of the slack bus equals one. Therefore, any attempts of the slack bus to maintain the system power balance in the marginal state are fully compensated by associated losses. In real-world power systems, a change in the slack bus location in the marginal state makes this steady state non-marginal. Only in the lossless power systems, the marginal states do not depend on a slack bus location.

Algorithm for Tool Path Offsetting Based on NURBS Surface

2014 ◽  
Vol 945-949 ◽  
pp. 111-114
Author(s):  
Ying Yue
Keyword(s):  
Tool Path ◽  
Computational Time ◽  
Machining Accuracy ◽  
Normal Vector ◽  
Nurbs Surface ◽  
Unit Normal Vector ◽  
Vector Direction ◽  
Normal Vectors ◽  
Offset Surface ◽  
Unit Normal

This paper presents an algorithm for tool path offsetting based on NURBS surface. First the progenitor free surface is fitted with a bi-cubic NURBS surface and the unit normal vectors of the NURBS surface is computed precisely, then the offset surface can be obtained by offsetting the NURBS surface in the normal vector direction with the required distance. Considerable extra computational time can be saved, especially when they are to be offset by several times. As the method successfully computes the unit normal vector of the progenitors, the offset error of this method is zero. The method can also be generalized to other degree NURBS surface, and it can improve the machining accuracy of the surface.

Sign in / Sign up

Export Citation Format

Share Document