Place the Vertices Anywhere on the Curve and Simplify

A polygonal curve is simplified to reduce its number of vertices, while maintaining similarity to its original shape. Numerous results have been published for vertex-restricted simplification, in which the vertices of the simplified curve are a subset of the vertices of the input curve. In curve-restricted simplification, i.e. when the vertices of the simplified curve are allowed to be placed on the edges of the input curve, the number of vertices may be much more reduced. In this paper, we present algorithms for computing curve-restricted simplifications of polygonal curves under the local Hausdorff distance measure.

An Image-Based Approach to Variational Path Synthesis of Linkages

This paper brings together computer vision, mechanism synthesis, and machine learning to create an image-based variational path synthesis approach for linkage mechanisms. An image-based approach is particularly amenable to mechanism synthesis when the input from mechanism designers is deliberately imprecise or inherently uncertain due to the nature of the problem. In addition, it also lends itself naturally to the creation of a unified approach to mechanism synthesis for different types of mechanisms, since for example, images are formed from a collection of pixels, which themselves could be generated from a four-bar or six-bar. Path synthesis problems have generally been solved for a set of precision points on the intended path such that the designed mechanism passes through those points. This approach usually leads to a small set of over-fitted solutions to particular precision points. However, most kinematic synthesis problems are concept generation problems, where a designer cares more about generating a large number of plausible solutions, which could reach given precision points only approximately. This paper models the input curve as a probability distribution of image pixels and employs a probabilistic generative model to capture the inherent uncertainty in the input. In addition, it gives feedback on the input quality and provides corrections for a more conducive input. The image representation allows for capturing local spatial correlations, which plays an important role in finding a variety of solutions with similar semantics as the input curve. This approach is also conducive to implementation for pressure-sensitive touch-based design interfaces, where the input is not a zero-thickness curve, but the sweep of a small patch on the finger.

An Image-Based Approach to Variational Path Synthesis of Linkages

This paper brings together computer vision, mechanism synthesis, and machine learning to create an image-based variational path synthesis approach for linkage mechanisms. An image-based approach is particularly amenable to mechanism synthesis when the input from mechanism designers is deliberately imprecise or inherently uncertain due to the nature of the problem. In addition, it also lends itself naturally to the creation of a unified approach to mechanism synthesis since pixels do not care if they were generated from a four-bar or six-bar. Path synthesis problem has generally been solved for a set of precision points on the intended path such that the designed mechanism passes through those points. This approach usually leads to a small set of over-fitting solutions to the particular precision points. However, most kinematic synthesis problems are concept generation problem where a designer cares more about generating a large number of plausible solutions. This paper models the input curve as a probability distribution of image pixels and employs a probabilistic generative model to capture the inherent uncertainty in the input. In addition, it gives feedback on the input quality and provides corrections for a more conducive input. The image representation allows for capturing local spatial correlations, which plays an important role in finding a variety of solutions with similar semantics as the input curve.

Design of Simulation Definite Integral Application learning Using Trapezoid Method based on VB.Net

The definite integral is one of the subjects that is difficult for students to understand because the process of calculating definite integral of functions is quite complicated and long because it requires mastery of some integrating rules so an interactive learning simulation application is needed to make it easier for students to calculate definite integral of functions and the depiction of the area the curve. One method for calculating definite integrals is the trapezoid method. The trapezoid method works by dividing the boundary into 2 intervals namely x = x0 to x = x1. Simulation media application learning will be designed with the VB.Net programming language. This simulation media learning starts with reading and checking data input. The process is continued by displaying the depiction of the input curve and ending with calculating the area of the curve. Simulation media learning provides a facility to store the input data, the results of the calculation of the area and the image of the curve function in the image format of * .bmp. In this media, the media and material expert’s the results of the average are produced by 88.68% included into media category is very valid media and the results of pre-test and post-test trials showed an increase with an average value of 48.3 for pre-test and 87 for the post-test of the passing grade requirement of 70.Keywords: Definite Integral, Trapezoid Method,VB.Net, Media Validation.

Inverse design of an isotropic suspended Kirchhoff rod: theoretical and numerical results on the uniqueness of the natural shape

Solving the equations for Kirchhoff elastic rods has been widely explored for decades in mathematics, physics and computer science, with significant applications in the modelling of thin flexible structures such as DNA, hair or climbing plants. As demonstrated in previous experimental and theoretical studies, the natural curvature plays an important role in the equilibrium shape of a Kirchhoff rod, even in the simple case where the rod is isotropic and suspended under gravity. In this paper, we investigate the reverse problem: can we characterize the natural curvature of a suspended isotropic rod, given an equilibrium curve? We prove that although there exists an infinite number of natural curvatures that are compatible with the prescribed equilibrium, they are all equivalent in the sense that they correspond to a unique natural shape for the rod. This natural shape can be computed efficiently by solving in sequence three linear initial value problems, starting from any framing of the input curve. We provide several numerical experiments to illustrate this uniqueness result, and finally discuss its potential impact on non-invasive parameter estimation and inverse design of thin elastic rods.

Starfruit Shape Defect Estimation Based on Concave and Convex Area of a Closed Planar Curve

Dalam kertas kerja ini, sebuah perwakilan bentuk berdasarkan kawasan cekung dan cembung di sepanjang keluk tertutup dipersembahkan. Teknik yang dicadangkan dalam kertas kerja ini melibatkan proses anggaran kekelukan daripada keluk masukan dan juga proses pencarian titik kritikal pada keluk masukan tersebut. Dengan mengasingkan titik kritikal tersebut kepada kategori cekung dan cembung, pengiraan kawasan cekung dan cembung dilakukan. Daripada ciri–ciri statistik ini, dua permasalahan berkaitan dengan bentuk disiasat. Di sini, teknik yang dicadangkan diuji terhadap proses penganggaran kerosakan bentuk dan pengenalan bentuk pada buah belimbing. Pada kes pertama, kerosakan bentuk belimbing diukur dengan mengira kuasa cekung di mana kuasa cekung ini adalah selanjar dengan kerosakan bentuk tersebut. Untuk kes pengenalpastian bentuk pula, tangkai belimbing adalah objek untuk dikenal pasti dan tangkai belimbing ini akan diasingkan daripada bentuk belimbing kerana ia akan menyumbang kepada kesalahan pengiraan kerosakan bentuk belimbing. Bagi kedua–dua kes, teknik yang dicadangkan diuji dengan tiga teknik penganggaran kekelukan untuk memastikan keberkesanan teknik yang dicadangkan. Kata kunci: Perwakilan bentuk, kekelukan, titik kritikal, kawasan cekung dan cembung In this paper, a shape representation based on concave and convex area along a closed curve is presented. The proposed technique involves the process of the curvature estimation from the input curve and search for its corresponding critical points. By splitting the critical points into concave and convex categories, the concave and convex area are computed. From these statistical features, two problems related to the shape (curve) are investigated. Here, the proposed technique is tested on shape defect estimation and shape recognition of starfruit. In the first case, defect is measured by computing concave energy, which is proportional to the defect. For shape recognition, starfruit’s stem is identified and removed from the starfruit’s shape, as it will contributes false computation of defect measurement. For both cases, the proposed technique is tested with three different curvature estimation techniques to validate the results. Key words: Shape representation, curvature, critical point, concave and convex area

SIMPLIPOLY: CURVATURE-BASED POLYGONAL CURVE SIMPLIFICATION

A curvature-based algorithm to simplify a polygonal curve is described, together with its implementation. The so-called SimpliPoly algorithm uses Bézier curves to approximate pieces of the input curve, and assign curvature estimates to vertices of the input polyline from curvature values computed for the Bézier approximations. The authors' implementation of SimpliPoly is interactive and available freely on-line. Additionally, a third-party implementation of SimpliPoly as a plug-in for the GNU Blender 3D modeling software is available. Empirical comparisons indicate that SimpliPoly performs as well as the widely-used Douglas-Peucker algorithm in most situations, and significantly better, because it is curvature-driven, in applications where it is necessary to preserve local features.