Bezier Curves, properties of Bezier Curves, Derivation for Quadratic Bezier Curve, Blending function specification for Bezier curve:, B-Spline Curves, properties of B-spline Curve?
A Bézier curve is a parametric curve frequently used in computer graphics and related fields. Generalizations of Bézier curves to higher dimensions are called Bézier surfaces, of which the Bézier triangle is a special case.
Bezier Curves, properties of Bezier Curves, Derivation for Quadratic Bezier Curve, Blending function specification for Bezier curve:, B-Spline Curves, properties of B-spline Curve?
A Bézier curve is a parametric curve frequently used in computer graphics and related fields. Generalizations of Bézier curves to higher dimensions are called Bézier surfaces, of which the Bézier triangle is a special case.
A frequently used class of objects are the quadric surfaces, which are described with second-degree equations (quadratics). They include spheres, ellipsoids, tori, paraboloids, and hyperboloids.
Quadric surfaces, particularly spheres and ellipsoids, are common elements of graphics scenes
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptxR&R Consult
CFD analysis is incredibly effective at solving mysteries and improving the performance of complex systems!
Here's a great example: At a large natural gas-fired power plant, where they use waste heat to generate steam and energy, they were puzzled that their boiler wasn't producing as much steam as expected.
R&R and Tetra Engineering Group Inc. were asked to solve the issue with reduced steam production.
An inspection had shown that a significant amount of hot flue gas was bypassing the boiler tubes, where the heat was supposed to be transferred.
R&R Consult conducted a CFD analysis, which revealed that 6.3% of the flue gas was bypassing the boiler tubes without transferring heat. The analysis also showed that the flue gas was instead being directed along the sides of the boiler and between the modules that were supposed to capture the heat. This was the cause of the reduced performance.
Based on our results, Tetra Engineering installed covering plates to reduce the bypass flow. This improved the boiler's performance and increased electricity production.
It is always satisfying when we can help solve complex challenges like this. Do your systems also need a check-up or optimization? Give us a call!
Work done in cooperation with James Malloy and David Moelling from Tetra Engineering.
More examples of our work https://www.r-r-consult.dk/en/cases-en/
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
2. A Hermite curve is a curve for which the user provides:
The endpoints of the curve
The parametric derivatives of the curve at the endpoints (tangents with
length)
The parametric derivatives are dx/dt, dy/dt, dz/dt
That is enough to define a cubic Hermite spline, more derivatives are
required for higher order curves.
Hermite curves
3. A cubic spline has degree 3, and is of the form:
For some constants a, b, c and d derived from the control points
Hermite curves
Constraints:
The curve must pass through p1 when t=0
The derivative must be ∆p1 when t=0
The curve must pass through p2 when t=1
The derivative must be ∆p2 when t=1
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4. Control point positions and first derivatives are given as constraints for each end-point.
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End point constraints for each segment is given as:
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5. These polynomials are called Hermite blending functions, and tells us how to
blend boundary conditions to generate the position of a point P(u) on the
curve.
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6. More degrees of freedom
Directly transformable
Dimension independent
No infinite slope problems
Separates dependent and independent variables
Inherently bounded
Easy to express in vector and matrix form
Common form for many curves and surfaces
Advantages of parametric forms
19. They generally follow the shape of the control polygon, which consists of the segments joining the
control points.
They always pass through the first and last control points.
They are contained in the convex hull of their defining control points.
The degree of the polynomial defining the curve segment is one less that the number of defining
polygon point. Therefore, for 4 control points, the degree of the polynomial is 3, i.e. cubic polynomial.
The direction of the tangent vector at the end points is same as that of the vector determined
by first and last segments.
The convex hull property for a Bezier curve ensures that the polynomial smoothly follows the
control points.
Bezier curves exhibit global control means moving a control point alters the shape of the
whole curve.
Properties of Bezier Curve
21. B-splines automatically take care of continuity, with
exactly one control vertex per curve segment
Many types of B-splines: degree may be different
(linear, quadratic, cubic,…) and they may be uniform
or non-uniform
With uniform B-splines, continuity is always one
degree lower than the degree of each curve piece
Linear B-splines have C0 continuity, cubic
have C2, etc
B-Splines – (Basis Spline)
25. The sum of the B-spline basis functions for any parameter value is 1.
Each basis function is positive or zero for all parameter values.
Each basis function has precisely one maximum value, except for k=1.
The maximum order of the curve is equal to the number of vertices of
defining polygon.
The degree of B-spline polynomial is independent on the number of vertices
of defining polygon.
B-spline allows the local control over the curve surface because each vertex
affects the shape of a curve only over a range of parameter values where its
associated basis function is nonzero.
Properties of B-Spline Curves
27. The choice of a knot vector directly influences the resulting curve.
Types of Knot vectors
Uniform (periodic)
Open-Uniform
Non-Uniform
Knot Vectors
28. Open curves expect that do not passes through the first and last
control points and therefore are not tangent to the first and last
segment of the control polygon.
Closed curves where the first and last control points curve
connected. Closed curves with the first and last control point
being the same (coincident ).
Open and closed B-spline curves
29. When the spacing between knot values is constant, the
resulting curve is called a uniform B-spline.
The spacing between knot values is not constant and hence
,any values and intervals can be specified for the knot vector
the curve is called a non uniform B-spline .
Different intervals which can be used to adjust spline shapes .
Uniform and non uniform B-spline curves
30.
31. Rational curves is defined as ratio of two polynomials.
Non rational curves is defined by one polynomials.
The most widely used rational curves are non uniform rational
B-splines (NURBS)
NURBS is capable of representing in a single form non –rational
B-splines and Bezier curves as well as linear and quadratic
analytic curves.
Rational Curves
32. Add weights to each points
Unweighted :
Where
Weighted
NURBS- Non Uniform Rational B-
Splines
34. Rational curve can handle both analytical and synthetic curves.
Rational curve represents a point with homogenous coordinate
system where a 3D coordinate system is expressed as (wi x, wi
y ,wi z,wi).
Using same control points with different weights ,different
curves can be generated.
The weight associated with each control point can affect the
curve locally and the curve is pulled towards the control point
with increases valued of its weight wi.
Characteristics of Rational curves