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Related Concept Videos

Adjusting a Traverse01:12

Adjusting a Traverse

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In the site survey of a four-sided traverse, internal angles are essential to ensure geometric accuracy. The survey revealed that the sum of the measured internal angles was 359 degrees and 48 minutes, which is 12 minutes less than the expected 360 degrees. This discrepancy signals an error likely arising from measurement inaccuracies during the fieldwork.To rectify this error, the adjustment process involved distributing the 12-minute shortfall equally across the four internal angles. By...
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Design Example: Traverse Angle Computations01:25

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Traverse angle computations are a critical component of surveying, used to compute the internal angles within a closed traverse. A traverse consists of a series of connected lines forming a closed loop, often used for land boundary delineation or mapping. Calculating the internal angles ensures accuracy in the traverse geometry and is essential for checking survey data integrity.The process begins with known azimuths and bearings of the traverse sides. Internal angles at each vertex are...
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Collisions in Multiple Dimensions: Problem Solving01:06

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In multiple dimensions, the conservation of momentum applies in each direction independently. Hence, to solve collisions in multiple dimensions, we should write down the momentum conservation in each direction separately. To help understand collisions in multiple dimensions, consider an example.
A small car of mass 1,200 kg traveling east at 60 km/h collides at an intersection with a truck of mass 3,000 kg traveling due north at 40 km/h. The two vehicles are locked together. What is the...
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Area Computation by the Alternative Coordinate Method01:24

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The alternative coordinate method, also known as the Shoelace Formula, is a technique for determining the area of a traverse using Cartesian coordinates. This method relies on the sequential arrangement of x and y coordinates for each point of the shape, ensuring accuracy and ease of application.In this approach, each corner's x and y coordinates are listed as fractions, with the x-coordinate as the numerator and the y-coordinate as the denominator. These coordinates are arranged sequentially...
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Relative Motion Analysis using Rotating Axes-Problem Solving01:29

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Consider a crane whose telescopic boom rotates with an angular velocity of 0.04 rad/s and angular acceleration of 0.02 rad/s2. Along with the rotation, the boom also extends linearly with a uniform speed of 5 m/s. The extension of the boom is measured at point D, which is measured with respect to the fixed point C on the other end of the boom. For the given instant, the distance between points C and D is 60 meters.
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Relative Motion Analysis using Rotating Axes - Acceleration01:22

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Consider a component AB undergoing a linear motion. Along with a linear motion, point B also rotates around point A. To comprehend this complex movement, position vectors for both points A and B are established using a stationary reference frame. The absolute velocity of point B is determined by adding the absolute velocity of point A, the relative velocity of point B in the rotating frame, and the effects caused by the angular velocity within the rotating frame.
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Updated: May 30, 2025

Magnetic Resonance Derived Myocardial Strain Assessment Using Feature Tracking
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A backtracking heuristic algorithm for two-dimensional strip packing with rotation.

Li Li1, Baoguo Liu1, Zhaoyun Wu1

  • 1School of Mechanical & Electrical Engineering, Henan University of Technology, Zhengzhou, China.

Science Progress
|January 31, 2025
PubMed
Summary
This summary is machine-generated.

A new backtracking heuristic algorithm (BHA) effectively solves the 2D rectangular strip packing problem. This efficient algorithm excels in large-scale industrial applications, demonstrating minimal result variance and superior performance.

Keywords:
Packingbacktracking heuristiclarge-scale instancelocal searchmulti-start improvement

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Area of Science:

  • Operations Research
  • Computer Science
  • Applied Mathematics

Background:

  • The two-dimensional rectangular strip packing problem is crucial for industrial applications like metal cutting.
  • Existing algorithms struggle with large-scale instances and rotations without guillotine cuts.

Purpose of the Study:

  • To develop an efficient and effective algorithm for the 2D rectangular strip packing problem.
  • To address challenges posed by rotations and the absence of guillotine cuts.

Main Methods:

  • A backtracking heuristic algorithm (BHA) was developed.
  • An improved fitness strategy was employed for rectangle selection.
  • Multi-start improvement and randomized local search procedures were utilized.

Main Results:

  • The BHA demonstrated effectiveness on benchmark problems of varying scales (10 to 75,032 rectangles).
  • The algorithm showed minimal result variation despite being non-deterministic.
  • BHA outperformed most compared algorithms, particularly for large-scale instances (>1000 rectangles).

Conclusions:

  • The proposed BHA is simple, effective, and suitable for mass industrial production.
  • The algorithm's performance is statistically verified and highly meaningful for real-world applications.