Resultant Vector Research Articles

Is There a Robust Technique for Selecting Aspect Ratios in Line Charts?

The aspect ratio of a line chart heavily influences the perception of the underlying data. Different methods explore different criteria in choosing aspect ratios, but so far, it was still unclear how to select aspect ratios appropriately for any given data. This paper provides a guideline for the user to choose aspect ratios for any input 1D curves by conducting an in-depth analysis of aspect ratio selection methods both theoretically and experimentally. By formulating several existing methods as line integrals, we explain their parameterization invariance. Moreover, we derive a new and improved aspect ratio selection method, namely the -LOR (local orientation resolution), with a certain degree of parameterization invariance. Furthermore, we connect different methods, including AL (arc length based method), the banking to 45 principle, RV (resultant vector) and AS (average absolute slope), as well as -LOR and AO (average absolute orientation). We verify these connections by a comparative evaluation involving various data sets, and show that the selections by RV and -LOR are complementary to each other for most data. Accordingly, we propose the dual-scale banking technique that combines the strengths of RV and -LOR, and demonstrate its practicability using multiple real-world data sets.

Assessment Tools for Identifying Functional Limitations Associated With Functional Ankle Instability

Assessment tools should identify functional limitations associated with functional ankle instability (FAI) by discriminating unstable from stable ankles. To identify assessment tools that discriminated FAI from stable ankles and determine the most accurate assessment tool for discriminating between FAI and stable ankles. Case-control study. Research laboratory. Fifteen individuals with FAI and 15 healthy individuals; participants with unilateral FAI reported "giving-way" sensations and ankle sprains, whereas healthy participants did not. Participants answered 12 questions on the Ankle Joint Functional Assessment Tool (AJFAT). They also performed a single-leg jump landing, which required them to jump to half their maximum jump height, land on a single leg, and stabilize quickly on a force plate. Receiver operating characteristic curves determined cutoff scores for discriminating between ankle groups for AJFAT total score and resultant vector (RV) time to stabilization. Accuracy values for discriminating between groups were determined by calculating the area under the receiver operating characteristic curves. The cutoff score for discriminating between FAI and stable ankles was > or =26 (sensitivity = 1, specificity = 1) and > or =1.58 seconds (sensitivity = 0.67, specificity = 0.73) for the AJFAT total score and RV time to stabilization, respectively. The area under the curve for the AJFAT was 1.0 (asymptotic significance <.05), whereas the RV time to stabilization had an area under the curve of 0.72 (asymptotic significance <.05). The AJFAT was an excellent assessment tool for discriminating between ankle groups, whereas RV time to stabilization was a fair assessment tool. Although both assessments discriminated between ankle groups, the AJFAT more accurately discriminated between groups than the RV time to stabilization did. Future researchers should confirm these findings using a prospective research design.