本文選題：幾何質(zhì)心 + 三維流形��； 參考：《計(jì)算機(jī)輔助設(shè)計(jì)與圖形學(xué)學(xué)報(bào)》2017年05期

【摘要】：針對(duì)傳統(tǒng)的物理質(zhì)心在形狀彎曲的情況下有可能落在物體外部的問(wèn)題,提出基于慣性矩的幾何質(zhì)心定義及計(jì)算方法.根據(jù)慣性矩把傳統(tǒng)的質(zhì)心定義拓展到三維流形上,首先基于熱傳導(dǎo)方程計(jì)算物體內(nèi)部距離得到物體關(guān)于某點(diǎn)的慣性矩;然后采用梯度下降法尋找慣性矩的極小值得到幾何質(zhì)心.該幾何質(zhì)心一定落于物體的內(nèi)部,并且當(dāng)輸入模型為凸時(shí)退化為物理質(zhì)心.實(shí)驗(yàn)結(jié)果表明,該方法對(duì)噪聲和姿勢(shì)變化不敏感,可用于形狀分析等目的..
[Abstract]:In order to solve the problem that the traditional physical centroid may fall outside the body in the case of shape bending, the definition and calculation method of geometric centroid based on moment of inertia are proposed. According to the moment of inertia, the traditional definition of the center of mass is extended to the three-dimensional manifold. First, the moment of inertia of the body is obtained by calculating the distance between the interior of the body based on the heat conduction equation, and then the gradient descent method is used to find the minimum value of the moment of inertia to the geometric center of mass. The geometric centroid must fall inside the object and degenerate into the physical centroid when the input model is convex. The experimental results show that the method is insensitive to noise and posture changes and can be used for shape analysis.
【作者單位】： 寧波大學(xué)信息科學(xué)與工程學(xué)院;浙江大學(xué)寧波理工學(xué)院信息科學(xué)與工程學(xué)院;寧波大紅鷹學(xué)院信息工程學(xué)院;
【基金】：國(guó)家自然科學(xué)基金(61300168,11226328,61571247) 浙江省自然科學(xué)基金(LY17F020018,LZ16F030001) 浙江省重中之重開(kāi)放課題(XKXL1429,XKXL1406) 浙江省教育廳科研項(xiàng)目(Y201534799) 寧波市自然科學(xué)基金(2016A610041) 寧波大學(xué)研究生教育教學(xué)研究項(xiàng)目(JGZDI201501) 寧波大學(xué)教研項(xiàng)目(JYXMxsj201405)
【分類(lèi)號(hào)】：TP301.6
，

本文編號(hào)：1834426