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Design Rule Checking
Published in Louis Scheffer, Luciano Lavagno, Grant Martin, EDA for IC Implementation, Circuit Design, and Process Technology, 2018
Robert Todd, Laurence Grodd, Katherine Fetty
In practice, if an IC design contains a total of N objects, then the number of objects intersecting the scan line is of O(sqrt(N)), since the objects are roughly the same size and cover the surface of the chip. This has advantages in both space and time. For space, only O(sqrt(N)) objects need to be in active memory for analysis. For time, each of the N layout objects must first be inserted, then removed, from the scan line. Since the scan line is kept sorted, each such operation takes O(log(sqrt(N)) = O(log N) time. Therefore, the time complexity [13] is approximately N∗O(logN)=O(NlogN)
Interactive Graphics Pipeline
Published in Aditi Majumder, M. Gopi, Introduction to Visual Computing, 2018
The rasterization process is applied to each primitive and it proceeds line by line from top left of the window to the bottom right. For every scanline, the intersection of the scanline is computed with all the edges of the polygon and the intersections sorted in the increasing order of their x (note all of them have the same y since we are dealing with a horizontal scanline). Consider the two triangles in Figure 13.10 and the black scanline. The intersection points when ordered will be p0, p1, p2, p3. Next, the pixels within pairs of their intersections are filled up. Therefore, p0 to p1 and p2 to p3 is filled up. When filling up these pixels, their color and depth are also interpolated. For every pixel on a scanline that has been detected to be inside the triangle, first its reciprocal of depth is interpolated from the reciprocal of the depths stored at the intersection points of the scanline and the edges. If the interpolated value is larger than the existing value at that pixel in the Z‐buffer (i.e. depth is smaller), only then the framebuffer is updated at that pixel with the interpolated color. Otherwise, this pixel is occluded and is not drawn in the framebuffer.
Geological input parameters for realistic DDA modeling
Published in Yossef H. Hatzor, Guowei Ma, Gen-hua Shi, Discontinuous Deformation Analysis in Rock Mechanics Practice, 2017
Yossef H. Hatzor, Guowei Ma, Gen-hua Shi
Since each joint set consists of individual members which are not perfectly parallel we can apply this weighting factor to each individual joint by using individual weighting factor 1/cosδi $ \cos \delta _{i} $ for each mapped joint, where δi $ \delta _{i} $ is the acute angle between the individual joint normal and the arbitrary scan line direction. We can thus define a “weighting factor” ω $ \omega $ for each member in a set as: ω=1cosδ $$ \begin{aligned} \omega = {\frac{{1}}{{\cos \delta }}} \end{aligned} $$
Enhancing process competency by forced cooling in laser bending process
Published in Journal of Thermal Stresses, 2022
Ramsingh Yadav, Dhruva Kumar Goyal, Ravi Kant
Laser bending is preferable in generating small bend angles with high precision and accuracy by deforming materials with negligible spring back. The bending is mostly carried out by temperature gradient mechanism (TGM) as it provides good control on the process outcome [1, 2]. TGM causes a steep temperature gradient in the worksheet material which leads to the formation of uneven plastic strain along the thickness. This irregular plastic strain is responsible for the bending of worksheet, which can be controlled by various process parameters such as laser power, scanning speed, number of scans, beam diameter, worksheet geometry, and thermomechanical properties of worksheet material [3–5]. A schematic diagram of laser forming is shown in Figure 1. The major limitations of this process are poor efficiency, small bend angle per scan, and non-uniform bend angle along the scan line (edge effect). Literature reports that the bend angle usually increases with laser power, number of scans and decreases with an increase in beam diameter, scanning speed, and sheet thickness [6, 7]. Several materials such as ceramics [8], metals [9, 10] and their alloys [11–13] have been explored to study the effect of the above-mentioned parameters on bend angle. In laser bending, the distribution of bend angle is not uniform along the scanning line as a result of edge effect [14]. The width of the worksheet may have a significant effect on the bend angle and edge effect due to rigid end effect [15, 16]. It is reported that the bend angle increases with the increase in the width of worksheet [17, 18]. Jha et. al observed that there is no significant effect of the worksheet width on the edge effect [19]. Shen et al. [20] proposed that the edge effect can be minimized by using a combination of acceleration and deceleration of scanning speed. Kant et al. found that laser parameters, scanning path [14], mechanical load [21, 22] and the number of scans [23] significantly affect the bending profile along the scan line. Thomsen et al. [24] reported that the application of forced cooling could reduce the edge effect. However, they did not investigate the effect of forced cooling on the bend angle.