DDA (Digital Differential Analyzer ) Line Drawing Algorithm.pptx
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The document discusses the Digital Differential Analyzer (DDA) line drawing algorithm. It begins with an introduction to DDA and how it is used to draw lines on a computer screen. It then covers the understanding, procedure, practice problems, advantages, limitations, and conclusion of the DDA algorithm. The core steps of the DDA algorithm include calculating delta X and Y values and the slope between starting and ending points, determining the number of steps, and generating new points along the line through rounding until the ending point is reached. While simple to implement, DDA has limitations such as a lack of smoothness from rounding, but remains a useful basic line drawing technique.
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This document discusses 2D graphics algorithms. It begins by describing output primitives like points, lines, polygons, text and images. It then covers key line drawing algorithms like DDA, midpoint and Bresenham's which incrementally determine pixel positions on a digital display. Next, it explains the midpoint circle drawing algorithm for rasterizing circles. Antialiasing techniques to smooth jagged edges are also mentioned. Finally, area fill algorithms to color interior regions of shapes are introduced.
Computer Graphics and Multimedia Output primitives
This document discusses 2D graphics algorithms. It begins by describing output primitives like points, lines, polygons, text and images. It then covers key line drawing algorithms like DDA, midpoint and Bresenheim's which incrementally calculate pixel positions on a line. The midpoint circle drawing algorithm is also summarized which uses a decision parameter to iteratively determine pixels on a circle. The document concludes with a brief overview of antialiasing techniques and fill area algorithms.
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二.真实使馆公证(即留学回国人员证明,不成功不收费)
三.真实教育部学历学位认证（教育部存档！教育部留服网站永久可查）
四.办理各国各大学文凭(一对一专业服务,可全程监控跟踪进度)
如果您处于以下几种情况：
◇在校期间，因各种原因未能顺利毕业……拿不到官方毕业证【q/微741003700】
◇面对父母的压力，希望尽快拿到；
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◇回国马上就要找工作，办给用人单位看；
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1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
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5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
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◆◆◆◆◆ — — — — — — — — 【留学教育】留学归国服务中心 — — — — — -◆◆◆◆◆
【主营项目】
一.毕业证【微信：176555708】成绩单、使馆认证、教育部认证、雅思托福成绩单、学生卡等！
二.真实使馆公证(即留学回国人员证明,不成功不收费)
三.真实教育部学历学位认证（教育部存档！教育部留服网站永久可查）
四.办理各国各大学文凭(一对一专业服务,可全程监控跟踪进度)
如果您处于以下几种情况：
◇在校期间，因各种原因未能顺利毕业……拿不到官方毕业证【微信：176555708】
◇面对父母的压力，希望尽快拿到；
◇不清楚认证流程以及材料该如何准备；
◇回国时间很长，忘记办理；
◇回国马上就要找工作，办给用人单位看；
◇企事业单位必须要求办理的
◇需要报考公务员、购买免税车、落转户口
◇申请留学生创业基金
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分→ 【关于价格问题（保证一手价格）
我们所定的价格是非常合理的，而且我们现在做得单子大多数都是代理和回头客户介绍的所以一般现在有新的单子 我给客户的都是第一手的代理价格，因为我想坦诚对待大家 不想跟大家在价格方面浪费时间
对于老客户或者被老客户介绍过来的朋友，我们都会适当给一些优惠。
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
选择实体注册公司办理，更放心，更安全！我们的承诺：可来公司面谈，可签订合同，会陪同客户一起到教育部认证窗口递交认证材料，客户在教育部官方认证查询网站查询到认证通过结果后付款，不成功不收费！
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DDA (Digital Differential Analyzer ) Line Drawing Algorithm.pptx
- 1. WELCOM E
- 2. Presentation Topic: DDA (Digital Differential Analyzer ) Line Drawing Algorithm
- 3. Table of Content Introduction Understanding The Algorithm Procedure Practice Problems Based On DDA Algorithm Advantages Limitations Conclusion
- 4. Introduction The line (vector) generation algorithms which determine the pixels that should be turned ON are called as digital differential analyzer (DDA). It is a simple and efficient algorithm used to draw lines on a computer screen. It is one of the technique for obtaining a rasterized straight line. This algorithm can be used to draw the line in all the quadrants. 4
- 5. Understanding The Algorithm DDA Algorithm is the simplest line drawing algorithm. Given the starting and ending coordinates of a line, DDA Algorithm attempts to generate the points between the starting and ending coordinates. 5
- 6. Procedure Given- Starting coordinates = (X0, Y0) Ending coordinates = (Xn, Yn) 6
- 7. Procedure (Cont.) • Step-01: • Calculate ΔX, ΔY and M from the given input. • These parameters are calculated as - ΔX = Xn – X0 ΔY =Yn – Y0 M = ΔY / ΔX 7
- 8. Procedure (Cont.) • Step-02: • Find the number of steps or points in between the starting and ending coordinates. if (absolute (ΔX) > absolute (ΔY)) Steps = absolute (ΔX); else Steps = absolute (ΔY); 8
- 9. Procedure (Cont.) • Step-03: • Suppose the current point is (Xp, Yp) and the next point is (Xp+1, Yp+1). • Find the next point by following the below three cases- 9
- 10. Procedure (Cont.) • Step-04: • Keep repeating Step-03 until the end point is reached or the number of generated new points (including the starting and ending points) equals to the steps count. 10
- 11. Practice Problems Based On DDA Algorithm • Problem-01: • Calculate the points between the starting point (5, 6) and ending point (8, 12). • Solution- • Given- Starting coordinates = (X0, Y0) = (5, 6) Ending coordinates = (Xn, Yn) = (8, 12) 11
- 12. Practice Problems Based On DDA Algorithm (cont.) • Step-01: • Calculate ΔX, ΔY and M from the given input. • ΔX = Xn – X0 = 8 – 5 = 3 • ΔY =Yn – Y0 = 12 – 6 = 6 • M = ΔY / ΔX = 6 / 3 = 2 • Step-02: • Calculate the number of steps. • As |ΔX| < |ΔY| = 3 < 6, so number of steps = ΔY = 6 12
- 13. • Step-03: • As M > 1, so case- 03 is satisfied. • Now, Step-03 is executed until Step- 04 is satisfied. Xp Yp Xp+1 Yp+1 Round off (Xp+1, Yp+1) 5 6 5.5 7 (6, 7) 6 8 (6, 8) 6.5 9 (7, 9) 7 10 (7, 10) 7.5 11 (8, 11) 8 12 (8, 12) 13 Practice Problems Based On DDA Algorithm (cont.)
- 14. 14 Practice Problems Based On DDA Algorithm (cont.)
- 15. Advantages The DDA algorithm is straight-forward to implement. It only requires basic arithmetic operations like addition and division. It can be used to draw lines in both positive and negative slopes. DDA draws the line faster than drawing the line by directly using the line equation. 15
- 16. Limitations There is an extra overhead of using round off( ) function. Using round off( ) function increases time complexity of the algorithm. Resulted lines are not smooth because of round off( ) function. The points generated by this algorithm are not accurate. 16
- 17. Conclusion The DDA line drawing algorithm is a simple and widely used method to draw lines on raster displays. While it has its limitations, it remains a valuable tool for many applications. 17
- 18. Thank You 18