A Fast and Simple Method for Curve Drawing -A New Approach Using Logarithmic Number Systems-

• Tomio, Kurokawa

• Takanari, Mizukoshi

抄録

A completely new but effective method is introduced for drawing curves on computer graphics. While most curve drawing methods employ "incremental"-type algorithms the method presented here simply computes a mathematical expression for a curve to generate dot addresses. It employs a logarithmic number system (LNS).To generate the curve of f(x y)=0 for example the curve expression should be in the form: y=g(x). Then y is directly computed for each x using the LNS. Since the arithmetic in an LNS is extremely fast and accurate the speed and the curve quality are naturally expected to be good. The specific procedure for drawing the curve of y=g(x) is as follows: For each x (1) convert x (integer) into the LNS by using a 1ookup table; (2) compute y using the LNS; (3) convert the resultant y into an integer by using another lookup table; (4) plot the point (x y).Some software experiments were done on a micro-computer to generate circles and ellipses. They showed that both the speed and the quality are surprisingly good. The former is comparable to or possibly faster than that of the fastest "incremental" algorithm. The latter is also very good but depends on the specific LNS used. The better the quality desired the longer the word length required and consequently the more memory required. However a practically high level of quality can be obtained with fairly little memory.

A completely new but effective method is introduced for drawing curves on computer graphics. While most curve drawing methods employ "incremental"-type algorithms, the method presented here simply computes a mathematical expression for a curve to generate dot addresses. It employs a logarithmic number system (LNS).To generate the curve of f(x,y)=0, for example, the curve expression should be in the form: y=g(x). Then, y is directly computed for each x, using the LNS. Since the arithmetic in an LNS is extremely fast and accurate, the speed and the curve quality are naturally expected to be good. The specific procedure for drawing the curve of y=g(x) is as follows: For each x, (1) convert x (integer) into the LNS by using a 1ookup table; (2) compute y, using the LNS; (3) convert the resultant y into an integer by using another lookup table; (4) plot the point (x, y).Some software experiments were done on a micro-computer to generate circles and ellipses. They showed that both the speed and the quality are surprisingly good. The former is comparable to or possibly faster than that of the fastest "incremental" algorithm. The latter is also very good, but depends on the specific LNS used. The better the quality desired, the longer the word length required and consequently the more memory required. However a practically high level of quality can be obtained with fairly little memory.

収録刊行物

• Journal of Information Processing

  Journal of Information Processing 14 (2), 144-152, 1991-07-31

  一般社団法人情報処理学会

詳細情報

• CRID: 1050564287846720896
• NII論文ID: 110002673564
• NII書誌ID: AA00700121
• ISSN: 18826652
• Web Site: http://id.nii.ac.jp/1001/00059702/
• 本文言語コード: en
• 資料種別: article
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