東京大学 情報理工学系研究科 創造情報学専攻 2007年8月実施 筆記試験 第3問

Author

itsuitsuki

Description (English)

Consider a method to find equations of two straight boundary lines of the two-colored regions like Fig. 1. Suppose the points in Fig. 2 are derived through processing the image of Fig. 1 and answer the following questions.

(1) The line that passes the point as in Fig. 3 is described as The point of the - parameter coordinates (Fig. 4) shows the line . Explain what the parameters of mean in the - coordinates.

(2) Rotate the line in Fig. 3 at the point . Illustrate the trajectory of the point in the - coordinates.

(3) Consider the three points on a line as in Fig. 5. Let be a line that passes . Rotate each line at . Illustrate the corresponding trajectories of the point in the - coordinates.

(4) Considering the methods described above, explain how to get the equations of the two straight boundary lines from the points of Fig. 2.