**** This queston is for Computer graphic class**** 3.1 I Section 3.2 e discusse

Question

**** This queston is for Computer graphic class****

3.1 I Section 3.2 e discussed scaling with eference to the origino, that is, with Oas a fixed point also possible to use a different fixed point, say C( yc), but, for such a scaling in two-dimensiona is ? space, we need a 3 x 3matrix M (and homogenous coordinates), writing [x, y, 1]=[x y 1]M Using scale factors s and sy for x and y again, find this matrix M. Hint: You can perform a translation from C to O, followed by a scaling as discussed in Section 3.2, but described by a 3 x 3 matrix, followed by a translation back from O to C. Alternatively, you can start with the following system of equations, which shows very clearly what actually happens: 3.2 Describe scaling in three-dimensional space with reference to a point C and three scale factors »x. Sy ? 3.2 Describe scaling in three-dimensional space with reference to a point C and three scale factors s Sy '? and sz Find the 4 x 4 matrix (similar to matrix M of Exercise 3.1) for this transformation

Explanation / Answer

3.1 We do not have coordinates for Sx and Sy

so M= Sx 0 0 0 Sy 0 and the third row would be found by taking Xc and Xy common so third row would be

Xc(1-Sx) Yc(1-Sy) 1

3.2 To form 4*4 matrix as 3.1 we can found the row by

Sx 0 0 0

0 Sy 0 0

0 0 Sz 0

Xc(1-Sx) Yc(1-Sy) Zc(1-Sz) 1

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.