assignments-writtencurvestexture

Written Assignment: Curves and Texture

Due on Tuesday, November 25th

Answer the following questions and turn them into Blayne. You may either give him the answers on paper, or send it to him by email. If you turn things in on paper, they must be in his Mailbox (on the 5th floor) before he arrives on Wednesday morning. (remember, you can’t get to the 5th floor without an OD key after 7pm, so plan accordingly).

These questions are meant to give you some practice thinking about things we’ve discussed in class - particularly things you might see on the exam.

Question 1 - Bezier Curves

1A. A quartic Bezier in 2D has its control points at (0,0), (0,1), (1,2), (2,1), (2,0). What is the value of the curve at u=.25? (the position of the point)

1B. If we want to cut the curve in part A into 2 pieces at u=.25, what would the control points be for each of the parts of the curve?

1C. What is the direction of the derivative (tangent vector) for the point in 1A? Give any vector that is parallel to the tangent vector. (getting the magnitude of the tangent vector is harder than getting a vector that is in the same direction. hint: use the answer to 1B)

1D. We want to connect another quartic Bezier curve to the end of the curve in 1A. If the two curves are to meet with C(1) continuity, where must its first two control points be?

1E. We want to connect a cubic Bezier curve to the end of the curve in 1A. If the two curves are to meet with C(1) continuity, where must its first two control points be?

Question 2 - Texture Map Coordinates

Consider a square pyramid (the base of the pyramid is a square) as shown in the picture. Texture coordinates are given for each point.

2A: Sketch what this pyramid would look like if the 2x2 checkerboard (texture 1) is applied.

2B: Suppose that you want to texture the pyramid with 4 horizontal stipes, but the only texture you had was the 4x4 checkerboard (Texture2). Give textue coordinates for the 5 vertices that would produce this. (note: every vertex only gets one texture coordinate).

2C: If mip-mapping is used, there are reasons why using the checkerboard texture might not be as good as using the more “obvious” texture (Texture3). Explain this.