Concern the subdivision of a Bzier curve shown in Figure 7. Let x(t) be the Bzier curve,

Concern the subdivision of a Bézier curve shown in Figure 7. Let x(t) be the Bézier curve, with control pointsp_0,........,p₃, and let y(t) and z(t) be the subdividing Bézier curves as in the text, with control points q_{0,.................,}q₃ and r_0,.........r₃,respectively.

Figure 7 From Section 8.6

a. Use equation (12) to show that q₁ is the midpoint of the segment from p₀ to p₁.

b. Use equation (13) to show that 8q₂ = 8q₃ + p₀ + p₁ – p₂ – p₃:

c. Use part (b), equation (8), and part (a) to show that q₂ is the midpoint of the segment from q₁ to the midpoint of the segment from p₁ to p₂. That is,

Transcribed Image Text:

Po 90 91 P₁ 92 93 = ro P₂ R P3 = 13