1 / 8

NUBS by Brian Wyvill

NUBS by Brian Wyvill. What’s that?. P 8. P 9. Y. t 10. P 1. P 3. Q 9. P 4. t 9. P 7. t 5. Q 5. t 3. Q 6. Q 8. Q 3. t 6. t 7. Q 4. t 8. P 0. t 4. Q 7. P 6. P 2. P 5. X. Uniform B-Splines. Basis functions for B-Splines. B-splines approximate a series of m+1

brittany-lynch
Télécharger la présentation

NUBS by Brian Wyvill

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. NUBS by Brian Wyvill What’s that?

  2. P8 P9 Y t10 P1 P3 Q9 P4 t9 P7 t5 Q5 t3 Q6 Q8 Q3 t6 t7 Q4 t8 P0 t4 Q7 P6 P2 P5 X Uniform B-Splines Basis functions for B-Splines. B-splines approximate a series of m+1 Control points. (P0, P1 .. Pm) M  3 M – 2 cubic curve segments (Q3, Q4 .. Qm) Parameter range for Qi is ti  t  ti+1 There is a knot between Qi andQi+1 at ti ti=knot value. (m-1 knots) t3=0 to t4=1 to t5=2 etc. Qm defined by points. (Pm-3, Pm-2, Pm-1, Pm ) over parameter range tm=m-3 to tm+1=m-2

  3. Uniform B-Splines Geometry Vector for B-Splines. GBs= Pi-3 Pi-2 Pi-1 Pi , 3  i  m T= [ (t - ti)3 (t - ti)2 (t - ti)1 1] Qi (t) = Ti * MB * GBs , ti t  ti+1

  4. Non-Uniform B-Splines Effect of Multiple Knots

  5. t0 t1 t2 t3 t4 t5 t6 t7 NUBS Piecewise continuous curve approximating control points P0 to Pm Knot Value sequence is non-decreasing sequence of knot values t0 through tm+4 ie there are 4 more knots than control points.

  6. NUBS Qi (t) = Pi-3 * Bi-3,4 (t) + Pi-2 * Bi-2,4 (t) + Pi-1 * Bi-1,4 (t) + Pi * Bi-4 (t) 3  i  m ti t < ti+1 Bi,1 (t) = 1, ti t < ti+1 otherwise zero. Bi,2 (t) = (t – ti) /(ti+1 – ti)Bi,1(t) + (ti+2 – t) /(ti+2 – ti+1)Bi+1,1 (t) Bi,3 (t) = Bi,4 (t) = B0,1 (t) = B1,1 (t) =B2,1 (t) = 0 B3,1 (t)=1 then 0 for i>3 B0,2 (t) = something* B0,1 (t) + something* B1,1 (t) = 0 B1,2 (t) = something* B1,1 (t) + something* B2,1 (t) = 0 B2,2 (t) = something* B2,1 (t) + (t4 – t) /(t4 – t3) * B3,1 (t) = (1-t)*1 This is 1 when t=0 and linearly decreasing until 0 at t=1

  7. The Haar Wavelet As

More Related