Beskjeder
There will be a tutorial on Tuesday 1215-1400 in room 108 (first floor), with a focus on oblig 4 and exam preparation. In the first part I will go through oblig 4 (unless one of you would like to present your solution - send me an email in that case)
In the second part I will give those of you who wish the opportunity to practice for the oral exam by presenting spline-material orally on the blackboard. You can choose any topic you like from the curriculum, for instance
A solution to one of the problems you have done in an oblig/weekly problem
The recursion formula and matrix notation for B-splines
Evaluation of B-splines
Derivatives of B-splines
Continuity of B-splines
Linear independence of B-splines...
Since this wednesday is a holiday, this weeks lecture will be given tuesday 1215-14 in undervisningsrom 108, see the lecture plan
Unfortunately there was a typo in 2a) in oblig 4:
The expression (xij, yij) = g(i * Uj/19) holds for i=0, 1, …, 19. (not for j=0,...,19 since j relates to the curve-numbers 1,2 , … 9).
The assignment text is now corrected.
Due to downtime on the uio servers yesterday the deadline for oblig 4 is extended by one day, until may 4th. Good luck!
Please submit your complete answers for Oblig 4 in one pdf with figures included. Working source-code should be submitted separately (not in the pdf) in the same email. Good luck!
Show that the tensor product B-splines are linearly independent and form a partition of unity (non-negative and sum to one) whenever the knot-vectors are p+1-regular.
Show the precise smoothness properties of Tensor-product B-splines.
Extra challenge: Construct a periodic cubic spline space over a uniform knot-vector, by making the domain and/or the B-splines periodic (not by enforcing boundary-conditions). Demonstrate your construction by approximating a circle with Cˆ2 continuity
Oblig 4 is given here as a pdf-document and the data is here The deadline is Wednesday May 3.
I will go through Oblig 3 on Tuesday March 28. at 1215-1400 in
Undervisningsrom 108 (NB: NOT in undervisningsrom 1036 or 107!!)
Martin
I will go through Oblig 3 on Tuesday March 28. at 1215-1400 in
Undervisningsrom 108 (NB: NOT in undervisningsrom 1036!!)
Martin
Oblig 3 is given here as a pdf-document The deadline is Thursday March 23.
I have revised Oblig 2 slightly: added a hint for 2.13 and I would prefer that you test your code on the spline with coefficients c=(-1,1,-1,1,-1,1,-1,1,-1), not on a single B-spline. If you already have tested you code on another spline / B-spline I will not require you to correct this.
I will be available for questions regarding oblig 2 on tuesday (february 28.) from 13 to 14 in room 1036 (NB: not from 1215!!)
Problem 2.12. No R_k matrices, use two for-loops. Plot the p+1 active B-splines on one nontrivial knot interval for degrees p up to 10.
Problem 3.2
Extra challenge: Implement the spline evaluation Alg. 2.20 both with for-loops and by a recursion. Compare the two implementations wrt. time-efficiency for various degrees, each with sufficiently many evaluations to make comparison possible/meaningful (one evaluation takes too little time).
Oblig 2 is given here as a pdf-document
The deadline is Wednesday March 1st
The date for the final oral exam is wednesday May the 31st (not the 29th as we first discussed)
I will be available for questions in our tuesday slot from 1215 and for as long as you have questions. Lecture room 1036 in the 10th floor in NHA, see the lecture plan
Good luck with the oblig, have a nice weekend
Martin
Note that the implementation of Neville-Aitken and deCastaljau is done using for-loops as indicated by the descriptions of the algorithms - use the same indexing in the for loops. But: if you use a programming language where vector indices start with 1 (e.g. matlab) you need to offset reads and writes wrt the vector with 1. E.g. for deCasteljau, something like (the vector q holds the coefficients, p+1 one of them before the first round of averaging)
q(j+1) = (1 − t)*q(j-1+1) + t*q(j+1)
Do NOT use matrices for the implementation (unless you see the vector of control points in the plane as a 2x(p+1) matrix). You should be able to "overwrite" the elements of a vector containing coefficients, either starting with the first or the last element so that you do not overwrite data that is used in a later calculation ;)
Oblig 1 consists of the following exercises in the compendium: 1.3, 1.4, 1.7, 2.1. The deadline is wednesday february the 8th.
Please send me your complete answers by email in one pfd-file, including figures. In addition you must submit your sourcecode for the programming exercises in the same email. You are free to choose the programming language and I recommend using Latex.
In exercise 1.3 you should parameterize the semicircle by (Cos(t),Sin(t)) and use uniform samples in the t-variable in the first part.
I will be available for questions on e-mail, after the next lectures, and if you wish in the tutorial time-slot tuesday the 7th of february at 12 o'clock.
Martin
As you can see in the lecture plan, the lecture on Tuesday this week is canceled, as will many of the Tuesday lectures.
We will use our Wednesday slots for lectures and some of our Tuesday slots for tutorials. I will let you know about tutorials through the lecture plan, and also by posting messages.
Martin
Illustrate Algorithm 1.1 for 2, 3 and 4 interpolation points, by making figures similar to Figure 1.12 a). Make sure that you understand how the algorithm works!
For those of you who wants an additional challenge: do problem 1.2
Welcome to the first lecture, which takes place Wednesday January 18th 1015-1200 in room UE32 in NHA, see the lecture plan