A Blossoming Development of Splines (Google eBook)

Front Cover
Morgan & Claypool Publishers, Jan 1, 2006 - Computers - 97 pages
0 Reviews
In this lecture, author Stephen Mann presents Bezier and B-spline curves and surfaces, mathematical representations for free-form curves and surfaces that are common in CAD systems. They are used to design aircraft and automobiles, as well as having uses in modeling packages used by the computer animation industry. Bezier/B-splines represent polynomials and piecewise polynomials in a geometric manner using sets of control points that define the shape of the surface.The primary analysis tool used in this lecture is blossoming, which gives an elegant labeling of the control points that allow us to analyze their properties geometrically. Blossoming is used to explore both Bezier and B-spline curves, and in particular to investigate continuity properties, change of basis algorithms, forward differencing, B-spline knot multiplicity, and knot insertion algorithms. We also look at triangle diagrams (which are closely related to blossoming), direct manipulation of B-spline curves, NURBS curves, and triangular and tensor product surfaces.
  

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

II
1
III
3
IV
4
V
5
VII
7
IX
12
XI
15
XII
16
XLIV
57
XLV
59
XLVII
61
XLVIII
65
XLIX
68
LI
71
LII
73
LIV
74

XIII
17
XIV
18
XV
19
XVII
23
XVIII
24
XIX
26
XXI
27
XXIII
29
XXV
30
XXVI
31
XXVII
32
XXIX
35
XXXI
37
XXXII
42
XXXIV
46
XXXV
47
XXXVII
49
XXXIX
51
XLI
55
XLIII
56
LV
75
LVI
76
LVIII
77
LX
78
LXI
79
LXII
81
LXIII
82
LXIV
83
LXVII
84
LXVIII
85
LXIX
86
LXX
87
LXXII
88
LXXVI
90
LXXVIII
91
LXXX
92
LXXXI
93
LXXXII
95
LXXXIII
97
Copyright

Common terms and phrases

Popular passages

Page 2 - Since every element of V can be written as a linear combination of the elements of 5, the set S spans the vector space V.

About the author (2006)

Stephen Mann joined the British Royal Navy at the age of fifteen. He has written the book "Sadism, Songs and Stolen Liberty" about his experiences in the Navy and how he tried for five and a half years to get out. He has spent his working life first as a chef, then a postal worker before becoming a telecoms engineer. Stephen has been a lifelong trade union activist and now works as a health and safety officer for the Communication Workers Union. Stephen lives in North London and supports his local football team, the Arsenal and he is active in their Independent Supporters Association. Stephen is a member of his local Labour Party and he likes music, reading, writing and enjoys a nice cup of tea.

Bibliographic information