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Bohumír Bastl The second reason for writing such a package followed from solving the project “Realization of interactively-information portal for scientific technical applications” which Department of Mathematics on our faculty obtained from Ministry of Education, Youth and Sports in 2004. The aim of this project is to create a new web portal, at this time located on http://webmath.zcu.cz, based on webMathematica software, which will provide different kinds of scientific computations. The computation and visualization of CAGD objects is also integrated to this web portal and anyone can use it. 2 Description of the package After loading the package to Mathematica kernel by standard Mathematica command Clamped,{{-10,-10},{-10,0}}] the figure (see Fig. 1 (right)) and the parametrization of the cubic spline for given points and boundary conditions (tangent vectors in the first and last points, here) are obtained. 50
CAGD PACKAGE FOR MATHEMATICA 10 7.5 5 2.5 6 4 2 -1 1 2 3 4 5 6 -2.5 -5 -7.5 -1 1 2 3 4 5 -2 -4 Figure 1: Quadratic and cubic splines. 10 2 6.1 9.1 1.1 4.1 0.1 7.1 8.1 3.1 5.1 2.1 8 6 4 2 4 6 8 10 1 Figure 2: Bézier and rational Bézier curves. Bézier objects belong to basic and very important CAGD objects. For given control polygon of n + 1 control points P i ,i = 0,...,n, or control net of (n + 1)(m + 1) control points P ij ,i = 0,...,n,j = 0,...,m respectively, the Bézier curve, or the Bézier surface respectively, is defined in the following way P(t) = n∑ P i Bi n (t), P(u,v) = i=0 n∑ i=0 j=0 m∑ P ij Bi n (u)Bj m (v) (1) where Bi n (t) are Bernstein polynomials of nth degree. The package provides functions Bernstein[] for computation of Bernstein polynomials, BezierCurve[] and BezierSurface[] for obtaining parametrizations andPlotBezierCurve[] andPlotBezierSurface[] for visualization of Bézier objects (see Fig. 2 (left) and 3 (left)). Rational Bézier objects are important for representation of curves or surfaces which cannot be parametrized by polynomial parametrizations, only by rational, e.g. arc of a circle. To each control point P i 51
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- Page 8 and 9: Table of Contents Petr Kahánek, Al
- Page 10 and 11: Table of Contents Daniela Velichov
- Page 13: PLENÁRNÍ PŘEDNÁŠKY PLENARY LEC
- Page 16 and 17: František Kuřina sítě čtyřdim
- Page 18 and 19: František Kuřina Kombinace těcht
- Page 20 and 21: František Kuřina 3 Matematika a v
- Page 22 and 23: František Kuřina řešení je alt
- Page 24 and 25: Gunter Weiss should show an own sci
- Page 26 and 27: Gunter Weiss “industrial reality
- Page 28 and 29: Gunter Weiss 5 “e-learning Geomet
- Page 30 and 31: Gunter Weiss In the following some
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- Page 35: REFERÁTY CONFERENCE PAPERS
- Page 38 and 39: Eva Baranová, Kamil Maleček S a a
- Page 40 and 41: Eva Baranová, Kamil Maleček extr
- Page 42 and 43: Eva Baranová, Kamil Maleček Obrá
- Page 44 and 45: ÊÓÞÔ×ÑÓ×ÓÙÖÒÔÞ×Ñ Å
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- Page 48 and 49: ÔÖØÓÑØÓÔÓÝÙ×ÓÙÖÓÚ
- Page 52 and 53: Bohumír Bastl 4 3 2 1 0 2 4 0 2 4
- Page 54 and 55: Bohumír Bastl the package that bot
- Page 56 and 57: Zuzana Benáková x B y z B B = u c
- Page 58 and 59: Zuzana Benáková Obrázek 4: třet
- Page 60 and 61: Michal Benes Since des t 2 = ds 2 +
- Page 62 and 63: Michal Benes The latter condition i
- Page 64 and 65: Michal Benes 4 Innitesimal deformat
- Page 66 and 67: Michal Benes where , 1, 2, ¢1, ¢2
- Page 68 and 69: Milan Bořík, Vojtěch Honzík sys
- Page 70 and 71: Milan Bořík, Vojtěch Honzík Dá
- Page 72 and 73: Milan Bořík, Vojtěch Honzík Obr
- Page 74 and 75: Jaromír Dobrý Example 2 Let’s c
- Page 76 and 77: Jaromír Dobrý M ϕ ϕ(M) ϑ V {o}
- Page 78 and 79: Jaromír Dobrý It is obvious from
- Page 80 and 81: Henryk Gliński distortion coeffici
- Page 82 and 83: Henryk Gliński polynomial. The coe
- Page 84 and 85: ÊÓÑÒÀõ ÎÖÚÑÓúÒÓÔÖÓ
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- Page 88 and 89: ÊÓÑÒÀõ ÈÖÓÖÑÓÒ ÒÑÞ
- Page 90 and 91: Oldřich Hykš foundations and simp
- Page 92 and 93: Oldřich Hykš The choice of the tr
- Page 94 and 95: Oldřich Hykš discussed together w
- Page 96 and 97: Petr Kahánek, Alexej Kolcun 2 Tria
- Page 98 and 99: Petr Kahánek, Alexej Kolcun of thi
Bohumír Bastl<br />
The second reason for writing such a package followed from solving<br />
the project “Realization of interactively-information portal for scientific<br />
technical applications” which Department of Mathematics on<br />
our faculty obtained from Ministry of Education, Youth and Sports<br />
in 2004. The aim of this project is to create a new web portal, at<br />
this time located on http://webmath.zcu.cz, based on webMathematica<br />
software, which will provide different kinds of scientific computations.<br />
The computation and visualization of CAGD objects is also<br />
integrated to this web portal and anyone can use it.<br />
2 Description of the package<br />
After loading the package to Mathematica kernel by standard Mathematica<br />
command Clamped,{{-10,-10},{-10,0}}]<br />
the figure (see Fig. 1 (right)) and the parametrization of the cubic<br />
spline for given points and boundary conditions (tangent vectors in<br />
the first and last points, here) are obtained.<br />
50
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