1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
|
\input preamble.tex
% ---------------------------------------------------------------------------
\begin{document}
\begin{center}
{\Huge \bf{I. Rational Quadratic Bezier Curves}}
\bigskip
\begin{lapdf}(16,20)(-8,-10)
\Dgray
\Dash(1)
\Polygon(-8,0)(0,10)(8,0) \Stroke
\Dash(0)
\Red
\Rcurve(64)(-8,0,7)(0,10,1)(8,0,7) \Stroke
\Green
\Rcurve(64)(-8,0,6)(0,10,1)(8,0,6) \Stroke
\Blue
\Rcurve(64)(-8,0,5)(0,10,1)(8,0,5) \Stroke
\Cyan
\Rcurve(64)(-8,0,4)(0,10,1)(8,0,4) \Stroke
\Magenta
\Rcurve(64)(-8,0,3)(0,10,1)(8,0,3) \Stroke
\Yellow
\Rcurve(64)(-8,0,2)(0,10,1)(8,0,2) \Stroke
\Black
\Rcurve(64)(-8,0,1)(0,10,1)(8,0,1) \Stroke
\Red
\Rcurve(64)(-8,0,1)(0,10,2)(8,0,1) \Stroke
\Green
\Rcurve(64)(-8,0,1)(0,10,3)(8,0,1) \Stroke
\Blue
\Rcurve(64)(-8,0,1)(0,10,4)(8,0,1) \Stroke
\Cyan
\Rcurve(64)(-8,0,1)(0,10,5)(8,0,1) \Stroke
\Magenta
\Rcurve(64)(-8,0,1)(0,10,6)(8,0,1) \Stroke
\Yellow
\Rcurve(64)(-8,0,1)(0,10,7)(8,0,1) \Stroke
\Black
\Rcurve(64)(-8,0,1)(0,10,0)(8,0,1) \Stroke
\Red
\Rcurve(64)(-8,0,7)(0,10,-1)(8,0,7) \Stroke
\Green
\Rcurve(64)(-8,0,6)(0,10,-1)(8,0,6) \Stroke
\Blue
\Rcurve(64)(-8,0,5)(0,10,-1)(8,0,5) \Stroke
\Cyan
\Rcurve(64)(-8,0,4)(0,10,-1)(8,0,4) \Stroke
\Magenta
\Rcurve(64)(-8,0,3)(0,10,-1)(8,0,3) \Stroke
\Yellow
\Rcurve(64)(-8,0,2)(0,10,-1)(8,0,2) \Stroke
\Point(1)(-8,0)
\Point(1)(+0,10)
\Point(1)(+8,0)
\Text(-8.0,0.2,rb){$P_0$}
\Text(+0.2,+10.3,rb){$P_1$}
\Text(+8.0,0.2,lb){$P_2$}
\end{lapdf}
\end{center}
All curves share the same Bezier points, but they differ in the weights of
the points. The black curve is a parabola {$w = 1$}. Above of this all
curves are hyperbolas with increasing weigts, below of this are elliptic curves
with decreasing weights. The line has a weight of {$w = 0$}. After this
the weights are negative increasing. The curves are the complementare
elliptical arcs to the positive counterparts.
\newpage
\unitlength1.16cm
\begin{center}
{\Huge \bf{II. Conic Curves}}
\bigskip
\begin{lapdf}(16,16)(0,0)
\Dgray
\Rcurve(64)(4,10.333,2)(0,3.4,1)(8,3.4,2)
\Rcurve(80)(4,10.333,2)(0,3.4,-1)(8,3.4,2) \Stroke
\Red
\Rcurve(64)(4,9.7,2)(0,4.7,1)(8,4.7,2)
\Rcurve(80)(4,9.7,2)(0,4.7,-1)(8,4.7,2) \Stroke
\Green
\Rcurve(64)(9.7,4,2)(4.7,0,1)(4.7,8,2)
\Rcurve(80)(9.7,4,2)(4.7,0,-1)(4.7,8,2) \Stroke
\Blue
\Rcurve(64)(16,16,1)(8,8,5)(16,0,1) \Stroke
\Cyan
\Rcurve(64)(0,16,1)(8,8,5)(0,0,1) \Stroke
\Magenta
\Rcurve(64)(0,16,1)(8,0,1)(16,16,1) \Stroke
\Yellow
\Rcurve(64)(0,0,1)(8,16,1)(16,0,1) \Stroke
\end{lapdf}
\large Circle, Ellipse, Parabola, Hyperbola
\end{center}
\end{document}
|
