1 // interp.h
2 //
3 // Copyright (C) 2003, 2004 Jason Bevins
4 //
5 // This library is free software; you can redistribute it and/or modify it
6 // under the terms of the GNU Lesser General Public License as published by
7 // the Free Software Foundation; either version 2.1 of the License, or (at
8 // your option) any later version.
9 //
10 // This library is distributed in the hope that it will be useful, but WITHOUT
11 // ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
12 // FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
13 // License (COPYING.txt) for more details.
14 //
15 // You should have received a copy of the GNU Lesser General Public License
16 // along with this library; if not, write to the Free Software Foundation,
17 // Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
18 //
19 // The developer's email is jlbezigvins@gmzigail.com (for great email, take
20 // off every 'zig'.)
21 //
22 module noise.interp;
23 
24 /// @addtogroup libnoise
25 /// @{
26 
27 /// Performs cubic interpolation between two values bound between two other
28 /// values.
29 ///
30 /// @param n0 The value before the first value.
31 /// @param n1 The first value.
32 /// @param n2 The second value.
33 /// @param n3 The value after the second value.
34 /// @param a The alpha value.
35 ///
36 /// @returns The interpolated value.
37 ///
38 /// The alpha value should range from 0.0 to 1.0.  If the alpha value is
39 /// 0.0, this function returns @a n1.  If the alpha value is 1.0, this
40 /// function returns @a n2.
41 double CubicInterp (double n0, double n1, double n2, double n3,
42   double a)
43 {
44   double p = (n3 - n2) - (n0 - n1);
45   double q = (n0 - n1) - p;
46   double r = n2 - n0;
47   double s = n1;
48   return p * a * a * a + q * a * a + r * a + s;
49 }
50 
51 /// Performs linear interpolation between two values.
52 ///
53 /// @param n0 The first value.
54 /// @param n1 The second value.
55 /// @param a The alpha value.
56 ///
57 /// @returns The interpolated value.
58 ///
59 /// The alpha value should range from 0.0 to 1.0.  If the alpha value is
60 /// 0.0, this function returns @a n0.  If the alpha value is 1.0, this
61 /// function returns @a n1.
62 double LinearInterp (double n0, double n1, double a)
63 {
64   return ((1.0 - a) * n0) + (a * n1);
65 }
66 
67 /// Maps a value onto a cubic S-curve.
68 ///
69 /// @param a The value to map onto a cubic S-curve.
70 ///
71 /// @returns The mapped value.
72 ///
73 /// @a a should range from 0.0 to 1.0.
74 ///
75 /// The derivitive of a cubic S-curve is zero at @a a = 0.0 and @a a =
76 /// 1.0
77 double SCurve3 (double a)
78 {
79   return (a * a * (3.0 - 2.0 * a));
80 }
81 
82 /// Maps a value onto a quintic S-curve.
83 ///
84 /// @param a The value to map onto a quintic S-curve.
85 ///
86 /// @returns The mapped value.
87 ///
88 /// @a a should range from 0.0 to 1.0.
89 ///
90 /// The first derivitive of a quintic S-curve is zero at @a a = 0.0 and
91 /// @a a = 1.0
92 ///
93 /// The second derivitive of a quintic S-curve is zero at @a a = 0.0 and
94 /// @a a = 1.0
95 double SCurve5 (double a)
96 {
97   double a3 = a * a * a;
98   double a4 = a3 * a;
99   double a5 = a4 * a;
100   return (6.0 * a5) - (15.0 * a4) + (10.0 * a3);
101 }
102 
103 // @}