dlib.math.interpolation.bezier source code

1 /*
2 Copyright (c) 2013-2021 Timur Gafarov
3 
4 Boost Software License - Version 1.0 - August 17th, 2003
5 
6 Permission is hereby granted, free of charge, to any person or organization
7 obtaining a copy of the software and accompanying documentation covered by
8 this license (the "Software") to use, reproduce, display, distribute,
9 execute, and transmit the Software, and to prepare derivative works of the
10 Software, and to permit third-parties to whom the Software is furnished to
11 do so, all subject to the following:
12 
13 The copyright notices in the Software and this entire statement, including
14 the above license grant, this restriction and the following disclaimer,
15 must be included in all copies of the Software, in whole or in part, and
16 all derivative works of the Software, unless such copies or derivative
17 works are solely in the form of machine-executable object code generated by
18 a source language processor.
19 
20 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
21 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
22 FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT
23 SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
24 FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,
25 ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
26 DEALINGS IN THE SOFTWARE.
27 */
28 
29 /**
30  * Bézier interpolation functions
31  *
32  * Copyright: Timur Gafarov 2013-2021.
33  * License: $(LINK2 boost.org/LICENSE_1_0.txt, Boost License 1.0).
34  * Authors: Timur Gafarov
35  */
36 module dlib.math.interpolation.bezier;
37 
38 import dlib.math.vector;
39 
40 /**
41  * Computes cubic Bézier curve 
42  */
43 T bezierCubic(T) (T A, T B, T C, T D, T t)
44 {
45     T s = cast(T)1.0 - t;
46     T s2 = s * s;
47     T s3 = s2 * s;
48     return s3 * A +
49            3.0 * t * s2 * B +
50            3.0 * t * t * s * C +
51            t * t * t * D;
52 }
53 
54 /// ditto
55 alias bezier = bezierCubic;
56 
57 /**
58  * Computes cubic Bézier curve tangent
59  */
60 T bezierCubicTangent(T)(T a, T b, T c, T d, T t)
61 {
62     T c1 = (d - (3.0 * c) + (3.0 * b) - a);
63     T c2 = ((3.0 * c) - (6.0 * b) + (3.0 * a));
64     T c3 = ((3.0 * b) - (3.0 * a));
65     return ((3.0 * c1 * t * t) + (2.0 * c2 * t) + c3);
66 }
67 
68 /// ditto
69 alias bezierTangent = bezierCubicTangent;
70 
71 /**
72  * Computes cubic Bézier curve in 2D space
73  */
74 Vector!(T,2) bezierVector2(T)(
75     Vector!(T,2) a,
76     Vector!(T,2) b,
77     Vector!(T,2) c,
78     Vector!(T,2) d,
79     T t)
80 {
81     return Vector!(T,2)
82     (
83         bezier(a.x, b.x, c.x, d.x, t),
84         bezier(a.y, b.y, c.y, d.y, t)
85     );
86 }
87 
88 /**
89  * Computes cubic Bézier curve in 3D space
90  */
91 Vector!(T,3) bezierVector3(T)(
92     Vector!(T,3) a,
93     Vector!(T,3) b,
94     Vector!(T,3) c,
95     Vector!(T,3) d,
96     T t)
97 {
98     return Vector!(T,3)
99     (
100         bezier(a.x, b.x, c.x, d.x, t),
101         bezier(a.y, b.y, c.y, d.y, t),
102         bezier(a.z, b.z, c.z, d.z, t)
103     );
104 }
105 
106 /**
107  * Computes cubic Bézier curve tangent in 2D space
108  */
109 Vector!(T,2) bezierTangentVector2(T)(
110     Vector!(T,2) a,
111     Vector!(T,2) b,
112     Vector!(T,2) c,
113     Vector!(T,2) d,
114     T t)
115 {
116     return Vector!(T,2)
117     (
118         bezierTangent(a.x, b.x, c.x, d.x, t),
119         bezierTangent(a.y, b.y, c.y, d.y, t)
120     );
121 }
122 
123 /**
124  * Computes cubic Bézier curve tangent in 3D space
125  */
126 Vector!(T,3) bezierTangentVector3(T)(
127     Vector!(T,3) a,
128     Vector!(T,3) b,
129     Vector!(T,3) c,
130     Vector!(T,3) d,
131     T t)
132 {
133     return Vector!(T,3)
134     (
135         bezierTangent(a.x, b.x, c.x, d.x, t),
136         bezierTangent(a.y, b.y, c.y, d.y, t),
137         bezierTangent(a.z, b.z, c.z, d.z, t)
138     );
139 }