Commit 8274976de63456d92a2048f8191e2a738ff7e8ca
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d522cf78
Add basic geometric transformations
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... | ... | @@ -25,6 +25,7 @@ use std::f64::consts::PI as FPI; |
25 | 25 | use fractional::fractional::{Fractional, from_vector, Continuous}; |
26 | 26 | use fractional::trigonometry::{sin, cos, tan, PI}; |
27 | 27 | use fractional::vector::{Vector}; |
28 | +use fractional::transform::{translate, rotate_x, rotate_y, rotate_z, rotate_v}; | |
28 | 29 | |
29 | 30 | fn mean(v: &Vec<i64>) -> Result<Fractional, TryFromIntError> { |
30 | 31 | let r = v.iter().fold(0, |acc, x| acc + x); |
... | ... | @@ -148,6 +149,55 @@ fn _vector() { |
148 | 149 | println!("{:>14} : {}", "v2 * v1", v2 * v1); |
149 | 150 | } |
150 | 151 | |
152 | +fn _transform() { | |
153 | + let v = Vector(1.into(), 1.into(), 1.into()); | |
154 | + let v1 = Vector(1.into(), 2.into(), 3.into()); | |
155 | + let mt = translate(v); | |
156 | + | |
157 | + println!("{:>14} : {}", "Vector v1", v1); | |
158 | + println!("{:>14} : {}", "translate v1", mt.apply(&v1)); | |
159 | + println!(); | |
160 | + | |
161 | + let v2 = Vector(1.into(), 1.into(), 0.into()); | |
162 | + println!("{:>14} : {}", "Vector v2", v2); | |
163 | + for d in [ 30, 45, 60, 90, 120, 135, 150, 180 | |
164 | + , 210, 225, 240, 270, 300, 315, 330 ].iter() { | |
165 | + let m = rotate_x(*d as i32); | |
166 | + println!("{:>14} : {}", format!("rot_x {} v2", d), m.apply(&v2)); | |
167 | + } | |
168 | + println!(); | |
169 | + | |
170 | + println!("{:>14} : {}", "Vector v2", v2); | |
171 | + for d in [ 30, 45, 60, 90, 120, 135, 150, 180 | |
172 | + , 210, 225, 240, 270, 300, 315, 330 ].iter() { | |
173 | + let m = rotate_y(*d as i32); | |
174 | + println!("{:>14} : {}", format!("rot_y {} v2", d), m.apply(&v2)); | |
175 | + } | |
176 | + println!(); | |
177 | + | |
178 | + for d in [ 30, 45, 60, 90, 120, 135, 150, 180 | |
179 | + , 210, 225, 240, 270, 300, 315, 330 ].iter() { | |
180 | + let m = rotate_x(*d as i32) * rotate_y(*d as i32); | |
181 | + println!("{:>14} : {}", format!("rot_xy {} v2", d), m.apply(&v2)); | |
182 | + } | |
183 | + println!(); | |
184 | + | |
185 | + let v3 = Vector(1.into(), 0.into(), 1.into()); | |
186 | + println!("{:>14} : {}", "Vector v3", v3); | |
187 | + for d in [ 30, 45, 60, 90, 120, 135, 150, 180 | |
188 | + , 210, 225, 240, 270, 300, 315, 330 ].iter() { | |
189 | + let m = rotate_z(*d as i32); | |
190 | + println!("{:>14} : {}", format!("rot_z {} v3", d), m.apply(&v3)); | |
191 | + } | |
192 | + println!(); | |
193 | + | |
194 | + for d in [ 30, 45, 60, 90, 120, 135, 150, 180 | |
195 | + , 210, 225, 240, 270, 300, 315, 330 ].iter() { | |
196 | + let m = rotate_v(&v, *d as i32); | |
197 | + println!("{:>14} : {}", format!("rot_v {} v2", d), m.apply(&v2)); | |
198 | + } | |
199 | +} | |
200 | + | |
151 | 201 | fn main() { |
152 | 202 | common_fractional(); |
153 | 203 | println!(); |
... | ... | @@ -164,4 +214,6 @@ fn main() { |
164 | 214 | _tan(); |
165 | 215 | println!(); |
166 | 216 | _vector(); |
217 | + println!(); | |
218 | + _transform(); | |
167 | 219 | } | ... | ... |
fractional/src/transform.rs
0 → 100644
1 | +// | |
2 | +// Transformation of vectors in a given coordinate system... | |
3 | +// | |
4 | +// Georg Hopp <georg@steffers.org> | |
5 | +// | |
6 | +// Copyright © 2019 Georg Hopp | |
7 | +// | |
8 | +// This program is free software: you can redistribute it and/or modify | |
9 | +// it under the terms of the GNU General Public License as published by | |
10 | +// the Free Software Foundation, either version 3 of the License, or | |
11 | +// (at your option) any later version. | |
12 | +// | |
13 | +// This program is distributed in the hope that it will be useful, | |
14 | +// but WITHOUT ANY WARRANTY; without even the implied warranty of | |
15 | +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
16 | +// GNU General Public License for more details. | |
17 | +// | |
18 | +// You should have received a copy of the GNU General Public License | |
19 | +// along with this program. If not, see <http://www.gnu.org/licenses/>. | |
20 | +// | |
21 | +use std::ops::{Mul}; | |
22 | +use crate::{Fractional, cos, sin, Vector}; | |
23 | + | |
24 | +pub struct TMatrix( (Fractional, Fractional, Fractional, Fractional) | |
25 | + , (Fractional, Fractional, Fractional, Fractional) | |
26 | + , (Fractional, Fractional, Fractional, Fractional) | |
27 | + , (Fractional, Fractional, Fractional, Fractional) ); | |
28 | + | |
29 | +pub fn translate(v :Vector) -> TMatrix { | |
30 | + let Vector(x, y, z) = v; | |
31 | + | |
32 | + TMatrix( (1.into(), 0.into(), 0.into(), 0.into()) | |
33 | + , (0.into(), 1.into(), 0.into(), 0.into()) | |
34 | + , (0.into(), 0.into(), 1.into(), 0.into()) | |
35 | + , ( x, y, z, 1.into()) ) | |
36 | +} | |
37 | + | |
38 | +pub fn rotate_x(a :i32) -> TMatrix { | |
39 | + TMatrix( (1.into(), 0.into(), 0.into(), 0.into()) | |
40 | + , (0.into(), cos(a), -sin(a), 0.into()) | |
41 | + , (0.into(), sin(a), cos(a), 0.into()) | |
42 | + , (0.into(), 0.into(), 0.into(), 1.into()) ) | |
43 | +} | |
44 | + | |
45 | +pub fn rotate_y(a :i32) -> TMatrix { | |
46 | + TMatrix( ( cos(a), 0.into(), sin(a), 0.into()) | |
47 | + , (0.into(), 1.into(), 0.into(), 0.into()) | |
48 | + , ( -sin(a), 0.into(), cos(a), 0.into()) | |
49 | + , (0.into(), 0.into(), 0.into(), 1.into()) ) | |
50 | +} | |
51 | + | |
52 | +pub fn rotate_z(a :i32) -> TMatrix { | |
53 | + TMatrix( ( cos(a), -sin(a), 0.into(), 0.into()) | |
54 | + , ( sin(a), cos(a), 0.into(), 0.into()) | |
55 | + , (0.into(), 0.into(), 1.into(), 0.into()) | |
56 | + , (0.into(), 0.into(), 0.into(), 1.into()) ) | |
57 | +} | |
58 | + | |
59 | +pub fn rotate_v(v :&Vector, a :i32) -> TMatrix { | |
60 | + let Vector(x, y, z) = *v; | |
61 | + | |
62 | + let zero :Fractional = 0.into(); | |
63 | + let one :Fractional = 1.into(); | |
64 | + | |
65 | + TMatrix( ( (one - cos(a)) * x * x + cos(a) | |
66 | + , (one - cos(a)) * x * y - sin(a) * z | |
67 | + , (one - cos(a)) * x * z + sin(a) * y | |
68 | + , zero ) | |
69 | + , ( (one - cos(a)) * x * y + sin(a) * z | |
70 | + , (one - cos(a)) * y * y + cos(a) | |
71 | + , (one - cos(a)) * y * z - sin(a) * x | |
72 | + , zero ) | |
73 | + , ( (one - cos(a)) * x * z - sin(a) * y | |
74 | + , (one - cos(a)) * y * z + sin(a) * x | |
75 | + , (one - cos(a)) * z * z + cos(a) | |
76 | + , zero ) | |
77 | + , (0.into(), 0.into(), 0.into(), 1.into()) ) | |
78 | +} | |
79 | + | |
80 | +pub fn scale(v :Vector) -> TMatrix { | |
81 | + let Vector(x, y, z) = v; | |
82 | + | |
83 | + TMatrix( ( x, 0.into(), 0.into(), 0.into()) | |
84 | + , (0.into(), y, 0.into(), 0.into()) | |
85 | + , (0.into(), 0.into(), z, 0.into()) | |
86 | + , (0.into(), 0.into(), 0.into(), 1.into()) ) | |
87 | +} | |
88 | + | |
89 | +impl TMatrix { | |
90 | + pub fn apply(&self, v :&Vector) -> Vector { | |
91 | + let TMatrix( (a11, a12, a13, a14) | |
92 | + , (a21, a22, a23, a24) | |
93 | + , (a31, a32, a33, a34) | |
94 | + , (a41, a42, a43, a44) ) = *self; | |
95 | + let Vector(x, y, z) = *v; | |
96 | + | |
97 | + let v = Vector( a11 * x + a21 * y + a31 * z + a41 | |
98 | + , a12 * x + a22 * y + a32 * z + a42 | |
99 | + , a13 * x + a23 * y + a33 * z + a43 ); | |
100 | + let Fractional(wn, wd) = a14 * x + a24 * y + a34 * z + a44; | |
101 | + | |
102 | + v.mul(&Fractional(wd, wn)) | |
103 | + } | |
104 | +} | |
105 | + | |
106 | +impl Mul for TMatrix { | |
107 | + type Output = Self; | |
108 | + | |
109 | + // ATTENTION: This is not commutative, nor assoziative. | |
110 | + fn mul(self, other :Self) -> Self { | |
111 | + let TMatrix( (a11, a12, a13, a14) | |
112 | + , (a21, a22, a23, a24) | |
113 | + , (a31, a32, a33, a34) | |
114 | + , (a41, a42, a43, a44) ) = self; | |
115 | + let TMatrix( (b11, b12, b13, b14) | |
116 | + , (b21, b22, b23, b24) | |
117 | + , (b31, b32, b33, b34) | |
118 | + , (b41, b42, b43, b44) ) = other; | |
119 | + | |
120 | + TMatrix( ( a11 * b11 + a12 * b21 + a13 * b31 + a14 * b41 | |
121 | + , a11 * b12 + a12 * b22 + a13 * b32 + a14 * b42 | |
122 | + , a11 * b13 + a12 * b23 + a13 * b33 + a14 * b43 | |
123 | + , a11 * b14 + a12 * b24 + a13 * b34 + a14 * b44 ) | |
124 | + , ( a21 * b11 + a22 * b21 + a23 * b31 + a24 * b41 | |
125 | + , a21 * b12 + a22 * b22 + a23 * b32 + a24 * b42 | |
126 | + , a21 * b13 + a22 * b23 + a23 * b33 + a24 * b43 | |
127 | + , a21 * b14 + a22 * b24 + a23 * b34 + a24 * b44 ) | |
128 | + , ( a31 * b11 + a32 * b21 + a33 * b31 + a34 * b41 | |
129 | + , a31 * b12 + a32 * b22 + a33 * b32 + a34 * b42 | |
130 | + , a31 * b13 + a32 * b23 + a33 * b33 + a34 * b43 | |
131 | + , a31 * b14 + a32 * b24 + a33 * b34 + a34 * b44 ) | |
132 | + , ( a41 * b11 + a42 * b21 + a43 * b31 + a44 * b41 | |
133 | + , a41 * b12 + a42 * b22 + a43 * b32 + a44 * b42 | |
134 | + , a41 * b13 + a42 * b23 + a43 * b33 + a44 * b43 | |
135 | + , a41 * b14 + a42 * b24 + a43 * b34 + a44 * b44 ) ) | |
136 | + } | |
137 | +} | ... | ... |
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