bspline 1.1.0

A simple generic library for computing B-splines
Documentation 
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
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190

extern crate image;
extern crate bspline;

use std::ops::{Mul, Add};
use std::iter;

#[derive(Copy, Clone, Debug)]
struct Point {
    x: f32,
    y: f32,
}
impl Point {
    fn new(x: f32, y: f32) -> Point {
        Point { x: x, y: y }
    }
}
impl Mul<f32> for Point {
    type Output = Point;
    fn mul(self, rhs: f32) -> Point {
        Point { x: self.x * rhs, y: self.y * rhs }
    }
}
impl Add for Point {
    type Output = Point;
    fn add(self, rhs: Point) -> Point {
        Point { x: self.x + rhs.x, y: self.y + rhs.y }
    }
}

/// Evaluate the B-spline and plot it to the image buffer passed
fn plot_2d(spline: &bspline::BSpline<Point, f32>, plot: &mut [u8], plot_dim: (usize, usize), scale: (f32, f32),
           offset: (f32, f32)) {
    let step_size = 0.001;
    let t_range = spline.knot_domain();
    let steps = ((t_range.1 - t_range.0) / step_size) as usize;
    for s in 0..steps + 1 {
        let t = step_size * s as f32 + t_range.0;
        let pt = spline.point(t);
        let ix = ((pt.x + offset.0) * scale.0) as isize;
        let iy = ((pt.y + offset.1) * scale.1) as isize;
        for y in iy - 1..iy + 1 {
            for x in ix - 1..ix + 1 {
                if y >= 0 && y < plot_dim.1 as isize && x >= 0 && x < plot_dim.0 as isize {
                    let px = (plot_dim.1 - 1 - y as usize) * plot_dim.0 * 3 + x as usize * 3;
                    for i in 0..3 {
                        plot[px + i] = 0;
                    }
                }
            }
        }
    }
    // Draw the control points
    for pt in spline.control_points() {
        let ix = ((pt.x + offset.0) * scale.0) as isize;
        let iy = ((pt.y + offset.1) * scale.1) as isize;
        for y in iy - 3..iy + 3 {
            for x in ix - 3..ix + 3 {
                if y >= 0 && y < plot_dim.1 as isize && x >= 0 && x < plot_dim.0 as isize {
                    let px = (plot_dim.1 - 1 - y as usize) * plot_dim.0 * 3 + x as usize * 3;
                    plot[px] = 255;
                    plot[px + 1] = 0;
                    plot[px + 2] = 0;
                }
            }
        }
    }
}

fn plot_test() {
    let points = vec![Point::new(-2.5, 1.5), Point::new(-2.0, -1.5),
                      Point::new(-1.5, 1.5), Point::new(-1.0, -1.5),
                      Point::new(-0.5, 1.5), Point::new(0.0, -1.5),
                      Point::new(0.5, 1.5), Point::new(1.0, -1.5),
                      Point::new(1.5, 1.5), Point::new(2.0, -1.5),
                      Point::new(2.5, 1.5)];
    let knots = vec![0.0, 0.0, 0.0, 0.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0,
                     10.0, 11.0, 12.0, 13.0, 14.0];
    let degree = 3;

    let plot_dim = (720, 540);
    let scale = (plot_dim.0 as f32 / 6.0, plot_dim.1 as f32 / 4.0);
    let offset = (3.0, 2.0);

    let mut plot: Vec<_> = iter::repeat(255u8).take(plot_dim.0 * plot_dim.1 * 3).collect();

    println!("Plotting B-spline with:\n\tpoints = {:?}\n\tknots = {:?}",
             points, knots);

    let spline = bspline::BSpline::new(degree, points, knots);

    println!("\tt range = {:?}", spline.knot_domain());

    plot_2d(&spline, &mut plot[..], plot_dim, scale, offset);
    match image::save_buffer("test.png", &plot[..], plot_dim.0 as u32, plot_dim.1 as u32, image::RGB(8)) {
        Ok(_) => println!("Test B-spline saved to test.png"),
        Err(e) => println!("Error saving test.png,  {}", e),
    }
}

/// Plot a simple 2D quadratic B-spline
fn plot_quadratic() {
    let points = vec![Point::new(-1.5, 0.0), Point::new(0.0, 1.5), Point::new(1.5, 0.0)];
    let knots = vec![0.0, 0.0, 0.0, 3.0, 3.0, 3.0];
    let degree = 2;

    let plot_dim = (720, 540);
    let scale = (plot_dim.0 as f32 / 4.0, plot_dim.1 as f32 / 4.0);
    let offset = (2.0, 2.0);

    let mut plot: Vec<_> = iter::repeat(255u8).take(plot_dim.0 * plot_dim.1 * 3).collect();

    println!("Plotting Quadratic B-spline with:\n\tpoints = {:?}\n\tknots = {:?}",
             points, knots);

    let spline = bspline::BSpline::new(degree, points, knots);

    println!("\tt range = {:?}", spline.knot_domain());

    plot_2d(&spline, &mut plot[..], plot_dim, scale, offset);
    match image::save_buffer("quadratic_2d.png", &plot[..], plot_dim.0 as u32, plot_dim.1 as u32, image::RGB(8)) {
        Ok(_) => println!("2D Quadratic B-spline saved to quadratic_2d.png"),
        Err(e) => println!("Error saving quadratic_2d.png,  {}", e),
    }
}
/// Plot a simple 2D cubic B-spline
fn plot_cubic() {
    let points = vec![Point::new(-1.5, -1.5), Point::new(-0.5, 1.5),
                      Point::new(0.5, -1.5), Point::new(1.5, 1.5)];
    let knots = vec![0.0, 1.0, 2.0, 2.0, 5.0, 5.0, 6.0, 7.0];
    let degree = 3;

    let plot_dim = (720, 540);
    let scale = (plot_dim.0 as f32 / 4.0, plot_dim.1 as f32 / 4.0);
    let offset = (2.0, 2.0);

    let mut plot: Vec<_> = iter::repeat(255u8).take(plot_dim.0 * plot_dim.1 * 3).collect();

    println!("Plotting Cubic B-spline with:\n\tpoints = {:?}\n\tknots = {:?}",
             points, knots);

    let spline = bspline::BSpline::new(degree, points, knots);

    println!("\tt range = {:?}", spline.knot_domain());
    println!("spline = {:?}", spline);

    plot_2d(&spline, &mut plot[..], plot_dim, scale, offset);
    match image::save_buffer("cubic_2d.png", &plot[..], plot_dim.0 as u32, plot_dim.1 as u32, image::RGB(8)) {
        Ok(_) => println!("2D Cubic B-spline saved to cubic_2d.png"),
        Err(e) => println!("Error saving cubic_2d.png,  {}", e),
    }
}
/// Plot a simple 2D quartic B-spline
fn plot_quartic() {
    let points = vec![Point::new(-1.8, -1.4), Point::new(-1.2, 0.5), Point::new(-0.2, -0.8),
                      Point::new(-0.6, 0.7), Point::new(0.0, 1.6), Point::new(1.0, 0.0),
                      Point::new(0.6, -0.3), Point::new(0.0, -1.0)];
    let knots = vec![0.0, 0.0, 0.0, 0.0, 0.2, 1.0, 2.0, 3.0, 5.0, 5.0, 5.0, 5.0, 5.0];
    let degree = 4;

    let plot_dim = (720, 540);
    let scale = (plot_dim.0 as f32 / 4.0, plot_dim.1 as f32 / 4.0);
    let offset = (2.0, 2.0);

    let mut plot: Vec<_> = iter::repeat(255u8).take(plot_dim.0 * plot_dim.1 * 3).collect();

    println!("Plotting Quartic B-spline with:\n\tpoints = {:?}\n\tknots = {:?}",
             points, knots);

    let spline = bspline::BSpline::new(degree, points, knots);

    println!("\tt range = {:?}", spline.knot_domain());

    plot_2d(&spline, &mut plot[..], plot_dim, scale, offset);
    match image::save_buffer("quartic_2d.png", &plot[..], plot_dim.0 as u32, plot_dim.1 as u32, image::RGB(8)) {
        Ok(_) => println!("2D Quartic B-spline saved to quartic_2d.png"),
        Err(e) => println!("Error saving quartic_2d.png,  {}", e),
    }
}

fn main() {
    let divider: String = iter::repeat('-').take(80).collect();
    plot_test();
    println!("{}\n\n{}", divider, divider);
    plot_quadratic();
    println!("{}\n\n{}", divider, divider);
    plot_cubic();
    println!("{}\n\n{}", divider, divider);
    plot_quartic();
}