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

/*
Copyright 2016 Martin Buck
This file is part of rust-3d.
rust-3d is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
rust-3d is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with rust-3d.  If not, see <http://www.gnu.org/licenses/>.
*/

//! interpolations within 2D space. E.g. bezier, linear, cosine

use std::f64::consts::PI;

use prelude::*;

fn factorial(number: usize) -> usize {
    let mut result = 1;

    for i in 1..number+1 {
        result *= i;
    }
    result
}

fn binominal_coefficient(n: usize, k: usize) -> usize {
    factorial(n) / (factorial(k) * factorial(n-k))
}

fn bernstein_polynomial(n: usize, i: usize, t: f64) -> f64 {
    (binominal_coefficient(n, i) as f64) * t.powi(i as i32) * (1.0 - t).powi((n-i) as i32)
}

fn control_polygon<P>(path: &PointCloud2D<P>, n_points: usize, t: f64) -> Box<P> where
    P: IsBuildable2D {

    let mut x : f64 = 0.0;
    let mut y : f64 = 0.0;

    for i in 0..n_points+1 {
        let bp = bernstein_polynomial(n_points, i, t);
        x += bp * path.data[i].x();
        y += bp * path.data[i].y();
    }
    P::new(x,y)
}

/// Returns the Bezier interpolation of the given base points
pub fn interpolate_bezier<P>(base_points: &PointCloud2D<P>, n_points: usize) -> Result<Box<PointCloud2D<P>>> where
    P: IsBuildable2D {

    if base_points.len() < 2 {
        return Err(ErrorKind::TooFewPoints);
    }

    let mut pc = PointCloud2D::with_capacity(n_points);
    let p_dist = 1.0 / (n_points as f64);

    for i in 0..n_points {
        pc.push(*control_polygon(base_points, base_points.len()-1, (i as f64) * p_dist));
    }
    Ok(Box::new(pc))
}

//@todo function names dont match interpolate vs interpolation...
/// Returns the Cosine interpolation of the given base points
pub fn interpolate_cosine<P>(base_points: &PointCloud2D<P>, n_points: usize) -> Result<Box<PointCloud2D<P>>> where
    P : IsBuildable2D {

    if base_points.len() < 2 {
        return Err(ErrorKind::TooFewPoints);
    }

    let mut pc = PointCloud2D::with_capacity(n_points);
    let p_dist = base_points.length() / (n_points - 1) as f64;

    for i in 0..n_points {
        let mut traveled : f64 = 0.0;
        let mut traveled_before : f64 = 0.0;

        for j in 1..base_points.len() {
            let ref p_prev = base_points.data[j-1];
            let ref p_now  = base_points.data[j];

            traveled += ( (p_now.x() - p_prev.x()).powi(2) + (p_now.y() - p_prev.y()).powi(2) ).sqrt();

            if traveled >= p_dist*(i as f64) {
                let proportion = ((i as f64)*p_dist - traveled_before) / (traveled - traveled_before);
                let proportion2 = (1.0 - (proportion*PI).cos() ) / 2.0;
                pc.push(*P::new(p_prev.x() + proportion * (p_now.x() - p_prev.x()),
                                p_prev.y() * (1.0 - proportion2) + p_now.y()*proportion2));
                break;
            }
            traveled_before = traveled;
        }
    }
    Ok(Box::new(pc))
}

/// Returns the linear interpolation of the given base points
pub fn interpolation_linear<P>(base_points: &PointCloud2D<P>, n_points: usize) -> Result<Box<PointCloud2D<P>>> where
    P : IsBuildable2D {

    if base_points.len() < 2 {
        return Err(ErrorKind::TooFewPoints);
    }

    let mut pc = PointCloud2D::with_capacity(n_points);
    let p_dist = base_points.length() / (n_points - 1) as f64;

    for i in 0..n_points {
        let mut traveled : f64 = 0.0;
        let mut traveled_before : f64 = 0.0;

        for j in 1..base_points.len() { //@todo fails if path too small, handle this
            let ref p_prev = base_points.data[j-1];
            let ref p_now  = base_points.data[j];

            traveled += ( (p_now.x() - p_prev.x()).powi(2) + (p_now.y() - p_prev.y()).powi(2) ).sqrt();

            if traveled >= p_dist*(i as f64) {
                let proportion = ((i as f64)*p_dist - traveled_before) / (traveled - traveled_before);
                pc.push(*P::new(p_prev.x() + proportion * (p_now.x() - p_prev.x()),
                                p_prev.y() + proportion * (p_now.y() - p_prev.y())));
                break;
            }
            traveled_before = traveled;
        }
    }
    Ok(Box::new(pc))
}