How can I interpolate elevation of points in a grid

help
1

Hello,
I have the elevation of reference points in a 2D square grid, and I would like to be able to interpolate the elevation of any points in that grid. As far as I understand, the spline crate should be able to help me, but I don't understand how to write a 2D -> 1D interpolation hello word. I didn't know what splines (the mathematical object) was before discovering this crate, so it may be the source of my confusion.

2

It seems like the spline crate is only for 1d interpolation. You can bilinearly interpolate with something like this:

/// x1, y1, x2, y2 forms a rectangle of coordinates
/// v11 represents the value at x1, y1
/// v12 represents the value at x1, y2
/// v21 represents the value at x2, y1
/// v22 represents the value at x2, y2
struct BilinearData {
    x1: f64,
    y1: f64,
    x2: f64,
    y2: f64,
    v11: f64,
    v12: f64,
    v21: f64,
    v22: f64,
}

// approximates the value of the function f at x,y using bilinear interpolation
fn interpolate(x: f64, y: f64, f: BilinearData) -> f64 {
    let dx1 = x - f.x1;
    let dx2 = f.x2 - x;
    let dy1 = y - f.y1;
    let dy2 = f.y2 - y;
    let scaled = f.v11 * dx2 * dy2
               + f.v21 * dx1 * dy2
               + f.v12 * dx2 * dy1
               + f.v22 * dx1 * dy1;
    scaled / ((f.x2 - f.x1) * (f.y2 - f.y1))
}
2 Likes
3

The spline crate implements methods for cgmath::Vector2. With a bit more research, this is what I got, but it still doesn't work.

use cgmath::Vector2;

let coordinates: Vec<Vector2<f64>> = vec![
    Vector2::new(0.0, 0.0), Vector2::new(0.0, 0.1), Vector2::new(0.0, 0.2), Vector2::new(0.0, 0.3),
    Vector2::new(1.0, 0.0), Vector2::new(1.0, 0.1), Vector2::new(1.0, 0.2), Vector2::new(1.0, 0.3),
    Vector2::new(2.0, 0.0), Vector2::new(2.0, 0.1), Vector2::new(2.0, 0.2), Vector2::new(2.0, 0.3),
    Vector2::new(3.0, 0.0), Vector2::new(3.0, 0.1), Vector2::new(3.0, 0.2), Vector2::new(3.0, 0.3),
];  
    
let alti_array: Vec<f64> = vec![
    00.0, 01.0, 02.0, 03.0,
    10.0, 11.0, 12.0, 13.0,
    20.0, 21.0, 22.0, 23.0,
    30.0, 31.0, 32.0, 33.0,
];
        
let keys: Vec<Key<_, _>>;
for (c, altitude) in Iterator::zip(coordinates.iter(), alti_array.iter()) {
    keys.push(Key::new(c, altitude, Interpolation::Linear));
}
let spline = Spline::from_vec(keys);

assert_eq!(00.0, spline.clamped_sample(Vector2::new(0.0, 0.0)));
assert_eq!(33.0, spline.clamped_sample(Vector2::new(3.0, 0.3)));

assert_eq!(11.5, spline.clamped_sample(Vector2::new(1.0, 0.15)));
assert_eq!(16.5, spline.clamped_sample(Vector2::new(1.5, 0.15)));
assert_eq!(21.5, spline.clamped_sample(Vector2::new(2.0, 0.15)));

assert_eq!(16.0, spline.clamped_sample(Vector2::new(1.5, 0.1)));
assert_eq!(16.5, spline.clamped_sample(Vector2::new(1.5, 0.15)));
assert_eq!(17.0, spline.clamped_sample(Vector2::new(1.5, 0.2)));

I have enable cgmath support in my Cargo.toml:

splines = { version = "3.3.0", features = ["std", "impl-cgmath"] }

But I get the following error:

error[E0277]: can't compare `cgmath::vector::Vector2<f64>` with `cgmath::vector::Vector2<f64>`
   --> src/main.rs:216:35
    |
216 |     let spline = Spline::from_vec(keys);
    |                                   ^^^^ no implementation for `cgmath::vector::Vector2<f64> < cgmath::vector::Vector2<f64>` and `cgmath::vector::Vector2<f64> > cgmath::vector::Vector2<f64>`
    |
    = help: the trait `std::cmp::PartialOrd` is not implemented for `cgmath::vector::Vector2<f64>`
    = note: required because of the requirements on the impl of `std::cmp::PartialOrd` for `&cgmath::vector::Vector2<f64>`
    = note: required by `splines::spline::Spline::<T, V>::from_vec`

It feels very strange that cgmath::Vector2 doesn't works out-of-the box. What I am missing?

4

Well it complains that Vector2 is not ordered, which is correct. Points in 2d space have no natural ordering.

5

This is what I am going to use for the moment. Thanks Alice.

6

I agree, but I don't understand how I'm supposed to create a Spline since both constructors requires the key to implement PartialOrd. It should be possible to create Spline from a Vector2, otherwise, why would would it implements the traits Linear and Interpolate when you activate the feature cgmath_impl?

7

Maybe you can still use the trait methods directly, even if you can't put it in a spline?

8

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