如何创建贝塞尔曲线而不是多点之间的直线？

Question

这对我来说是一个比较复杂的任务，我不能完全用标题来概括。

但问题是这样的：

我创建了一个音频可视化工具，可将原始音频数据转换为 Vec<f32>，其中向量中的元素按从 0hz 开始到 20_000hz
但现在我必须 normalize 向量，以便频率不是以线性方式而是以对数方式间隔，这更像是人类听觉的工作方式。这是执行此操作的函数：

fn normalize(buffer: Vec<f32>, volume: f32) -> Vec<f32> {
    let mut output_buffer: Vec<f32> = vec![0.0; buffer.len()];

    let mut start_pos: usize = 0;
    let mut end_pos: usize = 0;

    for i in 0..buffer.len() {
        // FIRST HALF
        let offset: f32 = (buffer.len() as f32 / (i + 1) as f32).sqrt();
        if ((i as f32 * offset) as usize) < output_buffer.len() {
            // normalized position
            let pos: usize = (i as f32 * offset) as usize;
            // stores positions needed for filling
            start_pos = end_pos;
            end_pos = pos;

            let y = buffer[i];

            // prevent volume loss, that could occur because of 'crunching' of higher freqs
            // by only setting the value of buffer if y is bigger
            if output_buffer[pos] < y {
                output_buffer[pos] = y;
            }
        }
        // SECOND HALF
        // linear filling of the values between 
        if end_pos - start_pos > 1 && (end_pos - 1) < output_buffer.len() {
            for s_p in (start_pos + 1)..end_pos {
                let percentage: f32 = (s_p - start_pos) as f32 / ((end_pos - 1) - start_pos) as f32;

                let mut y: f32 = 0.0;
                //(output_buffer[s_p] * (1.0 - percentage) ) + (output_buffer[end_pos] * percentage);
                y += output_buffer[start_pos] * (1.0 - percentage);
                y += output_buffer[end_pos] * percentage;
                output_buffer[s_p] = y;
            }
        }
    }

    output_buffer
}

在前半部分，我将缓冲区的值重新分配为对数，但是使用这种方法会跳过很多值，尤其是在低频范围内，然后看起来像这样：unfilled

     |
     |      |
     |      |
     |      | | | 
     |   |  | ||| 
|    |   |  | |||
+----+---+--+-+++

因此，我找到了一种方法来填补下半场的空白。现在它看起来像这样：filled

     |
    :|:     |
   ::|::   :|:
  :::|::: ::|:| | 
 ::::|:::|::|:||| 
|::::|:::|::|:|||
+----+---+--+-+++

为了可视化，我减少了条的数量，实际实现大约多了 10 倍'bars'，所以那里的线性更明显。

所以我的最后一个问题是，我想创建曲线而不是点之间的直线，这样可以更好地代表声音。

我需要能够访问曲线任意点的 'y' 坐标值。

有什么办法可以做到这一点，还是我这样做完全错了？

我创建了 audioviz that does all of this processing and where the code is from and audiolizer 一个应用程序，将这个库与 GUI 结合使用。

Answer 1

Splines 确实解决了我的确切问题。这是我的实现，增加了分辨率控制和音量标准化，可能不是必需的：

use splines::{Interpolation, Key, Spline};
fn normalize(buffer: Vec<f32>, volume: f32, resolution: f32) -> Vec<f32> {
    let mut output_buffer: Vec<f32> = vec![0.0; (buffer.len() as f32 * resolution ) as usize ];

    let mut pos_index: Vec<(usize, f32)> = Vec::new();

    for i in 0..buffer.len() {
        let offset: f32 = (output_buffer.len() as f32 / (i + 1) as f32 * resolution).sqrt();
        if ((i as f32 * offset) as usize) < output_buffer.len() {
            // space normalisation
            let pos: usize = (i as f32 * offset) as usize;
            
            // volume normalisation
            let volume_offset: f32 = (output_buffer.len() as f32 / (pos + 1) as f32).sqrt();
            let y = buffer[i] / volume_offset.powi(3) * 0.01;

            pos_index.push( ((pos as f32) as usize, y) );
        }
    }

    // Interpolation
    let mut points: Vec<Key<f32, f32>> = Vec::new();
    for val in pos_index.iter() {
        let x = val.0 as f32;
        let y = val.1 * volume;
        points.push(Key::new(x, y, Interpolation::Bezier(0.5)));
    }

    let spline = Spline::from_vec(points);

    for i in 0..output_buffer.len() {
        let v = match spline.sample(i as f32) {
            Some(v) => v,
            None => 0.0,
        };
        output_buffer[i] = v;
    }

    output_buffer
}

如何创建贝塞尔曲线而不是多点之间的直线？

How can I create bezier like curves instead of lines between multiple points?

audio

rust