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improve the bivariate normal pdf 3d plot example #197

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improve the bivariate normal pdf 3d plot example #197

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27 changes: 18 additions & 9 deletions examples/3d-plot2.rs
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Original file line number Diff line number Diff line change
@@ -1,11 +1,20 @@
use plotters::prelude::*;
use std::f64::consts::PI;
fn pdf(x: f64, y: f64) -> f64 {
const SDX: f64 = 0.1;
const SDY: f64 = 0.1;
const A: f64 = 5.0;
let x = x as f64 / 10.0;
let y = y as f64 / 10.0;
A * (-x * x / 2.0 / SDX / SDX - y * y / 2.0 / SDY / SDY).exp()
// see https://mathworld.wolfram.com/BivariateNormalDistribution.html
// assumes x_bar = 0 and y_bar = 0
const SDX: f64 = 0.3;
const SDY: f64 = 0.3;
const vx: f64 = SDX * SDX;
const vy : f64 = SDY * SDY;
const sdx_sdy: f64 = SDX * SDY;
const RHO : f64 = 0.9;
const c1: f64 = 1.0 - RHO * RHO;
let c2 : f64 = c1.sqrt();
let A: f64 = 1.0 / (2.0 * PI * sdx_sdy * c2);
let Z: f64 = x * x / vx - 2.0 * RHO * x * y / sdx_sdy + y * y / vy;
let res = A * (-Z / 2.0 / c1).exp();
res
}

fn main() -> Result<(), Box<dyn std::error::Error>> {
Expand All @@ -17,7 +26,7 @@ fn main() -> Result<(), Box<dyn std::error::Error>> {

let mut chart = ChartBuilder::on(&root)
.caption("2D Guassian PDF", ("sans-serif", 20))
.build_cartesian_3d(-3.0..3.0, 0.0..6.0, -3.0..3.0)?;
.build_cartesian_3d(-1.0..1.0, 0.0..3.0, -1.0..1.0)?;
chart.with_projection(|mut p| {
p.pitch = 1.57 - (1.57 - pitch as f64 / 50.0).abs();
p.scale = 0.7;
Expand All @@ -28,8 +37,8 @@ fn main() -> Result<(), Box<dyn std::error::Error>> {

chart.draw_series(
SurfaceSeries::xoz(
(-15..=15).map(|x| x as f64 / 5.0),
(-15..=15).map(|x| x as f64 / 5.0),
(-30..=30).map(|x| x as f64 / 30.0),
(-30..=30).map(|x| x as f64 / 30.0),
pdf,
)
.style_func(&|&v| {
Expand Down